Question

A light horizontal spring has a spring constant of 138 N/m. A 3.85 kg block is pressed against one end of the spring, compressing the spring 0.103 m. After the block is released, the block moves 0.290 m to the right before coming to rest. The acceleration of gravity is 9.81 m/s 2 . What is the coefficient of kinetic friction between the horizontal surface and the block?

Answer 1

0.06683

Step-by-step explanation:

m = Mass of block = 3.85 kg

g = Acceleration due to gravity = 9.81 m/s²

`\mu` = Coefficient of kinetic friction

x = Compression of spring = 0.103 m

k = Spring constant = 138 N/m

Work done against friction is given by

`W=m\mu gs\\\Rightarrow W=\mu 3.85* 9.81* 0.29\\\Rightarrow W=10.952865\mu`

The potential energy of the spring is given by

`P=(1)/(2)kx^2\\\Rightarrow P=(1)/(2)* 138* 0.103^2\\\Rightarrow P=0.732021\ J`

The potential energy and the work done against friction will balance the system

`0.732021=10.952865\mu\\\Rightarrow \mu=(0.732021)/(10.952865)\\\Rightarrow \mu=0.06683`

The coefficient of kinetic friction between the horizontal surface and the block is 0.06683