An 8.0 kg object moving with an initial velocity of 8.0 m/s on a surface comes to rest due to friction after it travels a horizontal distance of 11 m. What is the coefficient of kinetic friction between the object and the surface? Use g = 10 m/s².

Question

Quizplus · Accepted Answer

The first step is to use the kinematic equation:

v^2 = u^2 + 2as

where v = final velocity (0 m/s), u = initial velocity (8.0 m/s), a = acceleration (unknown), and s = distance (11 m).

Solving for a:

a = (v^2 - u^2)/2s = (0 - 8.0^2)/2(11) = -3.28 m/s^2

The negative sign indicates that the acceleration is in the opposite direction of the initial velocity, due to friction.

The second step is to use Newton's second law:

F = ma

where F = force of friction and m = mass (8.0 kg). We can rearrange this to solve for the coefficient of kinetic friction, μk:

μk = F/m = (ma)/mg = a/g

Substituting in the value for a:

μk = (-3.28 m/s^2)/(-10 m/s^2) = 0.328

Therefore, the coefficient of kinetic friction is 0.328, which is closest to choice C (0.29).

An 80 Kg Object Moving with an Initial Velocity of 8