Download THIS MS Word file

Energy Intro for AP Physics - There are many different types of energy, but we will begin with a few types as follows:
 Work, symbol W
 Kinetic energy, symbol K
 Potential Energy, symbol U but then like force with a subscript for example Ug gravitational potential energy. There are
other types of potential energy as well and we will discuss those as we go along.
These are discussed in more detail below: Please read these notes and then complete the basic problems that are given at the
bottom of the page.
Work = force X displacement, but only if both force and displacement (WHICH ARE BOTH VECTORS!!!) are parallel or lie
along the same line. If the previous statement is not true then the answer for work is zero. A vertical force cannot do work on an
object that has horizontal displacement. For example if you are asked what work is done by the force of gravity in displacing an
object horizontally, the answer would be zero. The unit of work is the energy unit that we will use for the entire chapter called the
Joule, abbreviated J. The equation for work is W = Fx cos θ, but I hate the cos θ because the AP test has a fondness for giving you
the angle that would not use cos θ. So use the equation
W = Fx (and remember ║).
Work or energy of any kind is not a vector and does not have direction. However there can be energy lost or energy gained and so
positive or negative energy must be considered. Consider a free body diagram of an object moving at a constant velocity which
has a horizontal push force that is equal to 10 N and a horizontal frictional force also equal to 10 N and the object displaces 10 m
horizontally. What is the work done by the push force? What is the work done by the frictional force? What is the net force on
the object? What is the net work done on the object?
Kinetic energy is energy of motion. It is ALWAYS POSITIVE. Kinetic energy is equal to one half times mass time velocity
squared. The equation is:
K = ½ m v2
The unit for kinetic energy is the Joule (J) also. Mass must be in kilograms and velocity must be in m/s.
Gravitational potential energy is given the symbol U and equals mass times acceleration due to gravity times height.
The equation is
Ug = mgh
Units of potential energy are Joules (J) again! Mass must be in kilograms and height must be in meters. The acceleration due to
gravity must be in m/s2 and on earth it is 10 m/s2. The height in the equation is really change of height with respect to some
specific reference, usually ground level so sometimes the equation is written Ug = mgΔh. Consider this thought example. What is
the gravitational potential energy of a baseball cap on top of my head? If you knew the mass of the cap and how tall I am you
could figure it out. But what if I am standing at the top of a cliff and the cap falls off my head and then to the bottom of the cliff.
Then h would be much larger and the energy would be much larger. In any given problem, you can choose where you want the
reference height to be again. Again it is usually ground level, but sometimes it is more convenient to make it another place such as
the lowest point in the problem or the lowest point that something falls to. Just choose one place and be consistent, reference it
and be consistent. Sometimes the problem will tell you what to consider as “ground level” or where h = 0.
Please skim Chapter 5 in College Physics (swimmer) and/or Chapter 6 in Principles of Physics (train) and see what you can learn
about these topics.
1. What work is done on a 1.1 kg object to move it to a vertical height of 3 m?
33 J
2. If 2.3 kg object is moving horizontally for 10 m, what work is done on the object by gravity?
0
3. A 7.7 kg object was already moving horizontally on a frictionless surface at a constant velocity and it moves a distance of 10
m, what work is done on the object?
0
4. An 85-kg object has a velocity of 8.8 m/s while traveling on a frictionless surface. The object comes to a stop in 3 seconds
because a horizontal push is exerted on it to stop it. (a) Draw a free body diagram. (b) What is the acceleration of the object?
(c) What amount of force had to be exerted to stop the object? (d) How far did the object travel during the time it was
topping? (e) What work did the stopping force do?
-2.93 m/s2, 249 N, 13.2 m, 3287 J
5. A 20-kg suitcase is carried up a flight of stairs and moves 8 m vertically and 5 m horizontally. What work is done to carry the
suitcase up the stairs?
1600 J
6.
I spin my 0.02 kg-keys in a circle of radius 43 cm for 3 full rotations taking place over 15 seconds while applying a tension
force of 1.34 N to the keys. What work is done by the centripetal force?
0
7. A 2.2 kg object is moving at 3.1 m/s. What is its kinetic energy?
10.6 J
8. A 4.4 kg object is 5.1 m off the ground. What is it gravitational potential energy?
224J
ANSWERS NOT IN ORDER, NOT INCLUDING 6 BECAUSE WE HAVEN’T STUDIED CIRCULAR MOTION
0, 0, 2.9, 10, 13, 33, 224, 249, 1600, 3290,