PhysicsLAB: Bouncing Steel Spheres

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_ballv_approach = m_ballv_rebound + M_platev_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 (R²) 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.