Question

A child pulls a 15kg sled containing a 5.0kg dog along a straight path on a horizontal surface. He exerts a force of 55N on the sled at an angle of 20° above the horizontal, as shown in the figure. The coefficient of friction between the sled and the surface is 0.22. 

a. On the dot below that represents the sled-dog system, draw and label a free-body diagram for the system as it is pulled along the surface.

b. Calculate the normal force of the surface on the system. 

c. Calculate the acceleration of the system. 

d. At some later time, the dog rolls off the side of the sled. The child continues to pull with the same force. On the axes below, sketch a graph of speed v versus time t for the sled. Include both the sled's travel with and without the dog on the sled. Clearly indicate with the symbol t_r the time at which the dog rolls off.

Answer 1

b. ΣFy = 0; N + Tsinθ – mg = 0 gives N = mg – T sinθ = 177N

c. f = µN = 38.9N and ΣF_x = ma; Tcosθ – f = ma yields a = 0.64m/s²