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A 0.45 kg mass sliding on a horizontal frictionless surface is attached to one e

ID: 1595252 • Letter: A

Question

A 0.45 kg mass sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (with k = 750 N/m) whose other end is fixed. The mass has a kinetic energy of 11.0 J as it passes through its equilibrium position (the point at which the spring force is zero).

At what rate is the spring doing work on the mass as the mass passes through its equilibrium position?

At what rate is the spring doing work on the mass when the spring is compressed 0.086 m and the mass is moving away from the equilibrium position?

Explanation / Answer

from the fiven question

mass=m =0.45kg

spring constant=k= 750N/m

Kinetic energy at equilibrium position= 11 J

as the mass passes through its equilibrium position, it is not compressed. so rate of work done is zero.

when spring is compressed by 0.086m,

by conservation of energy

1/2 m u2 = 1/2 kx2 + 1/2 mv2

11.0= 1/2 (750) ( 0.086)2 + 1.2 (0.45)(v2)

v2=36.56

v=6.04 m/s

rate of woek done = powwr= force * velocity

=k*x *v

=750 * 0.086 * 6.04 W

=389.58 W