Exam Review Name:______________________________ Show all your work for each problem (including math, pictures, force diagrams, etc.) so that I can understand what your reasoning is. thinking to me. This is better than just leaving it blank!!

testybelchΜηχανική

14 Νοε 2013 (πριν από 3 χρόνια και 11 μήνες)

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Exam Review




Name:______________________________



-

Show all your work for each problem (including math, pictures, force
diagrams, etc.) so that I can understand what your reasoning is.

-

If you get stuck on a problem and can’t solve it, describe your
thinking to
me. This is better than just leaving it blank!!

-

You CANNOT use kinematics or Newton’s 2
nd

Law to solve any problems
(although you may use them to check your answers)


1.

A 60kg skydiver steps out of an airplane 7000m above the ground. As she
des
cends, the average air drag force is 550N. She opens her parachute 1000m
above the ground. What is her speed when she opens her parachute? (Use energy
conservation)













2.

A child is pulling a 10kg wagon behind him. The handle of the wagon is 30
o

above the horizontal, and the wagon starts at rest. After being pulled for 3m the
wagon reaches a speed of 2m/s. What was the force with which the child pulled
on the handle? Ignore friction and use energy conservation.

















3.

An electron (mass

9.1 x 10
-
31
kg) is fired horizontally at a speed of 1000m/s
toward a sheet of gold foil. The electron bounces backward off the gold foil with
a speed of 700m/s at an angle of 20
o

above the horizontal.

a.

What was the impulse experienced by the electron?









b.

If the collision lasted for 1.0 x 10
-
6

s, what was the average force
experienced by the electron?







4.

a. A

110 kg football player running at 8 m/s slams into a 90 kg person moving in
the opposite direction at 9 m/s. If the collision is perfectly inelastic (i.e., they
‘stick’ together), what is their final velocity? Include the before and after pictures
in yo
ur solution.










b. Do a special
-
case analysis of your solution, using the standard IF… AND…
THEN… AND/BUT… THEREFORE… procedure.












5.

A 1000 kg car moving East at 30 m/s collides with a 5000 kg truck moving South
at 8 m/s. If the car and truck stick together after the collision,
what is the
magnitude
v

and direction
θ

of their final velocity?
Remember that
v =




2
2
y
x
v
v


and
θ =
tan
-
1

(
v
y

/ v
x
).
















6.

A 80 kg person is riding a rollercoaster at Cedar Point. When the coaster passes
through a dip of radius 10 m at point A (shown below), the normal force of the
seat on the person is 1000 N.

a. What is the speed of the rollercoaster at point A?




b. What is the
magnitude

centripetal acceleration of the rollercoaster at point A?
What
direction

is the centripetal acceleration in?







R=
10 m

Poin
t A

7.

A neutron star is an

extremely dense type of star, with a typical mass of 4.2 x
10
30
kg and radius of 10,000m.

a.

If a neutron star completes one rotation every 0.02s, what is its angular
velocity?







b.

The moment of inertia for a solid sphere (such as a neutron star) is
I =

(2/5)
MR
2
. What is the moment of inertia for the neutron star?






c.

Neutron stars gradually stop spinning due to drag forces from their
environment. If a neutron star stops spinning after 1000 years ( = 3.2 x
10
10

seconds), what was the net torque acting on the neutron star?





8.

In this totally everyday scenario, a 50kg woman stands 1m from the left end of a
3m plank. The plank is supported by two ropes (one at each end). If the mass of
the plank is 10kg, what is

the tension in each rope?












Rope 1

Rope 2

9.

A uniform beam of length 2m and mass 40kg is supported by a cable as shown
below. The cable is at an angle of 30
0

from the beam. In addition, a rope is
attached to the end of the beam at a 45
0
angle, and is being pulled with a tension of
100N.



a.

What is the
tension in the cable?















b.

What is the strength of the horizontal reaction force (
R
x
) acting on the
beam?







30
0

hinge

100N

45
0

10.


a.

Define each of the following terms:



Systematic Error:











Random Error:








b.

You’re

home, and you’re bored, so you and your buddy Scooter decide to do a
physics experiment to liven things up. Your goal is to determine the acceleration
of gravity at your location, which you will do by measuring the time it takes rocks
to fall a known hei
ght. You are outside, standing on grass. The plan is for
Scooter to drop a rock when you say “GO!” You will start a stopwatch when you
say “GO!”, and then stop the stopwatch when the rock hits the ground. You’ll
then use energy conservation (ignoring a
ir drag) to determine
g
.
Using

a meter
stick, you find that the height from which the rock will be released is 1.6m.


Describe one systematic error, including how it will skew your results. Also,
include two random errors, and what you would need to d
o to reduce the random
errors.




















Equation Sheet


______________________________________________________________________________

Work
-
Energy
:





units for work/energy are Joules (J = kg∙m
2
/s
2
)


K =
(1/2)
mv
2


v

is the speed of the object




U
g

= mgy


Must choose reference point for
y =
0 m. And
g

is +9.8 m/s
2



U
s

=
(1/2)
kx
2


x

is how much spring is compressed/stretched,
k

is spring constant


W
F

= F d cos
(θ) θ is the angle between line of moti
on and the direction of force
F

Only friction, pushing, and pulling forces do work. For Friction,

F
f

= μ
k

F
N


Energy Conservation:


Always draw initial/final pictures

K
i

+ U
g i

+ U
s i

+ W
ext

= K
f

+ U
g f

+ U
s f


______________________________________________________________________________

Momentum
-
Impulse
:




units for momentum/impulse are (kg m/s)


p

=
m
v


v

is the velocity of object (can be + or
-
, depending on direction)


J = F
avg

Δt

is the momentum given/take
n by the force
F


Momentum Conservation:

Always draw initial/final pictures

1
-
object:

p
i

+ J = p
f

Use if we only know the mass for one object in collision

2
-
objects:

p
1i

+ p
2i


= p
1f

+ p
2f


If collision is 2
-
dimensional
, then need x and y components

separately
.


If collision is
inelastic
: Objects stick together, so
v
1f

= v
2f


v
f

If collision is
perfectly
elastic
, then can also use energy conservation.

______________________________________________________________________________

Circular Motion:

Centripetal acceleration:


a = v
2
/R


points to middle of circle

Net force:



F
net

= ma = mv
2
/R

points to middle of circle


Period & Frequency:


T = 1/f = 2π/ω


When solving circular motion problems, choose + direction to be towards the middle of the

circle.
That way,
F
net

is always positive.

______________________________________________________________________________

Rotational Motion & Static Equilibrium:


torque has units of N∙m

Kinematics:


ω = angular velocity (rad/s)




α = angular accele
ration (rad/s
2
)


Velocity:

v = ω∙R



Converts between angular and linear velocities

Torque:


τ

= ±
F r sin
(θ)


where + if
F

tries to make object rotate counterclockwise







-

if
F

tries to make object rotate clockwise







r

is the dist
ance from hinge to where force
F

is applied






θ is the angle between
F

and the lever arm


Torque & Acceleration:


τ
net

= I α


where
I

is the moment of inertia (in kg∙m
2
)







and
α

is the angular acceleration (in radians / s
2
)



Static Equilibrium:

τ
net

=
0 N∙m


F
net
x

=
0 N


F
net
y

=
0 N