A ball of unknown mass m is tossed straight up with initial speed v. At the mome

Question

A ball of unknown mass m is tossed straight up with initial speed v. At the moment it is released, the ball is a height h above a spring-mounted platform, as shown in the figure below. The ball rises, peaks, and falls back toward the platform, ultimately compressing the spring a maximum distance d from its relaxed position. Assume that the spring is perfectly ideal with spring constant k, and that the mass of the spring and platform is negligible. What is the mass m, assuming that there is no friction or air resistance? Using g to represent the acceleration due to gravity, enter an expression for m in terms of g, h, d, k, and v.

Explanation / Answer

take gravitational potential energy is zero when spring is compressed maximum.

Apply conservation of energy

Initial mechaincal energy = final mechaincal energy

Initual kinetic energy + initial gravitational potentail energy = final elastic potentail energy

(1/2)*m*v^2 + m*g*(h+d) = 0.5*k*d^2

m*v^2 + 2*m*g*(h+d) = k*d^2

m*(v^2 + 2*g*(h+d) ) = k*d^2

m = k*d^2/(v^2 + 2*g*(h+d) )

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