AP Physics 1 FRQ: Pulling a sled across snow

Mathematical Routines, 10 pointsAbout 22 minutes · 10 points

A student pulls a sled of mass m across level snow with a rope. The rope makes a constant angle θ above the horizontal and exerts a force of constant magnitude F_T on the sled, as shown. The coefficient of kinetic friction between the sled and the snow is μₖ. The sled stays in contact with the snow and speeds up as it moves to the right.

(A) (i) Describe a free-body diagram of the sled as it moves. For each force, give its direction and a label that names it, and say how the lengths of the vertical forces compare. (ii) Starting from Newton's second law, derive an expression for the magnitude a of the sled's acceleration in terms of m, F_T, θ, μₖ and physical constants, as appropriate. 6 points

(B) The sled has a mass of 12 kg, the rope pulls with 50 N at 30° above the horizontal, and μₖ = 0.15. Calculate the magnitude of the sled's acceleration. 2 points

(C) The sled is loaded with snow until its total mass is twice as large, 24 kg. The same rope pulls with the same 50 N force at the same 30° angle on the same snow. Will the acceleration of the heavier sled be greater than half, equal to half, or less than half of the value in part B? Justify your answer without calculating a new value. 2 points