02.3d - Efficiency of Systems

1. The 0.075-kg Regular-Duty Felt ball was dropped in the testing system. It was found that the ball lost 15% of its original energy before passing through the photo-gate.

   1. Calculate the velocity of the Regular-Duty Felt ball as it passed through the photo-gate.

2. The ball lost an additional 7.5% (22.5% total) of its energy prior to hitting the extended spring.

   1. Calculate the compression of spring, your answer should be expressed in meters.

3. When the Regular-Duty Felt ball came into contact with the spring it had 1.71 Joules of kinetic energy, 40% of that energy was lost while in contact with the spring.

   1. Deduce that the ball will pass back through the photo-gate (traveling vertically).

4. The Extra-Duty Felt passed through the photo-gate with a velocity of 4.8 m/s.

   1. Show that the Extra-Duty Felt ball lost 41% of its energy prior to passing through the photo-gate.

   2. Comment on the difference in energy loss based upon the two different balls.

5. While in class Lary argued that the Extra-Duty Felt ball would compress the spring a GREATER amount than the Regular-duty Felt.

   1. Evaluate the quality of Lary's claim in regards to the compression of the spring due to the falling Extra-Duty Felt ball.

Aspiring IB students asked: What is the purpose of 'High-Altitude' Tennis balls. The response was:

High altitude balls don't contain as much pressure because normal balls become too active in the relatively lower atmospheric pressure of high altitudes. As you might expect, high altitude balls can be a bit more sluggish at sea level.

Using the same testing set up as with the Regular and Extra-Duty tennis balls, at sea level. The students found no changes in the velocity or energy lost compared to the Regular-Duty balls while falling. The High Altitude ball had 1.71 J of Kinetic energy when it came into contact the 100 N/m spring.

1. What can be deduced regarding the felt of the High Altitude ball compared to that of the Regular-Duty Ball?

2. After bouncing off the spring, the ball traveled exactly to the height of the photo-gate. Determine the efficiency of the ball-spring interaction (how much energy was lost as a percentage of the original).

3. Based on the results of the experiment, evaluate the claim in the response to the student's question.