Question

(b) (3 points) A ball of mass m is attached to a spring (with unstretched length lo and spring constant k) which hangs vertically. The ball is initially held at rest with the spring at its unstretched length. Then, the ball is let go. Consider the instant when the ball reaches its lowest position (the spring stretches to its maximum length and s instantaneously at rest), I was done by the spring force during this process (that is from release until ball is at lowest point)? 2k

Answer 1

Concept : here initial and final kinetic energy is zero, so we use the work energy principle and the net work done is zero. We use this find to find maximum extension and hence work done by the spring,

Let the spring stretches by x when ball is at lowest position, then w_spring + w_gravity = delta kE initial and final kE = 0, so, delta kE = 0 so, w_spring + w_gravity = 0 or, minus 1/2 kx^2 + mgx = 0 or, x = 2 mg/k so, w_spring = minus 1/2 kx^2 = minus 1/2 k (2 mg/k)^2 = minus 1/2 k 4 m^2 g^2/k^2 = minus 2 m^2 g^2/k

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