Question

A block with an initial velocity of 3 m/s slides 9 m across a rough horizontal surface before coming to rest. What is the coefficient of kinetic friction? Use g = 10 m/s².

A) 0.2
B) 0.3
C) 0.4
D) 0.5

Answer 1

The coefficient of kinetic friction is calculated using the work-energy principle and the given values for initial velocity, distance, and acceleration due to gravity. However, the calculated result (0.15) does not match any of the provided options.

Step-by-step explanation:

To find the coefficient of kinetic friction (μk), we can use the equation that arises from the work-energy principle:

Kinetic friction does negative work and reduces the kinetic energy of the block to zero. The work done by friction is equal to the frictional force times the distance (W = Ff × d). Also, the kinetic energy lost is equal to the initial kinetic energy of the block (KE = ½mv2). Equating the two gives us Ff × d = ½mv2.

The frictional force (Ff) is the product of the normal force (mg, because the surface is horizontal and there's no vertical acceleration) and the coefficient of kinetic friction (μk), thus Ff = μk × mg.

Substituting into the equation, we get μk × mg × d = ½mv2, which simplifies to μk = ½v2 / (gd).

Plugging in the values from the question (v = 3 m/s, g = 10 m/s2, d = 9 m), we calculate the coefficient of kinetic friction to be μk = (0.5 × (3 m/s)2) / (10 m/s2 × 9 m) = 0.15.

However, this result is not listed among the provided options A to D. There might be a mistake in the given options or in the interpretation of the question.