A ball of mass m = 1.90 kg is released from rest at a height h = 67.0 cm above a

Question

A ball of mass m = 1.90 kg is released from rest at a height h = 67.0 cm above a light vertical spring of force constant k as in Figure [a] shown below. The ball strikes the top of the spring and compresses it a distance d = 7.60 cm as in Figure [b] shown below. Neglecting any energy losses during the collision, find the following. Find the speed of the ball just as it touches the spring. Find the force constant of the spring. Your response differs significantly from the correct answer. Rework your solution from the beginning and check step carefully. kN/m

Explanation / Answer

a) Using the kinematic equation v² = u² + 2gh (initial vel u = 0)
v = (2 x 9.80 x 0.67m) =======> v = 3.62 m/s

b) At max compression (d=0.076 m) the total GPE lost = Elastic PE gained (KE = 0)
mgH = ½ke² .. (H = 0.67+0.076 = 0.746 m)
k = 2mgH / e²
k = (2 x 1.90kg x 9.80 x 0.746m)/(0.076m)² =======> k = 4809.74 N/m

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