Question

A mass of 2.1 kilograms is placed at height 0.3 meters above the dotted line above on a planar surface inclined at an angle of 30 degrees to the horizontal. The coefficient of kinetic friction between the mass and the inclined portion of the surface is 0.32. The mass is released, slides down the incline and compresses a spring with spring constant 900.1 N/m. What is the largest compression in meters experienced by this spring?

Answer 1

here,

mass ,m = 2.1 kg

height , h = 0.3 m

theta = 30 degree

the coefficient of kinetic friction , uk = 0.32

spring constant , K = 900.1 N/m

let the largest compression experienced by the
spring be x

using Work -energy theorm

work done by friction + Work done by conservative force = 0

- uk * m * g * cos(theta) * (h/sin(theta)) = 0.5 * K * x^2 - m * g * h

- 0.32 * 2.1 * 9.81 * cos(30) * ( 0.3 /sin(30)) = 0.5 * 900.1 * x^2 - 2.1 * 9.81 * 0.3

solving for x

x = 7.82 * 10^-2 m

the largest compression experienced by the
spring is 7.82 * 10^-2 m