Lab
Bouncing Steel Spheres
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In this lab you will examine the recoil energy of four bouncing steel spheres of differing mass and diameter. You will need the following supplies:
1 coefficient of restitution apparatus
4 steel balls
1 triple beam balance
The fifth steel ball in this collection will be given to you
by your instructor during the "prediction" phase of the lab.
Data Collection
After measuring the mass of each steel ball and its diameter, you will drop each ball a minimum of three times from the top of the tube and record its rebound height. Make sure that the spheres are released so that their "bottom" is at the 50-cm mark and that they fall down the middle of the tube, not along its edge. It might be necessary to drop each sphere more than three times in order to achieve three relatively consistent results. Most likely, you will be "observing" the top of the sphere's bounce, if that is true, remember that you must subtract the sphere's diameter to get its "true" rebound height.
Examine the vertical tube's scale carefully, there are 8 not 10 divisions between major centimeter markings. Every two small tick marks represent one-fourth of a centimeter!
diameter
mass
height 1
height 2
height 3
av rebound
(cm)
(g)
(cm)
(cm)
(cm)
(cm)
0.9
1.2
1.5
2.5
Calculating "Bounciness"
In a collision involving two masses, the coefficient of restitution,
e
, is defined as the ratio of their relative velocities of recession to their relative velocities of approach.
When the coefficient equals 0 then the collision is said to be
completely inelastic
; that is, the two objects will stick together. When the coefficient equals 1 then the collision is said to be
completely elastic
; that is, there is no loss of kinetic energy during the collision. Any value between 0 and 1 is a measure of the collision's "bounciness."
Having averaged the rebound heights for each of the three spheres in the previous data table, use conservation of energy methods to calculate each sphere's impact velocity
PE
_{release}
= KE
_{impact}
and rebound velocity
KE
_{rebound}
= PE
_{bounce}
with the strike plate.
Then use conservation of momentum to calculate the strike plate's "recoil velocity." In our lab, you may correctly assume that the strike plate has zero velocity before the collision.
m
_{ball}
v
_{approach}
= m
_{ball}
v
_{rebound}
+ M
_{plate}
v
_{recoil}
In this equation, you need to be VERY careful of SIGNS: remember that the ball is falling when it approaches the plate and that the ball is raising when it rebounds. Also recall that the recoil velocity of the strike plate will be "downward" since the ball's impact will "move it" in that direction - recall the behavior of the wooden blocks on the hoop lab's incline.
Attach ALL of your calculations for this table to your lab report!
Before completing the second data table, measure and record the mass of the strike plate in grams.
sphere
diameter
velocity
approach
velocity
rebound
recoil
velocity of plate
coefficient
of restitution
(cm)
(m/sec)
(m/sec)
(m/sec)
0.9
1.2
1.5
2.5
Data Analysis
When you have completed your calculations, open the EXCEL sheet
1-BouncingSteel.xls
and
fill in the cells that are highlighted in light green
. Once again, do
NOT
touch the cells that are
highlighted in light yellow
since they are pre-programmed to assist you in the analysis of your data. Save your file to your period folder as
LastnameLastnameBouncingSteel.xls
. Be careful that your data is in the requested unit of measure.
What is the filename of your graph?
What is the equation of your graph?
What is the correlation coefficient (R
^{2}
) of your graph?
Describe the relationship between the percent of energy lost calculated on your EXCEL graph and the coefficients of restitution you calculated in the previous data table.
Prediction
Based on mass information given to you by your instructor regarding the fifth, 1.8-cm sphere, use the equation of your graph to interpolate how high the sphere should bounce. Show your calculations on this lab paper and have your instructor initial them before witnessing your trials.
sphere
diameter
mass
predicted
height
rebound
#1
rebound
#2
average
rebound
percent
(cm)
(g)
(cm)
(cm)
(cm)
(cm)
error
1.8
Instructor's certification of calculations supporting your predicted rebound heights.
When this lab is completed and your lab group has submitted your results online, you need to turn in a copy of your EXCEL graph as well as this data/calculation paper.
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Conservation of Energy
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Power Production
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Work and Energy
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Cliffs
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Escape Velocity
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Gravitation #2
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Advanced Properties of Freely Falling Bodies #1
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Advanced Properties of Freely Falling Bodies #3
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Energy/Work Vocabulary
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Kinematics Along With Work/Energy
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Potential Energy Functions
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Practice: Momentum and Energy #1
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Practice: Momentum and Energy #2
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Rotational Kinetic Energy
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