Question

a student knows the amount of stored elastic potential energy in the spring before it is released. what additional quantity can the student determine using only this piece of information? a the mass of the ball b the distance the ball travels c the velocity of the ball just before it hits the ground d the kinetic energy of the ball just as the spring is fully released

Explanation:

Step1: Recall energy - conservation principle

According to the law of conservation of energy, the elastic potential energy stored in the spring $U_{s}=\frac{1}{2}kx^{2}$ is converted into kinetic energy when the spring is released. At the moment the spring is fully released, all of the initial elastic - potential energy is converted into kinetic energy of the ball (assuming no energy losses due to friction etc.). So $K = U_{s}$, where $K$ is the kinetic energy of the ball and $U_{s}$ is the elastic potential energy of the spring.

Step2: Analyze other options

• Option A: The mass of the ball cannot be determined from the elastic potential energy of the spring alone. We would need information about the velocity of the ball at some point and the kinetic - energy formula $K=\frac{1}{2}mv^{2}$ to find the mass.
• Option B: The distance the ball travels depends on the initial horizontal velocity (which we don't know without more information), the initial height, and the acceleration due to gravity. Just knowing the elastic potential energy of the spring is not enough.
• Option C: To find the velocity of the ball just before it hits the ground, we need to consider the initial height of the ball above the ground and the initial vertical and horizontal velocities. The elastic potential energy of the spring only gives us information about the initial kinetic energy when the spring is released, not about the final velocity just before hitting the ground.

Answer:

D. the kinetic energy of the ball just as the spring is fully released