Physics 083 - Dynamicsx - jimwiese

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Physics 083



Dynamics


Dynamics



the study of why things move.


Simply put, things move because of forces.



A force is a push or a pull on an object.



A force requires an agent, something that causes the push or pull.



A force can either contact an
object or act at a distance.



A force can be represented as a vector (both direction and magnitude).



Force

is measured in Newtons (N = kg
-
m/s
2
)



Drawing force vectors:

1.

Represent the object as a particle (a dot).

2.

Place the tail of the force vector on the pa
rticle.

3.

Draw the force vector as an arrow pointing in the proper direction and
with a length proportional to the size of the force.

4.

Give the vector an appropriate label.



Common force

vector
symbols


F
g



force of gravity


F
t



force of tension (in a rop
e or wire)


F
a



applied force


F
f


force of friction


F
f

=


F
n

(


= coefficient of friction)


F
n



normal force (perpendicular to surface)


F
net



net force


the sum of all forces acting on an object





Newton’s three laws of motion

1.

An object at rest

stays at rest and an object in straight
-
line motion (at a
constant velocity), stays in motion unless acted on by an outside force.
This is commonly known as the law of inertia.

2.

Forces lead to acceleration proportional to the force and in the same
directi
on. This leads to the formula: F = ma

3.

For every action, there is an equal but opposite reaction.


Free Body Diagrams (FBD)


an important part of any dynamics question.

A free body diagram shows the forces (both magnitude and direction) of the forces
acti
ng on a body.


Examples:











Force acting on a book on a table



Forces acting on a book in free fall











Forces acting on a book being pulled across a table




Problems

1.

A 1.5 kg mass is pulled across a frictionless surface with a force of
3 N. The
force is parallel to the surface. What is the acceleration of the mass?

What is its
velocity after 3.5 seconds if it starts from rest? How far will it travel?














2.

A 1.5 kg mass is pulled across a frictionless surface with a force of 3
N. The
force is applied at a 30° angle to the surface. What is the acceleration of the mass?
















Draw a FBD for an object stopped on an inclined plane. What is F
net
?




















The sum of the vectors in a FBD show
s

F
net
.




Common types

of problems


Weight


There is a misconception around the common use of the term and how it
is used in physics. In physics, weight is th
e force of gravity on an object, not what a
bathroom scale reads (F
g
).


An astronaut with mass 75 kg travels to Mars. What is his weight:


On earth











What is his weight on Mars where a
g

= 3.8 m/s
2
?












What is the value of a
g

on the top of a mountain, if the astronaut weights 683 N?


Force and acceleration


A
1000 kg rocket car moves along the highway at a constant velocity of 15 m/s. If a
thruster rocket with a force of 5000 N is fired for 4.5 seconds, what is the new
velocity of the rocket car? How far will it travel in that time?
Normal force


The normal for
ce is the force that a surface exerts on an object. It always works in a
direction perpendicular to the surface. The amount of the normal force depends on
the situation. Use the symbol F
n

for normal force.


A 5 kg book sits on a table. What is the normal f
orce exerted by the table on the
book?














A 5 kg book sits on an inclined plane of 30°. What is the normal force exerted by the
inclined plane on the book?


Friction


Friction is a force that opposes motion. It acts between the surface of the
object and
the object itself. There are two types of friction, static friction (F
fs
) that has to be
overcome before an object starts to move, and kinetic friction (F
fk
) that is used to
keep the object moving. The amount of frictional force that exists depe
nds on the
surfaces and are proportional to

, the coefficient of friction, a value between 0 and
1.


F
f
=


F
n




Common values of



Surface


s


k

Wood on wood

0.4

0.2

Ice on ice

0.1

0.03

Rubber of dry concrete

1.0

0.8

Rubber of wet concrete

0.7

0.6


A smooth wooden block is placed on a smooth wooden tabletop. You find you have
to exert a force of 14.0 N to keep the 40.0 N block moving at a constant velocity.

What is the coefficient of friction of the sliding block on the table?











If a 20.0
N brick is placed on the block, what force will be needed to keep the block
and brick moving at a constant velocity?

Elevators


A 3000 kg elevator moves: 1) up at a constant speed, 2) up with an acceleration of 3
m/s
2

and 3) down with an acceleration of
-
2 m/s
2
. What is the force of tension in the
elevator cable in each case?



Friction



A 3 kg object is pulled with a 3
0N force across a table with


= 0.3
5. What is the
acceleration of the object? What is its velocity

after 6 seconds?

How far does it move
in those 6 seconds?


Hanging Object with
out

Friction


A 5 kg mass hangs off a table. It’s connected by a wire pulled over a pulley to a 3 kg
mass sitting on a table. What is the acceleration of the 5 kg mass? What is

the force
of tension in the wire between them?

Hanging Object with Friction


A 5 kg mass hangs off a table. It’s connected by a wire over a pulley to a 3 kg mass
sitting on a table with


= 0.20. What is the acceleration of the 5 kg mass? What is
the for
ce of tension in the wire between them?


Pulley Problems


A 5 kg mass and a 3 kg mass are connected by a string hung over a frictionless
pulley. What is the acceleration of the 5 kg mass? What is the force of tension in the
string?