A ball of unknown mass is tossed straight up with initial speed . At the moment it is released, the ball is a height ℎ above a spring-mounted platform, as shown in the figure. The ball rises, peaks, and falls back toward the platform, ultimately compressing the spring a maximum distance from its relaxed position. Assume that the spring is perfectly ideal, with spring constant , and that the mass of the spring and platform is negligible. What is the mass of the ball, , assuming that there is no friction or air resistance?

Using to represent the acceleration due to gravity, enter an expression for in terms of , ℎ , , , and .

The sum of the energy in a isolated system is always constant, according to the  Law of Conservation of Energy

Reason:

According to the Law of Conservation of Energy, we have;

Mechanical energy of ball = Elastic potential energy gained by spring

M.E. = P.E. + K.E. =

The initial potential energy of the ball relative to the compressed spring, P.E. is given as follows;

P.E. = m·g·(h + d)

Therefore, we get;

Which gives;

The expression for m in terms of g, h, d, k, and v is therefore;

Learn more about the Law of Conservation of Energy here:

Explanation:

wavelength divides in half and speed stays the same.

truck y has a greater velocity than truck x.