Question

A light horizontal spring has a spring constant of 107 N/m. A 3.08 kg block is pressed against one end of the spring, compressing the spring 0.107 m. After the block is released, the block moves 0.226 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

To find the coefficient of kinetic friction between the horizontal surface and the block, we can use the equation: Frictional force = coefficient of friction × normal force.

Step-by-step explanation:

To find the coefficient of kinetic friction between the horizontal surface and the block, we first need to determine the net force acting on the block. The net force is equal to the force of friction, which can be calculated using the formula:

Frictional force = coefficient of friction × normal force

Since the block is coming to rest, we know that the net force is equal to zero. Therefore, we can set up the equation:

Frictional force = 0

By substituting the given values, we can solve for the coefficient of kinetic friction.

Answer 2

Given Information:

mass of block = m = 3.08 kg

spring constant = k = 107 N/m

compression length = x = 0.107 m

distance traveled after release = d = 0.226 m

Required Information:

coefficient of kinetic friction = μ = ?

Answer:

coefficient of kinetic friction = 0.089

Step-by-step explanation:

We know that work done against the friction is given by

W = Fd

W = μmgd

Where μ is the coefficient of kinetic friction, m is the mass of block and d is the distance traveled by block after it was released.

We know that potential energy stored in the spring is given by

U = ½kx²

Where k is the spring constant and x is the compression length

From the principle of work energy theorem,

W = U

μmgd = ½kx²

μ = kx²/2mgd

Put the given values into the above equation

μ = 107*0.107²/2*3.08*9.81*0.226

μ = 0.089

Therefore, the coefficient of kinetic friction between the horizontal surface and the block is 0.089.