A block of mass m is dropped onto a relaxed vertical spring with spring constant

Question

A block of mass m is dropped onto a relaxed vertical spring with spring constant k (see the figure). The block becomes attached to the spring and compresses the spring a distance d before momentarily stopping. While the spring is being compressed, what work is done on the block by (a) the gravitational force on it and (b) the spring force? (c) What is the speed of the block just before it hits the spring? (Assume that friction is negligible.) State your answers in terms of the given variables and g.

Explanation / Answer

a) W_gravity = -m*g*d

b) W_spring = -0.5*k*d^2

c) let v is the speed of the block just before hitting the spring.

now use work-energy throem

net workdone = change in kinetic energy

W_gravity + W_spring = Kf - Ki

-m*g*d - 0.5*k*d^2 = 0 - 0.5*m*v^2

m*g*d + 0.5*k*d^2 = 0.5*m*v^2

v^2 = 2*g*d + k*d^2/m

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

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