Class 18
Ball Dropped on a Spring
A. Find the velocity when the ball hits the spring by setting the energy when it is just dropped to the
point when it hits the spring
1. Set the zero position for the gravitational potential energy and the elastic potential energy
The zero of the Gravitational Potential Energy is set at the point that the ball hits the spring.
The zero of the Elastic Potential Energy is set at the point where the spring is NOT compressed.
2. Write the Conservation of Mechanical Energy for any point you want to calculate.
KE 1 PE G1 =KE 2 PE G1
1
0m g h= m v 21 0
2
(2.)
v 1= 2 g h
B. Find the maximum compression of the spring by writing the total mechanical energy when it hits
the spring set equal to the energy at maximum compression.
For this I set the zero of the gravitational potential energy at the point when the spring is at maximum
compression.
I call the distance that the spring is compressed Y
KE 2PE G2 PE E2= KE 3 PE G3 PE E3
Equation (2) gives me the kinetic energy when it hits the spring
KE 2=mgh
1
mgh0m g Y =00 k Y 2
2
(3.)
1
Class 18
C.
Find the maximum compression of the spring directly, without calculating the speed at the point
of impact.
For this I set the zero of the Gravitational Potential Energy at the point of maximum compression.
The zero of the elastic potential is naturally the point at which the spring is at its relaxed length
KE 1  PE G1 PE E1 =KE 3 PE G3 PE E3
1
0mg hY 0=00 k Y 2
2
(4.)
If you compare equation (3.) and equation (4.) you see that you get the same thing.
Using Conservation of Energy with a Non-Conservative Force
If you have a non-conservative force, say friction, then the work-energy principle becoms
the work done by the non-conservative force is equal to the change in the mechanical energy
W NC = KE PE
(5.)
The Law of Conservation of Energy
As seen in the above example, energy can be transformed from on form into another, e. g. from
potential energy into kinetic energy and into elastic potential energy.
If all the forms of energy are accounted for
The total energy is conserved.
Power – the rate of doing work
Units of Energy
The unit of energy is a Joule
Since work is force times distance, thus
Joule = Newton * meter
Units of Power
power=
Work
time
so the units of power, which are called Watts are
Watt =
Joule
second
By combining the definition of power and work we can obtain a formula to power in terms of force.
P=
W Fd
d
=
=F = F v
t
t
t
2
Class 18
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Class 18
Clicker Quiz #2
A man pushes a crate of mass = 10 kg across a floor with coefficient of friction = 0.2, for a distance of 3 m
at a constant speed. The work done by the man is
a. 55 J
b 59 J
c.
64 J
d. 70J
e none
Clicker Quiz #3
In the above example if it takes the man 20 seconds to push the box the 3 m, how much power is he putting
out.
a. 3W
b. 4W
c. 5W
d. 6W
e. none
Clicker #4
If the kinetic energy of a mass is doubled then the velocity increases by a factor of
a. 2
b. 4
c.
2
2
d
 2
e. none.
4
Class 18
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