Physics 121
6. Work and Energy
6.1 Work
6.3 Kinetic Energy
6.4 Potential Energy
6.5 Conservative and Non-conservative forces
6.6 Mechanical Energy / Problem Solving
6.8 Conservation of Energy
6.9 Dissipative Forces / Problem Solving
6.10 Power
Work
Work = Force x Distance
W=F.d
Example 6.1 . . . Work for Slackers!
You push a car with a force of 200 N over a
distance of 3 m. How much work did you
do?
200 N
Solution 6.1 . . . Work for Slackers!
W = F.d
W = 200x3
W = 600 Nm
W = 600 J
Note: A Joule (J) is just another term for
newton . meter (N m)
Energy
Energy is the capacity to do work
Kinetic Energy
Potential Energy
(motion)
(position)
Kinetic Energy
K.E. = 1/2 mv2
Example 6.2 . . . Kinetic Energy
The K.E. of a car is 600 J and its mass is
1000 kg. What is its speed?
Solution 6.2 . . . Kinetic Energy
K.E. = 1/2 m v2
600 = 1/2(1000)(v2)
v = 1.1 m/s
Example 6.3 . . . Save your work!
You lift a 2 kg book and put it on a shelf 3
meters high.
(a) How much work did you do?
(b) Was the work “lost”?
Solution 6.3 . . . Save your work!
(a)
W = F.d
W = mgh
W = 2x10x3
W = 60 J
(b)
Work was stored as Potential Energy
(hidden). So gravitational P.E. = mgh
Example 6.4 . . . Downhill
A 65 kg bobsled slides down a smooth (no
friction) snow-laden hill. What is its speed at
the bottom?
15 m
30 m
Solution 6.4 . . . Downhill
P.E. = K.E.
mgh = 1/2 mv2
9,555 = (1/2)(65) v2
v = 17.1 m/s
15 m
30 m
Example 6.5 . . . Sticky bobsled
Suppose the speed of the bobsled was
actually measured to be 14.8 m/s instead of
17.1 m/s
(a) What could have caused that?
(b) What was the work done by the bobsled
against friction?
Solution 6.5 . . . Sticky bobsled
(a) Not all the P.E. was converted to K.E. because
some work was lost (heat energy) in doing work
against friction: P.E. = K.E. + Wf
(b) mgh = 1/2 mv2 + Wf
9,555 = 1/2(65) (14.8)2 + Wf
Wf = 2,436 J
Stretching Springs
Hooke’s Law: The amount of stretch is
directly proportional to the force applied.
F=kx
Lab Experiment
Slope = “k”
F
x
Example 6.6 . . . Springy Spring
The spring constant (k) of a spring is 20 N/m.
If you hang a 50 g mass, how much will it
stretch?
Solution 6.6 . . . Springy Spring
F=kx
mg = kx
(50 /1000)(9.8) = (20)(x)
x = 2.5 cm
Lab Experiment
Example 6.7 . . . Body building
How much work would you have to do to
stretch a stiff spring 30 cm (k = 120 N/m)?
“Solution” 6.7 . . . Body building
W=F.d
W = (kx)(x)
W = kx2
W = (120)(0.3)2
W = 10.8 J
X

Correct Solution 6.7 . . . Body building
W=F.d
We must use the AVERAGE Force!
W = (1/2)(kx)(x)
W =1/2 kx2
W = (1/2)(120)(0.3)2
W = 5 .4 J


P.E. of a Spring = 1/2 kx2
Example 6.8 . . . Lugging the Luggage
What is the speed when the distance is 3 m?
40 N
10 kg
Hawaii or
Bust!
600
Solution 6.8 . . . Lugging the Luggage
What is the speed when the distance is 3 m?
F.d = 1/2 m v2
(40 cos 600)(3) = (1/2)(10)(v2)
v = 3.5 m/s
40 N
10 kg
Hawaii or
Bust!
Moral of the story
W = (F)(d)(cos)
600
Conservative Forces
If the work done against a force does not depend on
the path taken then that force is called a conservative
force. Examples are gravity and spring force. The
total mechanical energy (P.E. + K.E.) will remain
constant in this case.
If the work done against a force depends on the path
taken then that force is called a non-conservative
force. Example is friction. The total mechanical
energy (P.E. + K.E.) will not remain constant in this
case.
Vote Democrat . . . Just kidding!
Example 6.9 . . . Playing with Power
Power is the rate of doing work
P=W/t
A pump can lift at most 5 kg of water to a
height of 4 m every minute. What is the
power rating of this pump?
Solution 6.9 . . . Playing with Power
W = mgh
W = (5)(10)(4)
W = 200 J
P=W/t
P = 200 J / 60 s
P = 3.3 J / s
P = 3.3 W
Note: Watt (W) is just another term for Joules /
second (J / s)
That’s all folks!