A 1.6 k g box moves back and forth on a horizontal frictionless surface between

Question

A 1.6kg box moves back and forth on a horizontal frictionless surface between two different springs, as shown in the accompanying figure. The box is initially pressed against the stronger spring, compressing it 4.1cm , and then is released from rest.

box moves back and forth on a horizontal frictionless surface between two different springs, as shown in the accompanying figure. The box is initially pressed against the stronger spring, compressing it 4.1cm , and then is released from rest. By how much will the box compress the weaker spring? Express your answer using two significant figures. =?cm What is the maximum speed the box will reach? Express your answer using two significant figures. = ?m/s

Explanation / Answer

a)

Spring potential energy = 0.5 x k x X^2

Conservation of Spring potential energy,

0.5 x 32 x 0.041^2 = 0.5 x 16 x X^2

X = 0.057 m

= 5.7 cm.

b)

0.5 x k x X^2 = 0.5 x m x v^2

v^2 = 32 x 0.041^2 / 1.6

v = 0.183 m/s

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