Question

Problem 11.56 A 4.5 kg box slides down a 4.3-m -high frictionless hill, starting from rest, across a 1.7-m -wide horizontal surface, then hits a horizontal spring with spring constant 550 N/m The other end of the spring is anchored against a wall. The ground under the spring is frictionless, but the 1.7-m-long horizontal surface is rough. The coefficient of kinetic friction of the box on this surface is 0.27.

Answer 1

Velocity at the bottom of the ramp

v1^2 = 2 g h1 = 2* 9.8* 4.3

v1 = 9.18 m/s

Now, the box comes in contact with horizontal frictional surface, so the fricitonal acceleration is given by

a = u g

Velocity just before hitting spring

v2^2 = v1^2 - 2 ad = 9.18^2 - 2* 0.27* 9.8* 1.7

v2 = 8.676 m/s

Using energy conservation

0.5 k A^2 = 0.5 m v2^2

550 A^2 = 4.5* 8.676^2

A = 0.7848 m

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