Download Unit 4 Notetakers

Work, Energy & Momentum Notes
Chapter 9, 10 & 11
The two types of energy we will be working with in this unit are:
 _____________________(KE): Energy associated with ___________ of an object.
 _____________________(PE): Energy associated with the ______________ of an object.
Work
Work: the product of the component of the force along the direction of displacement and the magnitude of the
displacement.
d = displacement of object
= angle between displacement and force
Units of work: Joule (J) 1 J = 1N.m
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In order to do work, you must exert a force over a distance.
The con may expend energy when he pushes on the wall, but if it doesn’t move, no work is performed
on the wall.
The force must be in the _________________ as the movement. If not, you have to use a vector
component of the force that is in the same direction. Hence the cosine.
Example: A man cleaning his apartment pulls a vacuum cleaner with a force of _____ at an angle of 30.0. A
frictional force of magnitude _____ dampens the motion, and the vacuum is pulled a distance of 3.0 m.
Calculate:
a) the work done by the 50. N pull.
b) the work done by the frictional force.
c) the net work done on the vacuum by all forces acting on it.
Relating Work and Kinetic Energy (aka. The Work-Energy Theorem)
Wnet =
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KE =
Roughly speaking, ____________________________________________.
The net work done on an object by the force or forces acting on it is equal to the change in the kinetic
energy of the object.
o The speed of an object will ___________ if the net work done on it is _____________.
o The speed of an object will ___________ if the net work done on it is _____________.
Example: A _______ car has a net forward force of 4500 N applied to it. The car starts from rest and travels
down a horizontal highway. What are its kinetic energy and speed after it has traveled 100.m? (ignore friction
and air resistance)
Potential Energy
Gravitational potential energy: the energy an object has due to its position in space.
In working problems, choose the zero level for PE (the pt. at which the grav. PE=0) so that you can easily
calculate the difference in PE
Example: A ______ skier is at the top of a slope. At the initial point A, the skier is ____ vertically above point B.
Find the gravitational PE of the skier at A and B, and the difference in PE between the 2 pts.
Law of Conservation of Energy:
Ei = Ef
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Although energy cannot be destroyed, it can go places where we can never recover
Although energy may be changed into a different form, the final value will be the same as the initial
value (energy is not lost).
Example: Calculate the KE and PE energy at each of the 5 spots on the ski run. Assume the skier starts from rest.
(m = 51 kg) (First draw the route)
Example: A diver weighing _______ (mass = 77.0 kg) drops from a board 10 m above the surface of the pool of
water.
(a) Use the conservation of mechanical energy to find her speed at a point 5.00 m above the water surface.
(b) Find the speed of the diver just before she strikes the water.
Example: A sled and its rider together weigh ________ N. They move down a frictionless hill through a vertical
distance of 10.0 m. Use conservation of energy to find the speed of the sled-rider system at the bottom of the
hill, assuming the rider pushes off with an initial speed of _______.
Conservative / Nonconservative Forces
 A force is ______________________ if the work it does on an object between 2 points is
______________________ of the path the object takes between the 2 points. (The work done depends
only on the initial and final positions.)
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A force is ________________________ if the work it does on an object moving between 2 points
____________________ the path taken. (i.e. sliding friction)
Example: A 15 kg kid, initially at rest, slides down a _____ high slide. Ideally, what his is final velocity at the
bottom of the slide?
If the final velocity is only 10.0 m/s. where did the extra energy go? _________________________
Friction is an nonconservative force which used up some of the initial potential energy. To account for
friction, we need to add back in the work done by (or energy lost by) friction.
Note: Usually work done by friction is negative (because it is in the opposite direction). But since we are
ADDING BACK IN the work done by friction it is positive.
Example: How much work was done by friction as the kid (in the previous example) slid down the slide?
Potential Energy Stored in a Spring:
k = spring constant (N/m)
x = Distance spring is compressed or stretched (m)
Now we can add the potential energy of a spring into our conservation of energy equation:
Example: A block of mass 0.500 kg rests on a horizontal, frictionless surface. The block is pressed lightly against
a spring, having a spring constant k=80.0 N/m. The spring is compressed a distance of 2.00 cm and released.
Find the speed of the block at the instant it loses contact with the spring at the x = 0 position.
Example: The launching mechanism of a toy gun consists of a spring of unknown spring constant. By
compressing the spring a distance of 0.120 m, the gun is able to launch a 20.0-g projectile to a maximum height
of 20.0 m when fired vertically from rest. Determine the value of the spring constant.
Simple Machines:
 Machines make work easier.
 Work In = Work Out
Force x Distance = Force x Distance
Machines make work easier. But, the amount of work stays the same.
Power: The rate at which work is done.
SI Units:
English Units:
Example: A _________ car starts from rest and accelerates to a final velocity of +20.0 m/s in a time of 15.0 s.
Assume that the force of air resistance remains constant at a value of –500. N during this time.
(a) Find the average power developed by the engine (express in watts and hp).
(b) Find the instantaneous power when the car reaches its final velocity (in watts and hp).
Example: An elevator has a mass of 1000. kg and carries a maximum load of 800. kg. A constant frictional force
of 4000. N retards its motion upward. What minimum power must the motor deliver to lift the fully-loaded
elevator at a constant speed of 3.00 m/s? (In watts and horsepower)
Momentum and Collisions (Chapter 9)
Momentum and Impulse
The momentum of an object is the product of its mass and velocity:
units of momentum: kg·m/s
If the resultant force F is zero, the momentum of the object does not change.
Impulse-Momentum Theory:
If we exert a force on an object for a time interval t, the effect of this force is to change the momentum
of the object from some initial value mvi to some final value mvf
Example: A golf ball of mass 50. g is struck with a club. Assume that the ball leaves the club face with a velocity
of +44m/s.
(A) Estimate the impulse due to the collision.
(B) Estimate the length of time of the collision and the average force on the ball.
Example: In a crash test, a car of mass 1500 kg collides with a wall. The initial of the car is 15.0 m/s east and the
final velocity of the car is 2.6m/s west. If the collision lasts for 0.150 s, find
(A) Why does the car start off going east and end up going west?
(B) the impulse due to the collision
(C) the average force exerted on the car.
Applications of Impulse Momentum Theory:
 Follow through in golf swing, batting, tennis.
 Catching a water balloon.
 Moving with the punch in boxing.
 Padding boxing gloves, goalie gloves in hockey, baseball mitts, inside of helmets…
Conservation of Momentum
Law of conservation of momentum: when no external forces act on a system consisting of 2 objects, the total
momentum of the system before the collision = the total momentum of the system after the collision.
Example: A baseball player uses a pitching machine to help him improve his batting average. He places the 50.kg machine on a frozen pond. The machine fires a 0.15-kg baseball with a speed of 36 m/s in the horizontal
direction. What is the recoil velocity of the machine?
Elastic and Inelastic Collisions
Collisions
For any type of collision, the _______________ momentum is ________________________.
However, the total _____________________________ is generally _________ conserved.
Elastic Collisions
Elastic collisions: both momentum and kinetic energy are conserved.
Before:
After:
and
2
2
½ m1v1i + ½ m2v2i = ½ m1v1f2 + ½ m2v2f2
(Conservation of Energy)
Inelastic Collisions
Inelastic collisions: momentum is conserved, but kinetic energy is not.
When 2 objects collide and stick together, the collision is PERFECTLY INELASTIC; in this case, their final velocities
are the same.
For perfectly inelastic collisions,
Before:
After:
NOTE: NONE OF THE MOMENTUM EQUATIONS WILL BE GIVEN ON THE TEST. YOU NEED TO KNOW THE
ELASTIC & INELASTIC EQUATIONS ON YOUR OWN!!!!!!
Example (perfectly inelastic): A large luxury car with a mass of 1800. kg stopped at a traffic light is struck from
the rear by a compact car with a mass of 900. kg. The two cars become entangled as a result of the collision. If
the compact car was moving at 20.0 m/s before the collision, what is the velocity of the entangled mass after
the collision?
Before:
After:
Example (perfectly elastic):Two kids are playing marbles. The shooter rolls toward a stationary marble at 5.0
cm/s. They two collide and the smaller marble speeds away at 8.0 cm/s. What is the final velocity of the
shooter? Assume the shooter is three times as massive as the smaller marble. (have faith with the masses…)
Before:
After:
Mixed Problems
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If the _________ of the object stays the same it is a conservation of __________ problem.
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If the mass of the object ______________, it is a conservation of _____________ problem (inelastic
collision)
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If two objects _____________, it is a conservation of momentum problem (elastic collision)
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If there is a ___________, it is an _____________ problem
Example 1: A block with a mass of 25 kg starts from rest 6.0 m above the ground and slides down a frictionless
ramp.
(A) What is the velocity of the block at the bottom of the ramp?
(B) At the bottom of the ramp, the 25 kg block collides inelasticly with 10. kg toy car at rest. What is the
final velocity of the car-block combo?
Example 2: A 65 kg Olympic ice skater is coasting at 5.0 m/s on a frozen pond when his little brother (of mass 35
kg) falls from a tree and lands in his arms.
(A) Now how fast is the skater moving while still holding his brother? (ignore any velocity from his little
brother)
(B) The sudden appearance of his brother makes the skater hit a small stone and fall over. The friction
between his jeans and the ice bring him, still holding his brother, to a stop in 1.5 m. What is the force of
friction between his jeans and the ice?