AP Physics Chapter 4 Study Guide
Newton's
First Law of Motion:
An object at rest remains at rest as long as not net force acts on it.
An object moving, with constant velocity continues to move with the same speed
and in the same direction as long as no net force acts on it.
Inertia
What
does the cannon ball want to do?
Why can it not do that?
Two different perspectives mean that an observer sees different things if they are inside the train or outside the train.
Force
Force
is an agent of change.
The application of a force to a body (one that is free to move) changes the
body's state of motion, that is, it changes its velocity.
"If you insist upon a precise definition of force, you will never get it!" (Richard Feynman, 1963)
Force is a VECTOR!!!!
The net force, the resultant of all the forces acting, that changes the motion of a body.
The
force tending to stretch an object is called a tensile force, 
.
All of these will read the same on the spring scale.
Examples
Example 1
Determine the resultant, or net force, exerted on the stationary elephant by the two clowns in the above figure. What is the tension in the rope attached to the elephant?
Example 2
Determine the net force exerted on the ring by the three people in the figure below.
Example 3
In
a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally
on an automobile tire at the angles shown in the figure. The tire remains
stationary in spite of the three pulls. Alex pulls with a force 
of
magnitude 220 N, and Charles pulls with a force 
of
magnitude 170 N. The direction of is
not given. What is the magnitude of Betty's force 
?
Newton's Second Law
Momentum
(
)
is the product of the object's mass and velocity.
Newton's Second Law as stated by Newton used the idea of momentum instead of acceleration.
The force exerted on a body equals the resulting change in its momentum divided by the time elapsed in the process.
Jacob Hermann (1716) put this into it's current form of
A net force applied to an object causes it to accelerate at a rate that is inversely proportional to the mass of the object.
Example 4
The metal head of a hammer is loose. To tighten it, you drop the hammer down onto a table. Should you (a) drop the hammer with the handle end down, (b) drop the hammer with the head down, or (c) do you get the same result either way?
Free-Body Diagrams
Steps to construct a free-body diagram:
1. Sketch the Forces–Identify and sketch all of the external forces acting on an object.
2. Isolate the Object of Interest–Replace the object with a point particle of the same mass. Apply each of the forces acting on the object to that point.
3. Choose a Convenient Coordinate System–Any coordinate system will work; however, if the object moves in a known direction, it is often convenient to pick that direction for one of the coordinate axes. Otherwise, it is reasonable to choose a coordinate system that aligns with one or more of the forces acting on the object.
4. Resolve the Forces into Components–Determine the components of each force in the free-body diagram.
5. Apply Newton's Second Law to each Coordinate Direction–Analyze motion in each coordinate direction using the component form of Newton's Second Law.
Now for some examples of Newton's Second Law:
Example 5
Moe, Larry, and Curly push on a 752 kg boat that floats next to a dock. They each exert an 80.5 N force parallel to the dock. (a) What is the acceleration of the boat if they all push in the same direction? (b) What is the magnitude and direction of the boat's acceleration if Larry and Curly push in the opposite direction to Moe's push?
Example 6
Foamcrete
is a substance designed to stop an airplane that has run off the
end of a runway, without causing injury to passengers. It is solid
enough to support a car, but crumbles under the weight of a large
airplane. By crumbling, it slows the plane to a safe stop. For example,
suppose a 747 jetliner with a mass of 
and
an initial speed of 26.8 m/s is slowed down to a stop in 122 m. What
is the magnitude of the retarding force 
exerted
by the Foamcrete on the plane?
Example 7
A pitcher throws a 0.15 kg baseball, accelerating it from rest to a speed of about 90 mi/h. Estimate the force exerted by the pitcher on the ball.
Newton's Third Law of Motion
Newton's Third Law: For every force that acts on an object, there is a reaction force acting on a different object that is equal in magnitude and opposite in direction.
Example 8
Two
groups of canoeists meet in the middle of a lake. After a brief visit,
a person in canoe 1 pushes on canoe 2 with a force of 46 N to separate
the canoes. If the mass of canoe 1 and its occupants is 
,
and the mass of canoe 2 and its occupants is 
,
(a) find the acceleration the push gives to each canoe. (b) What is
the separation of the canoes after 1.2 s of pushing?
Free-body diagram
Example 9
Two
boxes–one large and heavy, the other small and light–rest
on a smooth, level floor. You push with a force on
either the small box or the large box. Is the contact force between
the two boxes (a) the same in either case, (b) when you push on the
large box, or (c) larger when you push on the small box?
Example 10
A
box of mass 
rests
on a smooth, horizontal floor next to a box of mass 
.
If you push on box 1 with a horizontal force of magnitude F = 20.0
N, (a) what is the acceleration of the boxes? (b) What is the force
of contact between the boxes?
What happens if the relative position of the boxes is reversed? (a) What is the acceleration of the boxes? (b) What is the force of contact between the boxes? (c) What is the total force acting on box 2?
