Question

a computer program calculates the amount of kinetic energy (ke) and elastic potential energy (pe) of the ball moving from left to right at three different positions. at position a, ke = 0.0 j and pe = 3.0 j. at position b, the spring has zero... what energy values would the computer most likely indicate for position b?
a. ke = 0.0 j, pe = 0.0 j
b. ke = 0.0 j, pe = 3.0 j
c. ke = 2.5 j, pe = 2.5 j
d. ke = 3.0 j, pe = 0.0 j

Explanation:

This problem is about energy conservation in a spring - mass system. At position A, \(KE = 0.0\space J\) and \(PE=3.0\space J\), so the total mechanical energy \(E = KE + PE=0 + 3=3.0\space J\). At position B, the spring is neither fully stretched (like at A) nor fully compressed (like at C). So, the potential energy (elastic potential energy of the spring) and kinetic energy should both be non - zero, and their sum should still be equal to the total mechanical energy (3.0 J) due to the law of conservation of mechanical energy (assuming no non - conservative forces like friction).

• Option A: \(KE = 0.0\space J\), \(PE = 0.0\space J\), total energy \(0\), which is not equal to 3.0 J, so incorrect.
• Option B: \(KE = 0.0\space J\), \(PE = 3.0\space J\), this would be the case when the object is at rest at the extreme position (like position A), not at position B, so incorrect.
• Option C: \(KE = 2.5\space J\), \(PE = 0.5\space J\), total energy \(2.5 + 0.5=3.0\space J\), which is consistent with the conservation of mechanical energy and the fact that at position B the object has both kinetic and potential energy.
• Option D: \(KE = 3.0\space J\), \(PE = 0.0\space J\), this would be the case when the spring is at its natural length (potential energy zero) and all energy is kinetic, but position B is not the position where the spring is at natural length (position C might be closer, but from the diagram, position B is in between), so incorrect.

Answer:

C. \(KE = 2.5\space J\), \(PE = 0.5\space J\)