A spring with spring constant 26 N/m is compressed a distance of 6.5 cm by a bal

Question

A spring with spring constant 26 N/m is compressed a distance of 6.5 cm by a ball with a mass of 213.5 g (see figure below). The bail is then released and rolls without slipping along a horizontal surface, leaving the spring at point A. The process is repeated, using a block instead, with a mass identical to that of the ball. The block compresses the spring by 6.5 cm and is also released, leaving the spring at point A. Each object travels up the incline shown in the figure before coming to rest momentarily. Assume the ball rolls, but ignore other effects of friction. (Assume the ball rolls without slipping up the incline until it comes to rest.) How high above the starting position is the ball when it comes to rest momentarily? How high above the starting position is the block when it comes to rest momentarily?

Explanation / Answer

here,

spring constant , k = 26 N/m

mass , m =0.2135 kg

distance compressed , x = 0.065 m

(a)

let the height achived by the ball be h

using conservation of energy

0.5 * k * x^2 = m * g * h

0.5 * 26 * 0.065^2 = 0.2135 * 9.8 * h

h = 0.026 m

(b)

let the height achived by the block be h

using conservation of energy

0.5 * k * x^2 = m * g * h

0.5 * 26 * 0.065^2 = 0.2135 * 9.8 * h

h = 0.026 m

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