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
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.
