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MR. SURRETTE
VAN NUYS HIGH SCHOOL
CHAPTER 4: WORK AND ENERGY
CLASSNOTES
MASS AND ENERGY
Scientists have categorized the universe into two general categories: mass and energy. Mass provides
inertia and takes up space. Energy is any resource that provides motion to mass.
ENERGY
Energy is present in the universe in a variety of forms including mechanical, chemical, electromagnetic,
heat, and nuclear energy.
CONSERVATION OF ENERGY
Although energy can be transformed from one form to another, the total amount of energy in the
universe remains the same.
WORK
Energy can be defined as “the ability to do work.” In order for work to be accomplished, an object must
undergo a displacement in the direction r. The SI unit of work is the Newton-meter (N.m) or joule [J].
WORK EQUATION
W = Fr
(Note: Work is a cosine function. In particular, r = ( distance[m] )(cos )
NET WORK
The sum of the work acting on a system is called the net work:
W = W1 + W2 + . . .
JOULES
A consequence of the work equation (W = Fr) is a unit of energy called a joule. A joule is equal to a
Newton (the unit of force) multiplied by a meter (the unit of distance): [J] = [N][m].
JOULES
Joules are also used to measure energy. Since a joule is equal to a Newton-meter, a joule can be reduced
to the following units:
[J] = [N][m] = [kg.m/s2][m] = [kg.m2/s2]
All these units are equivalent.
KINETIC ENERGY
One type of energy is kinetic energy. Kinetic energy is the energy of motion. Any object which has
mass m and speed v has kinetic energy. Kinetic energy has the same units as work (joules):
K = ½ mv2
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PHYSICS
MR. SURRETTE
VAN NUYS HIGH SCHOOL
CHANGE IN KINETIC ENERGY
The change in kinetic energy is equal to the final kinetic energy minus the initial kinetic energy:
K = KF – KI
Example 1. A ball hits a wall and bounces back at half the original speed. What part of the original
kinetic energy did it lose in the collision?
1A.
(1) KI = ½ mv2
(2) KF = ½ m(1/2 v)2
(3) KF = ½ m((1/4)v2)
(4) KF = 1/8 mv2
(5) KF = (1/4)KI
(6) The ball lost ¾ of its original kinetic energy.
GRAVITATIONAL POTENTIAL ENERGY
Gravitational potential energy Ug depends only on an object’s weight and its height above the surface of
the Earth:
Ug = mgh
WORK DONE BY GRAVITY
The work done by gravity is opposite to gravitational potential energy because it releases potential
energy:
Wg = - Ug
Example 2. A 40 N crate is pulled 5 m up an inclined plane at constant velocity. If the plane is inclined
at an angle of 37 degrees to the horizontal, what is the magnitude of the work done on the crate by the
force of gravity?
2A.
Determine ramp height: (1) (5 m)(sin 37o) = 3 m
Determine gravitational potential:
(2) Ug = mgh
(3) Ug = (40 N)(3 m)
(4) Ug = 120 J
(5) Wg = - Ug
(6) Wg = - 120 J
Example 3. A 3 kg object starting at rest falls from a height of 10 m to the ground. In this instance, the
force of the air is not negligible so that the magnitude of work done by this frictional force is 20 J. What
is the object’s kinetic energy prior to hitting the ground?
3A.
(1) v2 = vo2 + 2ad
(2) v2 = 0 + 2ad
(3) v2 = 2ad
(4) v = (2gd)1/2
(5) v = [(2)(9.8 m/s2)(10m)]1/2
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PHYSICS
MR. SURRETTE
3A.
(6)
(7)
(8)
(9)
(10)
VAN NUYS HIGH SCHOOL
(continued…)
v = 14.0 m/s
K = ½ mv2
K = ½ (3 kg)(14 m/s)2
K (possible) = 294 J
294 J – 20 J = 274 J
THE WORK-ENERGY THEOREM
The relationship between work and change in kinetic energy is stated in the work-energy theorem:
WNET = K
Example 4. A baseball catcher puts on an exhibition by catching a 0.15 kg ball dropped from a
helicopter at a height of 61 m. If the catcher “gives” with the ball for a distance of 0.75 m while
catching it, what average force is exerted on the mitt by the ball?
4A.
(1) Ug = mgh
(2) Ug = (0.15kg)(9.8 m/s2)(61 m)
(3) Ug = 89.7 J
(4) Ug = - Wg
(5) - Wg = - Fr
(6) Ug = - Fr (the negative sign means downward direction)
(7) F = Ug / r
(8) F = (89.7 J) / (0.75 m)
(9) F = 119 N
CONSERVATION OF MECHANICAL ENERGY
The sum of the kinetic energy plus the potential energy is called the total mechanical energy:
E=K+U
This is usually solved as the equation:
KI + UI = KF + UF
POWER
The average power supplied by a force is the ratio of the work done by the force to the time interval
over which the force acts. The average power can also be expressed in terms of the force and the
average speed of the object on which the force acts.
POWER EQUATIONS
P=W/t
P = Fv
The unit of power is the Watt [Joule/sec].
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PHYSICS
MR. SURRETTE
VAN NUYS HIGH SCHOOL
Example 5. A pulley-cable system on a crate hoists a container of cement with a total weight of 20,000
N to a height of 40 m. If this is accomplished in 2 minutes, what is the power output by the pulley-cable
system?
5A.
(1) P = W / t
(2) W = Fr
(3) P = Fr / t
(4) P = (20,000 N)(40 m) / 120 s
(5) P = 6,700 W
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PHYSICS