Name
Period
Date
Energy Worksheet 5 Quantitative Bar Graphs
1. Consider the falling motion of the ball in the following two frictionless situations.
Begin by identifying the system. Then indicate whether the energy of the system is
conserved. Finally, complete the energy bar graph/flow diagram quantitatively and
use it to find the speed of the 2 kg ball just prior to striking the ground.
E gi  100.J
E gi  100.J
E gf 
J
E gf 
J
E kf 
J
E kf 
J
vf 
m
vf 
m
s
System?
s
System?
Energy Conserved: Yes or No?
Energy Flow
Initial
Diagram
Ek Eg Ee
Energy Conserved: Yes or No?
Final
E k Eg Ee E d i s s
0
0
2. Use the Law of Conservation of Energy to fill in the blanks for the following system
(m = 2 kg). Neglect frictional forces. Finally, complete the energy bar graphs
quantitatively.
E g  10. J
Eg  2 J
Ek  0 J
h
v  0m
Ek 
m
s
Ek Eg Ee
10
10
0
0
Eg  0 J
J
h
m
v
m
Ek 
s
Ek Eg Ee
10
0
J
h
m
v
m
Eg 
J
Ek 
J
h
v  0m
m
s
s
Ek Eg Ee
10
0
Ek Eg Ee
Energy WS 5
page 2
For each situation in #3 - 7:
1. Define and state/show the system you choose to analyze.
Assume the systems to be frictionless, unless stated otherwise.
2. Complete the energy bar graph QUANTITATIVELY (numerically
accurate).
3. In the space below each diagram use conservation of energy
principles to solve for the quantity called for in the question.
3. A 2 kg ball moving at 2 m/s is rolling towards an inclined plane. It eventually rolls up
the hill to a position near the top where it momentarily stops prior to rolling back
down the incline. Determine the height to which the ball rises along the incline
before stopping.
System?
Initial
Ek Eg Ee
0
Energy Flow
Diagram
Ek
0
Final
Eg Ee E d i s s
Energy WS 5
page 3
4. A moving cart hits a spring, traveling at 5.0 m
at the time of contact. At the instant
s
the cart is motionless, by how much is the spring compressed?
System = _____________________
m = 8.0 kg
vi = 5.0 m/s
Initial
Ek Eg Ee
k = 50. N/m
vf = 0
Energy Flow
Diagram
0
Initial
Ek
Final
Eg Ee E d i s s
0
Final
5. Determine final velocity of the cart, assuming that 10.% of the energy is dissipated
by friction.
System = _______________________
height (m)
Initial
Ek Eg Ee
v
vi = 00
Energy Flow
Diagram
Ek
5.0
m = 20. kg
0
vf = ?
0
0
Final
Eg Ee E d i s s
Energy WS 5
page 4
6. A block is placed on a spring, compressing it 0.30 m . What height does the block
reach when launched by the spring?
System =
Initial
Ek Eg Ee
m = 500. g
vf = 0
k = 100. N/m
x = 0.30 m
0
Initial
Energy Flow
Diagram
Ek
0
Final
Eg Ee E d i s s
0
Final
7. The bullet strikes a block of wood that exerts, on average, a force of 50 000. N
opposing the motion of the bullet. How far does the bullet penetrate?
System = _______________________
m = 25 g
vi = 350 m/s
vf = 0
Initial
Final 0
Initial
Ek Eg Ee
Energy Flow
Diagram
Ek
0
Final
Eg Ee E d i s s
Energy WS 5
page 5
8. The diagram below depicts a popular loop-the-loop amusement park ride. The car
and riders are initially pulled up the incline on the left to a height "H" above the
ground. The car is then released, gaining enough speed as it goes down the incline
to successfully traverse the entire course. The car has brakes to stop it on the right
side of the course.
k  0
r  5 .0 m
h  14 m
m  1.0  10 3 kg
r
H
h
a. Draw and label a force diagram of
the car at the top of the loop at the
minimum speed the car could go
without falling off of the track.
b. What must be this minimum speed of
the car at the top of the loop?
c. What must be the minimum initial height " H " to insure that the car would not fall
off of the track? Complete the LOL diagram quantitatively to help determine
this height.
System =
Energy Flow
Initial
Final
D
i
a
g
r
a
m
Ek Eg Ee
E k Eg Ee E d i s s
0
0