[3.] A vertical spring with constant k is compressed a distance L and a ball wit

Question

[3.] A vertical spring with constant k is compressed a distance L and a ball with mass M is set on top of it. When the spring is released, the ball is fired upward a) Find the speed v of the ball when it leaves the spring b) Find the maximum height h above the uncompressed position of the spring reached c) If the spring constant is too small, the ball never leaves the spring. Find the minimum Show your work. Write your answers in terms of k, L, M, and g. Check units/dimensions by the ball value of the constant k for the ball to leave the spring. for each answer. HINT: don't forget gravity and place your origin at the uncompressed spring position.

Explanation / Answer

a) PE of the spring = 0.5*k*L^2

when mass leaves the spring PE will convert in to KE of mass

=> o.5*k*L^2 = 0.5*M*V^2

=> V = L(k/M)^0.5 m/s

b) max height reached

KE will convert in to gravitational PE= mgh

=> 0.5MV^2 = MgH

=> H = 0.5*V^2/g = 0.5*kL^2/Mg

so from uncompressed position max height reached = kL^2/(2Mg) - L

c) for minimum spring constant

kL = Mg

=> k = Mg/L

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