Calculate the acceleration of the skateboard, the force of friction on the skate board and the coefficient of friction between the skateboard and the sidewalk?

Question

A 15 kg boy on a 3 kg skateboard coasts to a rest from a speed of 6.7m/s while traveling a distance of 26m on the sidewalk. Draw a free body diagram for this situation and calculate the acceleration of the skateboard, the force of friction on the skate board and the coefficient of friction between the skateboard and the sidewalk?

Answer 1

Use the following kinematic equation

v_f² = v₀² + 2a(Δx)

v_f = final velocity = 0 m/s

v₀ = initial velocity = 6.7 m/s

Δx = displacement = 26 m

(v_f² - v₀²)/2(Δx) = a

a = -0.86 m/s²

Now, let's find the friction force.

F = ma

F = (15+3)(0.86)

F = 15.48 N

coefficient of friction.

F_f = μF_N

F_f = 15.48 N

F_N = mg = (15+3)(9.8) = 176.4 N

μ = 0.09