# Ch9.1 Solids, Liquids, Gases

Mechanics

Oct 24, 2013 (4 years and 6 months ago)

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Ch9.1

Solids, Liquids, Gases

Kinetic Theory (PME)

1. All matter is made of
p
articles.

2. Particles in constant
m
otion.

3. All collisions are perfectly
e
lastic. (No energy lost)

Ch9.1

Solids, Liquids, Gases

Kinetic Theory (PME)

1. All matter is made of
p
articles.

2. Particles in constant
m
otion.

3. All collisions are perfectly
e
lastic. (No energy lost)

Solids
-

particles have low KE, so intermolecular forces hold them into a crystalline

structure.

Definite shape, definite volume (for all practical purposes).

Ch9.1

Solids, Liquids, Gases

Kinetic Theory (PME)

1. All matter is made of
p
articles.

2. Particles in constant
m
otion.

3. All collisions are perfectly
e
lastic. (No energy lost)

Solids
-

particles have low KE, so intermolecular forces hold them into a crystalline

structure.

Definite shape, definite volume (for all practical purposes).

Liquids
-

higher KE breaks free of structure, but not enough to completely break free

of each other.

Definite volume, but takes shape of container.

Ch9.1

Solids, Liquids, Gases

Kinetic Theory (PME)

1. All matter is made of
p
articles.

2. Particles in constant
m
otion.

3. All collisions are perfectly
e
lastic. (No energy lost)

Solids
-

particles have low KE, so intermolecular forces hold them into a crystalline

structure.

Definite shape, definite volume (for all practical purposes).

Liquids
-

higher KE breaks free of structure, but not enough to completely break free

of each other.

Definite volume, but takes shape of container.

Gas
-

high KE, completely break free of each other.

Can change volume and shape.

Density

a comparison of an object’s mass to its volume.

‘roe’

Density

a comparison of an object’s mass to its volume.

ρ
H20

= 1 g/cm
3

= 1 g/ml

‘roe’

= 1000 kg/m
3

Ex1) Determine if a 500g sealed hollow tube with a radius of 2cm,

30cm length will float in water.

Ex2) Determine the density of an unknown solid if its mass is .4kg

and it displaces 21 mls of H
2
O.

Density

a comparison of an object’s mass to its volume.

ρ
H20

= 1 g/cm
3

= 1 g/ml

= 1000 kg/m
3

Ex1) Determine if a 500g sealed hollow tube with a radius of 2cm,

30cm length will float in water.

(sinks)

Ex2) Determine the density of an unknown solid if its mass is .4kg

and it displaces 21 mls of H
2
O.

Density

a comparison of an object’s mass to its volume.

ρ
H20

= 1 g/cm
3

= 1 g/ml

= 1000 kg/m
3

Ex1) Determine if a 500g sealed hollow tube with a radius of 2cm,

30cm length will float in water.

(sinks)

Ex2) Determine the density of an unknown solid if its mass is .4kg

and it displaces 21 mls of H
2
O.

Density

a comparison of an object’s mass to its volume.

ρ
H20

= 1 g/cm
3

= 1 g/ml

= 1000 kg/m
3

Ex1) Determine if a 500g sealed hollow tube with a radius of 2cm,

30cm length will float in water.

(sinks)

Ex2) Determine the density of an unknown solid if its mass is .4kg

and it displaces 21 mls of H
2
O.

21mls

Density

a comparison of an object’s mass to its volume.

ρ
H20

= 1 g/cm
3

= 1 g/ml

= 1000 kg/m
3

Ex1) Determine if a 500g sealed hollow tube with a radius of 2cm,

30cm length will float in water.

(sinks)

Ex2) Determine the density of an unknown solid if its mass is .4kg

and it displaces 21 mls of H
2
O.

(Move the decimal 2X for each

(21mls = 21cm
3

= 0.000021m
3
)

dimention.)

21mls

Atmospheric Pressure:

-

101,300 Pascals (N/m
2
)

-

1 atmosphere

-

760 mm Hg (10.3m H
2
O)

-

14.7 psi (pounds per inch
2
)

Atmospheric Pressure:

Four ways to affect fluid pressure:

-

101,300 Pascals (N/m
2
)

1. Increase or decrease volume:

-

1 atmosphere

-

760 mm Hg (10.3m H
2
O)

-

14.7 psi (pounds per inch
2
)

Atmospheric Pressure:

Four ways to affect fluid pressure:

-

101,300 Pascals (N/m
2
)

1. Increase or decrease volume:

-

1 atmosphere

-

760 mm Hg (10.3m H
2
O)

-

14.7 psi (pounds per inch
2
)

2. Increase or decrease temperature:

Atmospheric Pressure:

Four ways to affect fluid pressure:

-

101,300 Pascals (N/m
2
)

1. Increase or decrease volume:

-

1 atmosphere

-

760 mm Hg (10.3m H
2
O)

-

14.7 psi (pounds per inch
2
)

2. Increase or decrease temperature:

moles

3. Increase or decrease # of particles:

(R, Ideal Gas Law

Constant:

)

Atmospheric Pressure:

Four ways to affect fluid pressure:

-

101,300 Pascals (N/m
2
)

1. Increase or decrease volume:

-

1 atmosphere

-

760 mm Hg (10.3m H
2
O)

-

14.7 psi (pounds per inch
2
)

2. Increase or decrease temperature:

moles

3. Increase or decrease # of particles:

(R, Ideal Gas Law

Constant:

4. The weight of the fluid contributes.

)

Combined

Gas Law:

Combined

Gas Law:

Prove that P =
ρ
gh is true for any shape container:

1. Cylinder:

2. Rectangular prism:

Prove that P =
ρ
gh is true for any shape container:

1. Cylinder:

2. Rectangular prism:

Works for any shape container, and combinations!

Ex3) What total pressure acts on you when you swim to the bottom

of a 3m deep pool at sea level?

Ch9 HW#1 pg 331, 3,11,22,23,24,25,29

Ex3) What total pressure acts on you when you swim to the bottom

of a 3m deep pool at sea level?

Ch9 HW#1 pg 331, 3,11,22,23,24,25,29

Ch9 HW#1 p331 3,11,22,23,24,25,29

3. White Dwarf stars small and massive. A 1 in
3

chunk on Earth weighs 1 ton!

(2000 lbs) Determine density in SI units.

11. Cocaine: C
8
H
13
N(OOCC
6
H
5
)(COOCH
3
) atomic weight:

Ch9 HW#1 p331 3,11,22,23,24,25,29

3. White Dwarf stars small and massive. A 1 in
3

chunk on Earth weighs 1 ton!

(2000 lbs) Determine density in SI units.

11. Cocaine: C
8
H
13
N(OOCC
6
H
5
)(COOCH
3
) atomic weight:

Ch9 HW#1 p331 3,11,22,23,24,25,29

3. White Dwarf stars small and massive. A 1 in
3

chunk on Earth weighs 1 ton!

(2000 lbs) Determine density in SI units.

11. Cocaine: C
8
H
13
N(OOCC
6
H
5
)(COOCH
3
) atomic weight:

22. How tall should vertical pipe be filled with water if its
gauge pressure

reads 400 kPa?

23. Swimming pool 5m wide by 10m long filled to 3m depth, what is
gauge pressure

at bottom?

22. How tall should vertical pipe be filled with water if its
gauge pressure

reads 400 kPa?

23. Swimming pool 5m wide by 10m long filled to 3m depth, what is
gauge pressure

at bottom?

22. How tall should vertical pipe be filled with water if its
gauge pressure

reads 400 kPa?

23. Swimming pool 5m wide by 10m long filled to 3m depth, what is
gauge pressure

at bottom?

24. Rectangular tank 2m x 2m x 3.5m tall filled to depth of 2.5m with gasoline

( = 680kg/m
3
). What is the gauge pressure
2.0m

below the surface?

25. O
2

tank has an internal pressure of 5X atm. What outward force of each
square centimeter of inner wall?

29. Gauge pressure @ 11km down to bottom of the ocean.

{

24. Rectangular tank 2m x 2m x 3.5m tall filled to depth of 2.5m with gasoline

( = 680kg/m
3
). What is the gauge pressure 2.0m below the surface?

25. O
2

tank has an internal pressure of 5X atm. What outward force of each
square centimeter of inner wall?

29. Gauge pressure @ 11km down to bottom of the ocean.

{

24. Rectangular tank 2m x 2m x 3.5m tall filled to depth of 2.5m with gasoline

( = 680kg/m
3
). What is the gauge pressure 2.0m below the surface?

25. O
2

tank has an internal pressure of 5X atm. What outward force of each
square centimeter of inner wall?

29. Gauge pressure @ 11km down to bottom of the ocean.

{

24. Rectangular tank 2m x 2m x 3.5m tall filled to depth of 2.5m with gasoline

( = 680kg/m
3
). What is the gauge pressure 2.0m below the surface?

25. O
2

tank has an internal pressure of 5X atm. What outward force of each
square centimeter of inner wall?

29. Gauge pressure @ 11km down to bottom of the ocean.

{

Ch9.2
-

Buoyancy

Pascal’s principle
-

if a pressure is exerted on a fluid, that pressure is transmitted thru
out the entire fluid.

Energy
is conserved
:

W
in

=
W
out

F
in
.
s
in
=
F
out
.
s
out

Atmospheric pressure

-
exerts 101,300 N/m
2

at STP

Barometer

Straw

Evaporation and Boiling

Bernoulli Effect

As the cross sectional area decreases, the speed of the fluid

increases.

As the speed of a fluid increases, the pressure it exerts
perpendicular

decreases.

A
1

A
2

Volume rate of flow
:

Bernoulli Effect

As the cross sectional area decreases, the speed of the fluid

increases.

As the speed of a fluid increases, the pressure it exerts
perpendicular

decreases.

A
1

A
2

Volume rate of flow
:

Bernoulli Effect

As the cross sectional area decreases, the speed of the fluid

increases.

As the speed of a fluid increases, the pressure it exerts
perpendicular

decreases.

A
1

A
2

Volume rate of flow
:
V

Units:

Bernoulli Effect

As the cross sectional area decreases, the speed of the fluid

increases.

As the speed of a fluid increases, the pressure it exerts
perpendicular

decreases.

A
1

A
2

Volume rate of flow
:
V

Units:

As the cross
-
sectional
area decreases, the
velocity increases.

Bernoulli Effect

As the cross sectional area decreases, the speed of the fluid

increases.

As the speed of a fluid increases, the pressure it exerts
perpendicular

decreases.

A
1

A
2

Volume rate of flow
:
V

Units:

As the cross
-
sectional
area decreases, the
velocity increases.

Continuity
eqn
:

Higher velocity

Lower
velocity

Bernoulli Effect

As the cross sectional area decreases, the speed of the fluid

increases.

As the speed of a fluid increases, the pressure it exerts
perpendicular

decreases.

Lower
velocity

Higher
pressure

Higher velocity

Lower
pressure

A
1

A
2

Volume rate of flow
:
V

Continuity
eqn
:

As the cross
-
sectional
area decreases, the
velocity increases.

Buoyant force

force of a fluid acting on an object. The fluid will make the
object lighter by an amount equal to the weight of the fluid it displaces.

Ex1) A rock is lowered into a beaker of water, displacing 120ml of water.

If the rock weighs 4N dry, what is its weight while immersed in water?

(Basically, what is the tension in the rope?)

The net force of the fluid on the object
pushes the object upward.

Buoyant force

force of a fluid acting on an object. The fluid will make the
object lighter by an amount equal to the weight of the fluid it displaces.

Ex1) A rock is lowered into a beaker of water, displacing 120ml of water.

If the rock weighs 4N dry, what is its weight while immersed in water?

(Basically, what is the tension in the rope?)

The net force of the fluid on the object
pushes the object upward.

If an object weighs
more

than the weight of

the volume of water it displaces, it sinks.

If an object weighs
less

that the weight of

the volume of water it displaces, it floats.

If an object weighs the
same

as the volume

of water displaced it will remain suspended.

Ch9 HW#2 pg 331 30,31,48,51,52,56,59

Find this

volume

Find this

volume

Ch9 HW#2 pg331 30,31,48,51,52,56,59

30. In a large apartment house water is stored in a tank on the roof 30.5m

above a faucet in the kitchen. What is the gauge pressure at the faucet?

31. How deep must you dive in fresh water before the gauge equals

1.00 atmospheres?

Ch9 HW#2 pg331 30,31,48,51,52,56,59

30. In a large apartment house water is stored in a tank on the roof 30.5m

above a faucet in the kitchen. What is the gauge pressure at the faucet?

31. How deep must you dive in fresh water before the gauge equals

1.00 atmospheres?

Ch9 HW#2 pg331 30,31,48,51,52,56,59

30. In a large apartment house water is stored in a tank on the roof 30.5m

above a faucet in the kitchen. What is the gauge pressure at the faucet?

31. How deep must you dive in fresh water before the gauge equals

1.00 atmospheres?

48. Consider a narrow horizontal cylindrical chamber permanently sealed

at one end and closed off at the other end with a tightly fitted

moveable piston having an area of 0.050m
2
. The chamber is filled

with oil, and a compressive force of 1000N is applied to the liquid

via the piston. Determine the pressure read by a sensor (a) at the

flat far end and (b) halfway in along the wall.

piston

51. A hydraulic press consists of two connected cylinders:

one 8.00cm in diameter, the other 20.00cm.

The cylinders are sealed with moveable pistons

and the whole system is filled with oil. If a force

of 600N is then applied to the smaller piston,

what force will be exerted on the larger piston?

48. Consider a narrow horizontal cylindrical chamber permanently sealed

at one end and closed off at the other end with a tightly fitted

moveable piston having an area of 0.050m
2
. The chamber is filled

with oil, and a compressive force of 1000N is applied to the liquid

via the piston. Determine the pressure read by a sensor (a) at the

flat far end and (b) halfway in along the wall.

piston

51. A hydraulic press consists of two connected cylinders:

one 8.00cm in diameter, the other 20.00cm.

The cylinders are sealed with moveable pistons

and the whole system is filled with oil. If a force

of 600N is then applied to the smaller piston,

what force will be exerted on the larger piston?

48. Consider a narrow horizontal cylindrical chamber permanently sealed

at one end and closed off at the other end with a tightly fitted

moveable piston having an area of 0.050m
2
. The chamber is filled

with oil, and a compressive force of 1000N is applied to the liquid

via the piston. Determine the pressure read by a sensor (a) at the

flat far end and (b) halfway in along the wall.

piston

51. A hydraulic press consists of two connected cylinders:

one 8.00cm in diameter, the other 20.00cm.

The cylinders are sealed with moveable pistons

and the whole system is filled with oil. If a force

of 600N is then applied to the smaller piston,

what force will be exerted on the larger piston?

52. The area of the face of the small piston of a hydraulic press is 10cm
2
.

An input force of 100N is applied to that piston and we wish to have

the large piston exert a corresponding output force of 9600N.

What must be the area in cm
2
of the face of the larger piston?

56. A hydraulic lift consists of two interconnected pistons filled with common

working liquid. If the areas of the piston faces are 64.0cm
2
and

3200cm
2
and if a 900kg car rests on the latter, how much force must

be exerted to raise the vehicle very slowly? If the car must be raised

2.00m, how far must the input piston be depressed?

52. The area of the face of the small piston of a hydraulic press is 10cm
2
.

An input force of 100N is applied to that piston and we wish to have

the large piston exert a corresponding output force of 9600N.

What must be the area in cm
2
of the face of the larger piston?

56. A hydraulic lift consists of two interconnected pistons filled with common

working liquid. If the areas of the piston faces are 64.0cm
2
and

3200cm
2
and if a 900kg car rests on the latter, how much force must

be exerted to raise the vehicle very slowly? If the car must be raised

2.00m, how far must the input piston be depressed?

52. The area of the face of the small piston of a hydraulic press is 10cm
2
.

An input force of 100N is applied to that piston and we wish to have

the large piston exert a corresponding output force of 9600N.

What must be the area in cm
2
of the face of the larger piston?

56. A hydraulic lift consists of two interconnected pistons filled with common

working liquid. If the areas of the piston faces are 64.0cm
2
and

3200cm
2
and if a 900kg car rests on the latter, how much force must

be exerted to raise the vehicle very slowly? If the car must be raised

2.00m, how far must the input piston be depressed?

59. What is the buoyant force exerted on a sunken treasure chest that has

come to rest on a few small rocks at the bottom of a fresh
-
water lake?

The chest is 1.00
-
m long, 0.50
-
m wide, and 0.60
-
m high and contains

10kg of pure gold.

59. What is the buoyant force exerted on a sunken treasure chest that has

come to rest on a few small rocks at the bottom of a fresh
-
water lake?

The chest is 1.00
-
m long, 0.50
-
m wide, and 0.60
-
m high and contains

10kg of pure gold.

(F
B

= weight of the fluid displaced.)

Volume = 1m x .5m x .6m = .3m
3

F
B

F
g

Ch9

Buoyant Force FRQ

Ex1) While exploring a sunken ocean liner, a researcher found the absolute
pressure on the robot observation submarine at the level of the ship to be
about 413 atmospheres. The density of seawater is 1025 kg/m
3
.

a. Calculate the gauge pressure, P
G
, on the sunken ocean liner.

b. Calculate the depth D of the sunken ocean liner.

c. Calculate the magnitude F of the force due to the water on a viewing port of
the submarine at this depth if the viewing port has a surface area

of 0.0100m
2
.

Ch9

Buoyant Force FRQ

Ex1) While exploring a sunken ocean liner, a researcher found the absolute
pressure on the robot observation submarine at the level of the ship to be
about 413 atmospheres. The density of seawater is 1025 kg/m
3
.

a. Calculate the gauge pressure, P
G
, on the sunken ocean liner.

b. Calculate the depth D of the sunken ocean liner.

c. Calculate the magnitude F of the force due to the water on a viewing port of
the submarine at this depth if the viewing port has a surface area

of 0.0100m
2
.

= 4x10
7
Pa

Ch9

Buoyant Force FRQ

Ex1) While exploring a sunken ocean liner, a researcher found the absolute
pressure on the robot observation submarine at the level of the ship to be
about 413 atmospheres. The density of seawater is 1025 kg/m
3
.

a. Calculate the gauge pressure, P
G
, on the sunken ocean liner.

b. Calculate the depth D of the sunken ocean liner.

c. Calculate the magnitude F of the force due to the water on a viewing port of
the submarine at this depth if the viewing port has a surface area

of 0.0100m
2
.

= 4x10
7
Pa

4x10
7
N/m
2
= (1025 kg/m
3
)(9.8m/s
2
)(h)

h = 4155m

Ch9

Buoyant Force FRQ

Ex1) While exploring a sunken ocean liner, a researcher found the absolute
pressure on the robot observation submarine at the level of the ship to be
about 413 atmospheres. The density of seawater is 1025 kg/m
3
.

a. Calculate the gauge pressure, P
G
, on the sunken ocean liner.

b. Calculate the depth D of the sunken ocean liner.

c. Calculate the magnitude F of the force due to the water on a viewing port of
the submarine at this depth if the viewing port has a surface area

of 0.0100m
2
.

= 4x10
7
Pa

4x10
7
N/m
2
= (1025 kg/m
3
)(9.8m/s
2
)(h)

h = 4155m

F =
PA
= (4x10
7
N/m
2
)(.01m
2
)

=4x10
5
N

Suppose the ocean liner came to rest at the surface of the ocean before it
started to sink. Due to the resistance of the seawater, the sinking ocean
liner then reached a terminal velocity of 10.0 m/s after falling for 30 s.

d. Determine the magnitude
a
of the average acceleration

of the ocean liner during

this period of time.

e. Assuming the acceleration was constant,

calculate the distance
d
below the surface at which

the ocean liner reached

this terminal velocity.

f. Calculate the time
t
it took the ocean liner to sink

from the surface to the bottom

of the ocean.

Suppose the ocean liner came to rest at the surface of the ocean before it
started to sink. Due to the resistance of the seawater, the sinking ocean
liner then reached a terminal velocity of 10.0 m/s after falling for 30 s.

d. Determine the magnitude
a
of the average acceleration

of the ocean liner during

this period of time.

e. Assuming the acceleration was constant,

calculate the distance
d
below the surface at which

the ocean liner reached

this terminal velocity.

f. Calculate the time
t
it took the ocean liner to sink

from the surface to the bottom

of the ocean.

Suppose the ocean liner came to rest at the surface of the ocean before it
started to sink. Due to the resistance of the seawater, the sinking ocean
liner then reached a terminal velocity of 10.0 m/s after falling for 30 s.

d. Determine the magnitude
a
of the average acceleration

of the ocean liner during

this period of time.

e. Assuming the acceleration was constant,

calculate the distance
d
below the surface at which

the ocean liner reached

this terminal velocity.

f. Calculate the time
t
it took the ocean liner to sink

from the surface to the bottom

of the ocean.

Suppose the ocean liner came to rest at the surface of the ocean before it
started to sink. Due to the resistance of the seawater, the sinking ocean
liner then reached a terminal velocity of 10.0 m/s after falling for 30 s.

d. Determine the magnitude
a
of the average acceleration

of the ocean liner during

this period of time.

e. Assuming the acceleration was constant,

calculate the distance
d
below the surface at which

the ocean liner reached

this terminal velocity.

f. Calculate the time
t
it took the ocean liner to sink

from the surface to the bottom

of the ocean.

Ch9 HW#3

Ch9 HW#3

Buoyant Force Free Response

1. While conducting a strange pressure experiment a gold bar

is placed in a large container of Mercury, and is allowed to sink

to the bottom. A researcher found the absolute pressure at

the bottom of the container to be about 4 atm. The density

of mercury is 13,550 kg/m
3
.

a. Calculate the gauge pressure
p
G

of a pressure gauge

lowered to the bottom of the container.

b. Calculate the depth D of the sunken gold bar.

c. Calculate the magnitude F of the force due to the mercury

on a 1cm
2

section of the gold.

303,900N/m
2
=
(13,550kg/m
3
)(9.8m/s
2
)(h
)

h =

Ch9 HW#3

Buoyant Force Free Response

Suppose that the gold bar was held at the surface of the mercury

then released. Due to the resistance of the fluid, the sinking gold

bar reached a terminal velocity of 2.0 m/s after falling for 1.5s.

d. Determine the magnitude a of the average acceleration

of the bar during this period of time.

e. Assuming the acceleration was constant; calculate the distance d

below the surface at which the bar reached this terminal velocity.

f. Calculate the time t it tool the bar to sink from the surface

to the bottom of the container.

d = 2.3m

1.5m

= .79m

Ch9 cont.

Fluid Dynamics and Hydrostatics Equations You Should Know!

(You are authorized to highlight your cheat sheet.)

Fluid Dynamics and Hydrostatics Equations You Should Know!

(You are authorized to highlight your cheat sheet.)

Bernoulli Equation:

P
in

= P
out

P
1

+
ρ
gh
1

+ ½
ρ
v
1
2

= P
2

+
ρ
gh
2

+ ½
ρ
v
2
2

Ex1) The large container shown is filled with

a liquid of density
1.1x10
3

kg/m
3
. A small

hole of area
2.5x10
-
6

m
2

is opened in the

h

side of the container a distance h below

the liquid surface, which allows a stream

of liquid to flow through the hole and into

d

a beaker placed to the right of the container.

At the same time, liquid is added to the

x

container at an appropriate rate so that h

remains constant. The amount of liquid

collected in the beaker in 2.0min is
7.2x10
-
4

m
3
.

a. Calculate the volume rate of flow of liquid from the hole in
m
3
/s
.

b. Calc the speed of liquid as it exits from the hole.

c. Calc the height h of liquid needed above the hole to cause the speed you
determined in part (b)

d. Calc the force of the fluid passing thru the hole.

e. If the height, d, of the hole to the base of the container, is 10cm,

how far away should a beaker be placed to catch the fluid?

Ex1) The large container shown is filled with

a liquid of density
1.1x10
3

kg/m
3
. A small

hole of area
2.5x10
-
6

m
2

is opened in the

h

side of the container a distance h below

the liquid surface, which allows a stream

of liquid to flow through the hole and into

d

a beaker placed to the right of the container.

At the same time, liquid is added to the

x

container at an appropriate rate so that h

remains constant. The amount of liquid

collected in the beaker in 2.0min is
7.2x10
-
4

m
3
.

a. Calculate the volume rate of flow of liquid from the hole in
m
3
/s
.

b. Calc the speed of liquid as it exits from the hole.

Ex1) The large container shown is filled with

a liquid of density
1.1x10
3

kg/m
3
. A small

hole of area
2.5x10
-
6

m
2

is opened in the

h

side of the container a distance h below

the liquid surface, which allows a stream

of liquid to flow through the hole and into

d

a beaker placed to the right of the container.

At the same time, liquid is added to the

x

container at an appropriate rate so that h

remains constant. The amount of liquid

collected in the beaker in 2.0min is
7.2x10
-
4

m
3
.

a. Calculate the volume rate of flow of liquid from the hole in
m
3
/s

b. Calc the speed of liquid as it exits from the hole.

Ex1) The large container shown is filled with

a liquid of density
1.1x10
3

kg/m
3
. A small

hole of area
2.5x10
-
6

m
2

is opened in the

h

side of the container a distance h below

the liquid surface, which allows a stream

of liquid to flow through the hole and into

d

a beaker placed to the right of the container.

At the same time, liquid is added to the

x

container at an appropriate rate so that h

remains constant. The amount of liquid

collected in the beaker in 2.0min is
7.2x10
-
4

m
3
.

c. Calc the height h of liquid needed above the hole to cause the speed you
determined in part (b)

P
1

+
ρ
gh
1

+ ½
ρ
v
1
2

= P
2

+
ρ
gh
2

+ ½
ρ
v
2
2

Ex1) The large container shown is filled with

a liquid of density
1.1x10
3

kg/m
3
. A small

hole of area
2.5x10
-
6

m
2

is opened in the

h

side of the container a distance h below

the liquid surface, which allows a stream

of liquid to flow through the hole and into

d

a beaker placed to the right of the container.

At the same time, liquid is added to the

x

container at an appropriate rate so that h

remains constant. The amount of liquid

collected in the beaker in 2.0min is
7.2x10
-
4

m
3
.

c. Calc the height h of liquid needed above the hole to cause the speed you
determined in part (b)

P
1

+
ρ
gh
1

+ ½
ρ
v
1
2

= P
2

+
ρ
gh
2

+ ½
ρ
v
2
2

ρ
gh
1

= ½
ρ
v
2
2

h
1

= 0.29m

Ex1) The large container shown is filled with

a liquid of density
1.1x10
3

kg/m
3
. A small

hole of area
2.5x10
-
6

m
2

is opened in the

h

side of the container a distance h below

the liquid surface, which allows a stream

of liquid to flow through the hole and into

d

a beaker placed to the right of the container.

At the same time, liquid is added to the

x

container at an appropriate rate so that h

remains constant. The amount of liquid

collected in the beaker in 2.0min is
7.2x10
-
4

m
3
.

d. Calc the force of the fluid passing thru the hole.

Ex1) The large container shown is filled with

a liquid of density
1.1x10
3

kg/m
3
. A small

hole of area
2.5x10
-
6

m
2

is opened in the

h

side of the container a distance h below

the liquid surface, which allows a stream

of liquid to flow through the hole and into

d

a beaker placed to the right of the container.

At the same time, liquid is added to the

x

container at an appropriate rate so that h

remains constant. The amount of liquid

collected in the beaker in 2.0min is
7.2x10
-
4

m
3
.

d. Calc the force of the fluid passing thru the hole.

Ex1) The large container shown is filled with

a liquid of density
1.1x10
3

kg/m
3
. A small

hole of area
2.5x10
-
6

m
2

is opened in the

h

side of the container a distance h below

the liquid surface, which allows a stream

of liquid to flow through the hole and into

d

a beaker placed to the right of the container.

At the same time, liquid is added to the

x

container at an appropriate rate so that h

remains constant. The amount of liquid

collected in the beaker in 2.0min is
7.2x10
-
4

m
3
.

e. If the height, d, of the hole to the base of the container, is 10cm,

how far away should a beaker be placed to catch the fluid?

Ex1) The large container shown is filled with

a liquid of density
1.1x10
3

kg/m
3
. A small

hole of area
2.5x10
-
6

m
2

is opened in the

h

side of the container a distance h below

the liquid surface, which allows a stream

of liquid to flow through the hole and into

d

a beaker placed to the right of the container.

At the same time, liquid is added to the

x

container at an appropriate rate so that h

remains constant. The amount of liquid

collected in the beaker in 2.0min is
7.2x10
-
4

m
3
.

e. If the height, d, of the hole to the base of the container, is 10cm,

how far away should a beaker be placed to catch the fluid?

s
y

=
v
iy
t

+ ½at
2

s
x
=
v
x
t

.10 = ½(9.8)t
2

= (0.29m/s)(0.14s)

t = 0.14s

= 0.34m

Ch9 HW#4 (Pass out worksheet)

Ch9 HW#4 Fluid Pressure Free Response

1. The large container shown is filled with

a liquid of density
1000kg/m
3
. A small hole

of area
0.0000010m
2

is opened in the side

of the container a distance
h

below the liquid

surface, which allows a stream of liquid to

flow through the hole and into a beaker placed

to the right of the container. At the same time,

liquid is added to the container at an appropriate

rate so that
h

remains constant. The amount of

liquid collected in the beaker in
1.0

minute is
0.00040m
3
.

a. Calculate the volume rate of flow of liquid from the hole in
m
3
/s
.

b. Calculate the speed of liquid as it exits from the hole.

c. Calculate the height h of liquid needed above the hole

to cause the speed you determined in part (b)

d. Suppose that there is now less liquid in the beaker so that the height h is reduced to
h/2. In relation to the beaker, where will the liquid hit the tabletop?

___left of the beaker ___In the beaker ___right of the beaker

Justify your answer.

2. Prove, that the pressure at the bottom of a rectangle tank is Start at

3. Prove, that the pressure at the bottom of a triangular tank is Start at

1. The large container shown is filled with

a liquid of density
1000kg/m
3
. A small hole

of area
0.0000010m
2

is opened in the side

of the container a distance
h

below the liquid

surface, which allows a stream of liquid to

flow through the hole and into a beaker placed

to the right of the container. At the same time,

liquid is added to the container at an appropriate

rate so that
h

remains constant. The amount of

liquid collected in the beaker in
1.0

minute is
0.00040m
3
.

a. Calculate the volume rate of flow of liquid from the hole in
m
3
/s
.

b. Calculate the speed of liquid as it exits from the hole.

c. Calculate the height h of liquid needed above the hole

to cause the speed you determined in part (b)

d. Suppose that there is now less liquid in the beaker so that the height h is reduced to
h/2. In relation to the beaker, where will the liquid hit the tabletop?

___left of the beaker ___In the beaker ___right of the beaker

Justify your answer.

1. The large container shown is filled with

a liquid of density
1000kg/m
3
. A small hole

of area
0.0000010m
2

is opened in the side

of the container a distance
h

below the liquid

surface, which allows a stream of liquid to

flow through the hole and into a beaker placed

to the right of the container. At the same time,

liquid is added to the container at an appropriate

rate so that
h

remains constant. The amount of

liquid collected in the beaker in
1.0

minute is
0.00040m
3
.

a. Calculate the volume rate of flow of liquid from the hole in
m
3
/s
.

b. Calculate the speed of liquid as it exits from the hole.

c. Calculate the height h of liquid needed above the hole

to cause the speed you determined in part (b)

a. Calculate the volume rate of flow of liquid

from the hole in
m
3
/s
.

b. Calculate the speed of liquid as it exits from the hole.

c. Calculate the height h of liquid needed above the hole

to cause the speed you determined in part (b)

P
1

+
ρ
gh
1

+ ½
ρ
v
1
2

= P
2

+
ρ
gh
2

+ ½
ρ
v
2
2

ρ
gh
1

= ½
ρ
v
2
2

h
1

= 2.23m

d. Suppose that there is now less liquid in the beaker so that the height h is reduced to
h/2. In relation to the beaker, where will the liquid hit the tabletop?

___left of the beaker ___In the beaker ___right of the beaker

Justify your answer.

2. Prove, that the pressure at the bottom of a rectangle tank is
P =
ρ
gh

Start at

3. Prove, that the pressure at the bottom of a triangular tank is
P =
ρ
gh

Start at

2. Prove, that the pressure at the bottom of a rectangle tank is
P =
ρ
gh

Start at

3. Prove, that the pressure at the bottom of a triangular tank is
P =
ρ
gh

Start at

2. Prove, that the pressure at the bottom of a rectangle tank is
P =
ρ
gh

Start at

3. Prove, that the pressure at the bottom of a triangular tank is
P =
ρ
gh

Start at

Ch9.3 More Hydrostatics

Ex1) A drinking fountain projects water at an initial angle

of
50
°

above the horizontal, and the water reaches a

maximum height of
0.150m

above the point of exit.

Air resistance is negligible.

a. Calc the speed at which the water leaves the fountain.

b. The radius of the fountain’s exit hole is
4.0x10
-
3

m
.

Calc the volume rate of flow.

c. The fountain is fed by a pipe that at one point has a radius of
7.0x10
-
3
m

and is
3.0m

below the fountain’s opening. The density of water is
1.0x10
3
kg/m
3
.

Calculate the gauge pressure in the feeder pipe at this point.

v
iy

v
ix

50
°

Ex1) A drinking fountain projects water at an initial angle of
50
°

above the horizontal,

and the water reaches a maximum height of
0.150m

above the point of exit.

a. Calc the speed at which the water leaves the fountain.

b. The radius of the fountain’s exit hole is
4.0x10
-
3

m
. Calc the volume rate of flow.

c. The fountain is fed by a pipe that at one point has a radius of
7.0x10
-
3
m

and is
3.0m

below the fountain’s opening. The density of water is
1.0x10
3
kg/m
3
.

Calculate the gauge pressure in the feeder pipe at this point.

v
fy
2

= v
iy
2

+ 2as
y

v
iy
2

= v
i
.
sin
θ

0 = v
iy
2

+ 2(
-
9.8)(0.15) v
i

= 2.24 m/s

v
iy

= 1.71 m/s

v
iy

50
°

v
ix

Ex1) A drinking fountain projects water at an initial angle of
50
°

above the horizontal,

and the water reaches a maximum height of
0.150m

above the point of exit.

a. Calc the speed at which the water leaves the fountain.

b. The radius of the fountain’s exit hole is
4.0x10
-
3

m
. Calc the volume rate of flow.

c. The fountain is fed by a pipe that at one point has a radius of
7.0x10
-
3
m

and is
3.0m

below the fountain’s opening. The density of water is
1.0x10
3
kg/m
3
.

Calculate the gauge pressure in the feeder pipe at this point.

v
fy
2

= v
iy
2

+ 2as
y

v
iy
2

= v
i
.
sin
θ

0 = v
iy
2

+ 2(
-
9.8)(0.15) v
i

= 2.24 m/s

v
iy

= 1.71 m/s

v
iy

50
°

v
ix

b.

(The radius of the fountain’s exit hole is
4.0x10
-
3

m,
v
fountain

= 2.24 m/s)

c. The fountain is fed by a pipe that at one point has a radius of
7.0x10
-
3
m

and is 3.0m below the fountain’s opening. The density of water is 1.0x10
3
kg/m
3
.

Calculate the gauge pressure in the feeder pipe at this point.

Gauge

(The radius of the fountain’s exit hole is
4.0x10
-
3

m,
v
fountain

= 2.24 m/s)

c. The fountain is fed by a pipe that at one point has a radius of
7.0x10
-
3
m

and is 3.0m below the fountain’s opening. The density of water is 1.0x10
3
kg/m
3
.

Calculate the gauge pressure in the feeder pipe at this point.

Find height above
f
ountain:

P
1

+
ρ
gh
1

+ ½
ρ
v
1
2

= P
2

+
ρ
gh
2

+ ½
ρ
v
2
2

ρ
gh
f

=

½
ρ
v
f
2

(9.8)
.
h
f

= ½(2.4)
2

h
f

= 0.26m

Therefore height to pipe with gauge:

h
p

= 0.26 + 3.0 = 3.26m

Gauge

Total pressure to the depth of the pipe:

ρ
gh
p

= (1000)(9.8)(3.26) = 31,948Pa

Gauge would read this if water wasn’t flowing.

h
f

h
p

(The radius of the fountain’s exit hole is
4.0x10
-
3

m,
v
fountain

= 2.24 m/s)

c. The fountain is fed by a pipe that at one point has a radius of
7.0x10
-
3
m

and is 3.0m below the fountain’s opening. The density of water is 1.0x10
3
kg/m
3
.

Calculate the gauge pressure in the feeder pipe at this point.

Find height above
f
ountain:

P
1

+
ρ
gh
1

+ ½
ρ
v
1
2

= P
2

+
ρ
gh
2

+ ½
ρ
v
2
2

ρ
gh
f

=

½
ρ
v
f
2

(9.8)
.
h
f

= ½(2.4)
2

h
f

= 0.26m

Therefore height to pipe with gauge:

h
p

= 0.26 + 3.0 = 3.26m

Gauge

Total pressure to the depth of the pipe:

We need the
vel

in bottom pipe:

ρ
gh
p

= (1000)(9.8)(3.26) = 31,948Pa

A
f
.
v
f

=
A
p
.
v
p

Gauge would read this if water wasn’t flowing.
π
(4x10
-
3
)
2
(2.24) =
π
(7x10
-
3
)
2
(
v
p
)

Instead it reads
ρ
gh
p

½
ρ
v
p
2

v
p

= 0.73 m/s

P
g

=
ρ
gh
p

½
ρ
v
p
2

= 31,948

½(1000)(.73)
2

= 31,948

266.5 = 31681.5 Pa

Ch9 HW#5

h
f

h
p

Lab9.1

Hydrostatics

-

due tomorrow

-

Ch9 HW#4 due @ beginning of period

-

Ch9 Lab HW 1

3 due tomorrow

Ch9 HW#4

1. A drinking fountain projects water at an initial angle

of 80
°

above the horizontal, and the water reaches a

maximum height of 0.20m above the point of exit.

Air resistance is negligible.

a. Calc the speed at which the water leaves the fountain.

b. The radius of the fountain’s exit hole is 2.0x10
-
3

m.

Calc the volume rate of flow.

c. The fountain is fed by a pipe that at one point has a radius of 5.0x10
-
3
m

and is 2.0m below the fountain’s opening. The density of water is 1.0x10
3
kg/m
3
.

Calculate the gauge pressure in the feeder pipe at this point.

v
fy
2

= v
iy
2

+ 2as
y

v
iy
2

= v
i
.
sin
θ

0 = v
iy
2

+ 2(
-
9.8)(0.2) v
i

=

v
iy

= 1.98 m/s

v
iy

80
°

v
ix

b.

Ch9 HW#4

1. A drinking fountain projects water at an initial angle

of 80
°

above the horizontal, and the water reaches a

maximum height of 0.20m above the point of exit.

Air resistance is negligible.

a. Calc the speed at which the water leaves the fountain.

b. The radius of the fountain’s exit hole is 2.0x10
-
3

m.

Calc the volume rate of flow.

c. The fountain is fed by a pipe that at one point has a radius of 5.0x10
-
3
m

and is 2.0m below the fountain’s opening. The density of water is 1.0x10
3
kg/m
3
.

Calculate the gauge pressure in the feeder pipe at this point.

v
fy
2

= v
iy
2

+ 2as
y

v
iy
2

= v
i
.
sin
θ

0 = v
iy
2

+ 2(
-
9.8)(0.2) v
i

= 2.01 m/s

v
iy

= 1.98 m/s

v
iy

80
°

v
ix

b.

Ch9 HW#4

1. A drinking fountain projects water at an initial angle

of 80
°

above the horizontal, and the water reaches a

maximum height of 0.20m above the point of exit.

Air resistance is negligible.

a. Calc the speed at which the water leaves the fountain.

b. The radius of the fountain’s exit hole is 2.0x10
-
3

m.

Calc the volume rate of flow.

c. The fountain is fed by a pipe that at one point has a radius of 5.0x10
-
3
m

and is 2.0m below the fountain’s opening. The density of water is 1.0x10
3
kg/m
3
.

Calculate the gauge pressure in the feeder pipe at this point.

v
fy
2

= v
iy
2

+ 2as
y

v
iy
2

= v
i
.
sin
θ

0 = v
iy
2

+ 2(
-
9.8)(0.2) v
i

= 2.01 m/s

v
iy

= 1.98 m/s

v
iy

80
°

v
ix

b.

1b. The radius of the fountain’s exit hole is
2.0x10
-
3

m. Calc the volume rate of flow.

c. The fountain is fed by a pipe that at one point has a radius of
5.0x10
-
3
m

and is 2.0m below the fountain’s opening. The density of water is 1.0x10
3
kg/m
3
.

Calculate the gauge pressure in the feeder pipe at this point.

Height of fountain:
ρ
gh
f

=

½
ρ
v
f
2

h
f

h
f

= _______

h
p

Therefore height to pipe with gauge:

h
p

= _______

Total pressure to the depth of the pipe:

We need the
vel

in bottom pipe:

ρ
gh
p

= (1000)(9.8)(2.206)

A
f
.
v
f

=
A
p
.
v
p

=______ Pa

π
(2x10
-
3
)
2
(2.01) =
π
(5x10
-
3
)
2
(
v
p
)

v
p

= ____ m/s

P
g

=
ρ
gh
p

½
ρ
v
p
2

1b. The radius of the fountain’s exit hole is
2.0x10
-
3

m. Calc the volume rate of flow.

c. The fountain is fed by a pipe that at one point has a radius of
5.0x10
-
3
m

and is 2.0m below the fountain’s opening. The density of water is 1.0x10
3
kg/m
3
.

Calculate the gauge pressure in the feeder pipe at this point.

Height of fountain:
ρ
gh
f

=

½
ρ
v
f
2

(9.8)
.
h
f

= ½(2.01)
2

h
f

h
f

= 0.206m

h
p

Therefore height to pipe with gauge:

h
p

= 0.206 + 2.0 = 2.206m

Total pressure to the depth of the pipe:

We need the
vel

in bottom pipe:

ρ
gh
p

= (1000)(9.8)(2.206)

A
f
.
v
f

=
A
p
.
v
p

=21,619 Pa

π
(2x10
-
3
)
2
(2.01) =
π
(5x10
-
3
)
2
(
v
p
)

v
p

= 0.32 m/s

P
g

=
ρ
gh
p

½
ρ
v
p
2

= 21,619

½(1000)(.32)
2

= 21,567.8 Pa

Ch9.1 Lab HW

1. A lab group makes a boat out of clay. The clay has a mass of 44 g.

How much water must be displaced to allow the boat to float?

F
net

=
F
g

F
B

0 = mg

ρ
Vg

2. A large cruise ship weighs 225,000 tons, or 2x10
8
kg. If density of sea water

is 1025kg/m
3
, how much sea water does it displace?

F
net

=
F
gs

F
B

0 = mg

ρ
Vg

3. A smaller cruise ship displaces 100,000m
3

of sea water. What is its weight?

F
net

=
F
gs

F
B

0 =
F
gs

ρ
Vg

Ch10.1

Elasticity and Oscillations

Hooke’s Law ∆F=
-
k(∆x)

Ex1) A 9.0 cm long spring is suspended from a hook.

A 20g mass is attached and it stretches to 10cm.

A 40g mass is attached and it stretches to 15.5cm.

A 50g mass is attached and it stretches to 18.5cm.

a. Please graph F vs. x

b. Find the spring constant 2 ways

1.0

F (N)

0.5

5 10 15 20 25

distance (cm)

Ch10.1

Elasticity and Oscillations

Hooke’s Law ∆F=
-
k(∆x)

Ex1) A 9.0 cm long spring is suspended from a hook.

A 20g mass is attached and it stretches to 10cm.

A 40g mass is attached and it stretches to 15.5cm.

A 50g mass is attached and it stretches to 18.5cm.

a. Please graph F vs. x

b. Find the spring constant 2 ways

.55
-

.2

=.35

.2
-

.1 = .1

c. How far will the spring stretch to if a 100g mass is attached?

d. How much work is done by gravity to stretch the spring 18.5 cm?

1.0

F (N)

0.5

5 10 15 20 25

distance (cm)

Ch10.1

Elasticity and Oscillations

Hooke’s Law ∆F=
-
k(∆x)

Ex1) A 9.0 cm long spring is suspended from a hook.

A 20g mass is attached and it stretches to 10cm.

A 40g mass is attached and it stretches to 15.5cm.

A 50g mass is attached and it stretches to 18.5cm.

a. Please graph F vs. x

b. Find the spring constant 2 ways

.55
-

.2

=.35

.2
-

.1 = .1

c. How far will the spring stretch to if a 100g mass is attached?

d. How much work is done by gravity to stretch the spring 18.5 cm?

1.0

F (N)

0.5

5 10 15 20 25

distance (cm)

Ch10.1

Elasticity and Oscillations

Hooke’s Law ∆F=
-
k(∆x)

Ex1) A 9.0 cm long spring is suspended from a hook.

A 20g mass is attached and it stretches to 10cm.

A 40g mass is attached and it stretches to 15.5cm.

A 50g mass is attached and it stretches to 18.5cm.

a. Please graph F vs. x

b. Find the spring constant 2 ways

.5

c. How far will the spring stretch to if a 100g mass is attached?
20

5 = .15m

d. How much work is done by gravity to stretch the spring 18.5 cm?

Ch10 HW #1 pg. 374 1,3,6,8,9,11

1.0

F (N)

0.5

5 10 15 20 25

distance (cm)

Ch10 HW#1 p374 1,3,6,8,9,11

1. A helical spring 20
-
cm long extends to a length of 25 cm when it supports a
load of 50 N. Determine the

spring constant.

3. A steel spring is suspended vertically from its upper end and a monkey
weighing 10.0 N grabs hold of its bottom end and hangs motionlessly from
it. If the elastic constant of the spring is 500 N/m, by how much

will the monkey stretch it?

6. A long metal wire hangs from the roof truss in a factory building.

A 1000
-
kg machine is attached to it so that the load is suspended above

the floor. If the wire stretches 0.500 cm, what is the k?

Ch10 HW#1 p374 1,3,6,8,9,11

1. A helical spring 20
-
cm long extends to a length of 25 cm when it supports a
load of 50 N. Determine the

spring constant.

3. A steel spring is suspended vertically from its upper end and a monkey
weighing 10.0 N grabs hold of its bottom end and hangs motionlessly from
it. If the elastic constant of the spring is 500 N/m, by how much

will the monkey stretch it?

6. A long metal wire hangs from the roof truss in a factory building.

A 1000
-
kg machine is attached to it so that the load is suspended above

the floor. If the wire stretches 0.500 cm, what is the k?

Ch10 HW#1 p374 1,3,6,8,9,11

1. A helical spring 20
-
cm long extends to a length of 25 cm when it supports a
load of 50 N. Determine the

spring constant.

3. A steel spring is suspended vertically from its upper end and a monkey
weighing 10.0 N grabs hold of its bottom end and hangs motionlessly from
it. If the elastic constant of the spring is 500 N/m, by how much

will the monkey stretch it?

6. A long metal wire hangs from the roof truss in a factory building.

A 1000
-
kg machine is attached to it so that the load is suspended above

the floor. If the wire stretches 0.500 cm, what is the k?

Ch10 HW#1 p374 1,3,6,8,9,11

1. A helical spring 20
-
cm long extends to a length of 25 cm when it supports a
load of 50 N. Determine the

spring constant.

3. A steel spring is suspended vertically from its upper end and a monkey
weighing 10.0 N grabs hold of its bottom end and hangs motionlessly from
it. If the elastic constant of the spring is 500 N/m, by how much

will the monkey stretch it?

6. A long metal wire hangs from the roof truss in a factory building.

A 1000
-
kg machine is attached to it so that the load is suspended above

the floor. If the wire stretches 0.500 cm, what is the k?

8.
How much energy is stored in a spring with an elastic constant
pf

50 N/m
when compressed 0.05 m?

9. A helical spring is 55
-
cm long when a load of 100 N is hung from it and 57
-
cm long when the load is 110 N.

Find its spring constant.

11. A
Hookean

spring is suspended vertically and a mass of 2.00 kg is hung
from its end. The spring then stretches 10.0 cm. How much more will it
elongate if an additional 0.50 kg is attached to the first mass?

First find k:

Then find new ∆x:

8.
How much energy is stored in a spring with an elastic constant
pf

50 N/m
when compressed 0.05 m?

9. A helical spring is 55
-
cm long when a load of 100 N is hung from it and 57
-
cm long when the load is 110 N.

Find its spring constant.

11. A
Hookean

spring is suspended vertically and a mass of 2.00 kg is hung
from its end. The spring then stretches 10.0 cm. How much more will it
elongate if an additional 0.50 kg is attached to the first mass?

First find k:

Then find new ∆x:

8.
How much energy is stored in a spring with an elastic constant
pf

50 N/m
when compressed 0.05 m?

9. A helical spring is 55
-
cm long when a load of 100 N is hung from it and 57
-
cm long when the load is 110 N.

Find its spring constant.

11. A
Hookean

spring is suspended vertically and a mass of 2.00 kg is hung
from its end. The spring then stretches 10.0 cm. How much more will it
elongate if an additional 0.50 kg is attached to the first mass?

First find k:

Then find new ∆x:

8.
How much energy is stored in a spring with an elastic constant
pf

50 N/m
when compressed 0.05 m?

9. A helical spring is 55
-
cm long when a load of 100 N is hung from it and 57
-
cm long when the load is 110 N.

Find its spring constant.

11. A
Hookean

spring is suspended vertically and a mass of 2.00 kg is hung
from its end. The spring then stretches 10.0 cm. How much more will it
elongate if an additional 0.50 kg is attached to the first mass?

First find k:

Then find new ∆x:

Ch10.2

Simple Harmonic Motion

-

object oscillates in a continuous pattern, under the influence of simple

forces.

-

the periodic motion of the object can be graphed as a sine or cosine wave.

Period

-

time it takes to complete 1 cycle. (T)

Frequency
-

# of cycles completed per second (hertz)

Ch10.2

Simple Harmonic Motion

-

object oscillates in a continuous pattern, under the influence of simple

forces.

-

the periodic motion of the object can be graphed as a sine or cosine wave.

Period

-

time it takes to complete 1 cycle. (T)

Frequency
-

# of cycles completed per second (hertz)

Angular frequency (
ω
)
-

rotations per second

Ex1) A wheel completes one revolution every 2.5 seconds.

What is its angular frequency?

Ch10.2

Simple Harmonic Motion

-

object oscillates in a continuous pattern, under the influence of simple

forces.

-

the periodic motion of the object can be graphed as a sine or cosine wave.

Period

-

time it takes to complete 1 cycle. (T)

Frequency
-

# of cycles completed per second (hertz)

Angular frequency (
ω
)
-

rotations per second

Ex1) A wheel completes one revolution every 2.5 seconds.

What is its angular frequency?

T = 2.5sec

Different springs = diff oscillations (diff spring constants)

Each has its own natural frequency,
ω
.

Sine wave

Cosine wave

or

or

Different springs = diff oscillations (diff spring constants)

Each has its own natural frequency,
ω
.

Sine wave

Cosine wave

Period

x = A
.
sin
ω
t

x = A
.
cos
ω
t

or

or

or

or

Ex2) A 1 N bird lands on a branch that bends and goes into SHM with a period
of .5 sec. Determine the effective elastic spring constant for the branch.

Ex2) A 1 N bird lands on a branch that bends and goes into SHM with a period
of .5 sec. Determine the effective elastic spring constant for the branch.

k=?

F
g

= 1N

T = 0.5s

k = 15.6N/m

Ex3) A 1 kg cart is attached to a spring and pulled back with a force of 10N

a distance of 5 cm, as shown.

a) What is the value of the spring constant?

b) What is the period of oscillation?

d) Where will the cart be .20s

after release.

c) Write an equation to represent it’s motion.

Ex3) A 1 kg cart is attached to a spring and pulled back with a force of 10N

a distance of 5 cm, as shown.

a) What is the value of the spring constant?

b) What is the period of oscillation?

d) Where will the cart be .20s

after release.

c) Write an equation to represent it’s motion.

Ex3) A 1 kg cart is attached to a spring and pulled back with a force of 10N

a distance of 5 cm, as shown.

a) What is the value of the spring constant?

b) What is the period of oscillation?

d) Where will the cart be .20s

after release.

c) Write an equation to represent it’s motion.

Ex3) A 1 kg cart is attached to a spring and pulled back with a force of 10N

a distance of 5 cm, as shown.

a) What is the value of the spring constant?

b) What is the period of oscillation?

d) Where will the cart be .20s

after release.

c) Write an equation to represent it’s motion.

Ex3) A 1 kg cart is attached to a spring and pulled back with a force of 10N

a distance of 5 cm, as shown.

a) What is the value of the spring constant?

b) What is the period of oscillation?

d) Where will the cart be .20s

after release.

c) Write an equation to represent it’s motion.

e) At what time will it pass thru the

equilibrium position?

Ex3) A 1 kg cart is attached to a spring and pulled back with a force of 10N

a distance of 5 cm, as shown.

a) What is the value of the spring constant?

b) What is the period of oscillation?

d) Where will the cart be .20s

after release.

c) Write an equation to represent it’s motion.

e) At what time will it pass thru the

equilibrium position?

t = .11s

Ex 4) A 2.0 kg bag of candy is hung vertically from a spring that elongates 50
cm under the load, just out of reach of a child. His mean big brother pushes
it up 25cm and releases it, setting it in SHM. If the kid can only reach the
bag at its lowest point, when will he grab the candy? (Solve 2 ways)

Ch10 HW#2 WS

Ex 4) A 2.0 kg bag of candy is hung vertically from a spring that elongates 50
cm under the load, just out of reach of a child. His mean big brother pushes
it up 25cm and releases it, setting it in SHM. If the kid can only reach the
bag at its lowest point, when will he grab the candy? (Solve 2 ways)

Ch10 HW#2 WS

Ex 4) A 2.0 kg bag of candy is hung vertically from a spring that elongates 50
cm under the load, just out of reach of a child. His mean big brother pushes
it up 25cm and releases it, setting it in SHM. If the kid can only reach the
bag at its lowest point, when will he grab the candy? (Solve 2 ways)

1
st

way:

2
nd

way:

If released from top,

gets to bottom in half the period.

Ch10 HW#2 WS

Lab10.1

Hooke’s Law and Periodic Motion

-

due tomorrow

-

Ch10 HW#2 due @ beginning of period.

-

Lab HW is to complete the backside of the lab perfectly.

Ch10 HW#2

SHM WS

1. An antique phonograph record is turning uniformly at 78rpm while an ant
sitting at rest on its rim is being viewed by a child whose eyes are in the
plane of the record. Describe the ant’s motion as seen by the child.

What is the frequency of the ant? What is the angular frequency?

78 rot 1 min = 1.3Hz

min 60 sec

2. A 1 kg mass is attached to a spring, stretching it 10 cm.

a. What is the value of the spring constant?

b. If it is pushed up 2 cm, what is the period of its oscillation?

c. Write a cosine expression representing its motion.

Ch10 HW#2

SHM WS

1. An antique phonograph record is turning uniformly at 78rpm while an ant
sitting at rest on its rim is being viewed by a child whose eyes are in the
plane of the record. Describe the ant’s motion as seen by the child.

What is the frequency of the ant? What is the angular frequency?

78 rot 1 min = 1.3Hz