1. Work & Energy
In the past…
v, a, x, t  How things move, Kinematics
F, a, m  What makes them move, Dynamics
Now we will look at WHY they move!!! Energy!
Energy  The ability to do work.

2. Work = Force x Displacement
1 Joule = 1 Newton x 1 Meter
(jewel)
1. Object must move.
2. Force & Displacement must be on the
same plane
3. Don’t forget air friction is negligible.

3. Anything that puts a force on an object displacing it will
cause work.
Which of the following do work on the box?
gravity  No. Doesn’t move up or down
normal force  No. Doesn’t move up or down
you pulling it  Yes, but only the x component
friction  Yes
Positive  energy is + if it is going into the object/system
Negative  energy is – if it is coming out of the object/system

4. How much work will the road do on an 1800 kg
car when its brakes are applied, if the
coefficient of friction between the road and the
wheels is 0.5 and the car skids 6 m?
W = F d = Ff d = µ Fg d = µ m g d
= (0.5) (1800) (9.8) (6)
W = -52, 920 J

5. F vs d Constant Forces
How do you find work on
F F vs d graph?
Work = F d
= Area under the curve
d F vs d
Nonconstant forces
ΔW = F Δd
F
W = F ∫d
d

6. Gravitational Potential Kinetic Energy
Energy  energy due to motion
 energy due to position KE = ½ mv 2
PE = mgh
Ex. How much KE does an 1800
Ex. You lift a 1.2 kg book from kg car going 25 mph (11.2 m/s)
the first floor to your social have?
studies class on the 2nd floor 5
m up. How much potential KE = ½ mv2
energy does the book have? = ½(1800)(11.2)2
= 113 000 J
PE =mgh
= (1.2) (9.8) (5) How much work would friction
= 58.8 J need to do to stop it?
W = KE = -113 000 J
How much work did you do?
Conservation!!!
W = PE = 58.8 J

8. Law of All the energy in = All the energy
out
Conservatio W + PE + KE = PE + KE (+W)
n of Energy (Work out is done by friction. If no
 Energy friction, then no work out.)
cannot be
created or A 600 kg roller coaster car is lifted to
destroyed the top of the first hill, 55 m above the
ground.
a. How much potential energy does it have? PE = m g h
b. How much work was done to get the cart to the top of the first
hill? W = PE PE = KE = ½ mv2
c. How fast is it going at the bottom of the first hill?
d. If the second hill is 40 m high, then how fast will the cart be going
when it crests the hill? PE = PE + KE

9. Sample Problem
A disgruntled physics student drops
her book off a 4 story building (12 m),
how fast is the book going before it
hits the ground?
h = 12 m
m = 1.7 kg h=
Energy in = Energy out 12 m
PE + KE = PE + KE
Double check with kinematics!

10. Describe the energy transfer in the following
Different Scenarios
• Dropping an object off a building
• Throwing an object off a building
• Car being slowed down by friction
• You throwing a ball
• A bullet shot; then embedded in a tree
• You lifting your backpack up to math

12. Work Energy Theorem
W = ΔKE W = ΔPE
In order to change any type of energy,
work must be done.

15. Power = Work/Time
Tells you how much energy you use in a
certain amount of time.
Metric Unit: Watts
English Unit: Horsepower.
746 Watts = 1 HP

17. A school bus pulls into an intersection. A car
traveling 35 km/h approaches and hits a patch
of ice. The driver locks the brakes causing the
car to slide toward the intersection. If the car
is originally 26 m away and the coefficient of
friction between the car’s tires and the icy road
is 0.25, does the car hit the bus and poor
innocent school children lose their lives … or
does the car stop just in the nick of time letting
the little children grow up to do physics
problems involving school buses and icy
roads?

19. Variable Forces
Force the spring applies
is directly proportional to
Springs how far it is stretched.
Fαx F=kx
k is called the spring constant
FS F if k is large, spring is stiff
if k is small, spring is loose
FS F
Hooke’s Law
(Robert Hooke)
Xi Xf

20. Energy in a Spring
F + Fi F kx 1
How would you find the F= = = = kx
2 2 2 2
work you put into
stretching a spring? W = Fd = ( 1 kx ) x
W=Fd
2
But the Force changes over W = 1 kx 2
2
the distance…
So let’s find the average
force… When you do work on a
spring, where does that
energy go?
Potential Energy!!!
W = PEs = ½kx2

21. Sample Problem
A woman weighing 600 N steps on a
bathroom scale containing a spring. The
spring is compressed 1.0 cm under her
weight. Find the force constant of the
spring and the total work done on it during
compression. F = kx
k = F/x = 600/0.01
= 60,000 N/m
W=½ kx2=½ (60,000) (0.01)2
W = 3.0 Nm = 3.0 J

22. Garage Door
A large garage door spring is stretched a
distance of 2.50 m when a force of 160 N is
applied. Find:
a. the spring constant
b. the work done on the spring
c. the force needed to stretch the spring 1.90 m
d. the power used if the spring is stretched
1.20 m in 3.00 secs.