A heavy dart and a light dart are launched horizontally on a frictionless table by identical ideal springs.Both springs were initially compressed by the same amount.Which of the following statements about these darts are correct? (There could be more than one correct choice. )
A)The darts both have the same kinetic energy just as they move free of the spring.
B)The lighter dart leaves the spring moving faster than the heavy dart.
C)The heavy dart had more initial elastic potential energy than the light dart.
D)Both darts move free of the spring with the same speed.
E)Both darts had the same initial elastic potential energy.

Question

Quizplus · Accepted Answer

The kinetic energy imparted to both darts is the same because it depends on the energy stored in the spring, which is the same for both as the springs were compressed by the same amount (A). Since kinetic energy is given by $ \frac{1}{2}mv^2 $, for the same amount of kinetic energy, the lighter dart must have a higher velocity to compensate for its lower mass, making (B) correct. The initial elastic potential energy in the spring is solely a function of how much the spring is compressed, not on the mass of the dart, so both darts had the same initial elastic potential energy, making (E) correct.

A Heavy Dart and a Light Dart Are Launched Horizontally