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:

what is the speed of a softball that travels 20m in 2secs

speed = 20/2 = 10 m/s

the small 0.38-kg slider is known to move from position a to position b along the vertical-plane slot. determine (a) the work done on the body by its weight and (b) the work done on the body by the spring. the distance r = 0.70 m, the spring modulus k = 154 n/m, and the unstretched length of the spring is 0.53 m

explanation:

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