A sled of mass 10 kg starts out at an initial speed of 5 m/s on a horizontal surface.The coefficient of kinetic friction with the snow is 0.05.How far does it go before it comes to a stop (within 5% accuracy)?
A)25 m
B)50 m
C)320 m
D)640 m
E)1280 m

Question

Quizplus · Accepted Answer

The sled stops due to the work done against friction. The force of friction (F_friction) is given by μN, where μ is the coefficient of kinetic friction and N is the normal force. On a horizontal surface, N equals the weight of the sled, mg. Thus, F_friction = μmg. The work done by friction (W) equals the force of friction times the distance (d), and it also equals the change in kinetic energy, which is 1/2 m v^2 (where v is the initial velocity). Setting these equal gives us μmgd = 1/2 m v^2. Solving for d gives d = v^2 / (2μg). Substituting the given values (v = 5 m/s, μ = 0.05, g = 9.8 m/s^2) yields d ≈ 25.5 m, which is within 5% accuracy of choice A, 25 m.

A Sled of Mass 10 Kg Starts Out at an Initial