A block of mass is attached to the lower end of a light vertical spring of force constant

PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

A block of mass

m

is attached to the lower end of a light vertical spring of force constant

k

. The upper end of the spring is fixed. The block is pulled down to compress the spring by a distance

x_{0}

and released from rest. Throughout the motion, neglect air resistance. (i) Derive an expression for the speed

v

of the block when the spring is compressed by a general distance

x

(0\le x\le x_{0})

during its upward motion. (ii) Using your expression, obtain the maximum speed attained by the block during the subsequent oscillation. (iii) Evaluate the speed when

x = 0.020\,\text{m}

for

m = 0.40\,\text{kg}

k = 150\,\text{N\,m}^{-1}

and

x_{0} = 0.050\,\text{m}

. Express your answer correct to two significant figures.

Related theory

Simple Harmonic Motion (SHM)
Potential Energy
Work done on a spring and elastic potential energy
Work, Energy and Power
Simple harmonic motion
Potential energy of a spring
Oscillations

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