Question

A small object of mass M is shot horizontally from a spring launcher that is attached to a table. All frictional forces are considered to be negligible. The ball
strikes the ground a distance D from the base of the table, as shown in the figure. A second object of mass is launched from the same launcher such that
the spring is compressed the same distance as in the original scenario. The distance from the base of the table that the object lands is
А
greater than but less than D
B
D
greater than D but less than 2D
greater than or equal to 2D.

Answer 1

Answer:

  C.  greater than D, but less than 2D

Explanation:

The amount of potential energy in the system is a function of the compression of the spring. That is the same for both masses.

The potential energy is transferred to kinetic energy when the spring is released. The kinetic energy is jointly proportional to the mass and the square of the velocity. That is, the velocity is inversely proportional to the square root of the mass, for the same kinetic energy.

The horizontal distance traveled will be proportional to the launch velocity. So a halving of the mass will increase the velocity by a factor of ...

  v2 = v1·√(1/(1/2)) = v1·√2

This means the second mass will land at a distance of about D√2, a value ...

  greater than D but less than 2D.