To test out some ideas about Conservation of Momentum and Conservation of Angula

Question

To test out some ideas about Conservation of Momentum and Conservation of Angular Momentum, your lab group has been given an hour's time at the local ice rink. You have rigged some overhead cameras with which to measure puck speeds before and after various collisions. It is easy to observe that there is some small amount of friction between the pucks and the ice; however, your group has decided that, if the collisions are sufficiently violent, then the internal forces between the pucks during the collisions will be much much larger than the external forces due to friction. Therefore, your group has decided to restrict their observations to a small interval of time before and after the collisions; during that time frictional forces can be ignored. The pucks your group is using for the collisions are a regulation puck of mass 170.0  gramsand a practice puck of mass 255.0  grams . Each puck has a radius of 3.810  cm .

Your group has been asked to examine collisions in which the pucks stick together after the collision. To get the pucks to stick together, your group has wrapped the circumference of each puck with velcro (the regulation puck has the velcro hooks and the practice puck has the velcro loops) with the hooks or loops outward in each case. To get consistent puck speeds before the collision, your group has constructed a pair of rubber-band launchers, in which a very strong rubber band is stretched tightly between two posts and then used like a slingshot. A few trials are sufficient to determine that these launchers, if used carefully, can launch the pucks with predictable speeds and with essentially no spin.

Your group videotapes many trials. In each and every trial, the regulation puck is traveling due East before the collision and the practice puck is traveling due West. Your group quickly finds that it is difficult to get a perfectly a head-on collision. In almost every trial, the paths of the two pucks are not quite perfectly aligned; as a result, after the collision the two pucks end up attached to one another and spinning about their common center-of-mass. After many trials, your group does succeed in getting one trial in which the collision is perfectly head-on. Your group decides to analyze this collision and one other, one in which the paths of the two pucks are purposely misaligned by several centimeters so as to maximize the differences between the two collisions.

For the analysis, your group splits up into two teams. One team will analyze the puck motions before the collisions and then predict the motions after the collision; while the second team will analyze the puck motions after the collision as a check on the calculations of the first team. You have been assigned to Team 1, which is analyzing the "before" motions of the pucks and predicting the "after" motions.

The Head-On Collision

Collision number 1 is perfectly head-on. Your video analysis indicates that the regulation puck has a speed of 3.10  m/s before the collision, and the practice puck has a speed of 9.10  m/s .

Part A

Assuming that frictional forces between the pucks and the ice are small enough to ignore during the collision, what is the velocity of the two pucks (now stuck together) after the collision? Also, how much thermal energy was created by this collision?

Give your answers as an ordered pair, with the velocity first, followed by a comma, followed by the thermal energy. Give the East-West component of velocity, with East considered positive.

The Glancing Collision

In Collision 2, the paths of the two pucks are misaligned by 4.90  cm . In other words, if a straight line is drawn for the path of each puck before the collision, then the line for the regulation puck is 4.90  cm to the North of the line for the practice puck. Once again, your video analysis indicates that the regulation puck has a speed of 3.10  m/s before the collision, and the practice puck has a speed of 9.10  m/s , indicating that the speed control of the rubber-band launchers was quite reliable.

Part B

You should find that the center-of-mass velocity is purely East-West both before and after this collision. Give the center-of-mass velocity, and give the North-South location of the line of travel of the center of mass.

Give your answers as an ordered pair, with the velocity first, followed by a comma, followed by the position. Give the East-West component of velocity, with East considered positive. Give the position as a distance to the North of the original (before the collision) line of travel of the practice puck. Give the position in centimeters.

Questions About the Angular Momentum of the Two-Puck System During Collision 2

Imagine an axis perpendicular to the ice and passing through the line-of-travel of the center of mass; call this axis A. This axis can be anywhere on the line-of-travel of the center of mass. Your team has decided to use axis A for the purpose of checking Conservation of Angular Momentum for Collision 2.

Part C

Assuming that frictional forces between the pucks and the ice are small enough to ignore during the collision, what is the angular momentum (about axis A) of the two-puck system after the collision?

Give the component of angular momentum about the selected axis. Let counterclockwise (when looking down) be positive.

Part D

What is the spin rate of the two pucks (now stuck together) after the collision has occurred?

Give the magnitude of the angular velocity of the two pucks after the collision.

Part E

How much thermal energy was created during this collision?

Explanation / Answer

m1=.17 kg

m2=.255 kg

v1=3.1 m/s

v2=9.1 m/s

v1'={(m2-m1)/(m1+m2)}v1=.62m/s

v2'={(2m1)/(m1+m2)}v1=2.48m/s

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