Esther has put her puppy, Molly, on a skateboard, and has attached a rope to the skateboard in order to give Molly a ride. At time t = 0, Esther starts pulling on the rope. She is pulling upward at an angle of 37^o. Once she is up to speed (at time t₁), she runs along at a constant rate until a time t₂. A little after that, her mother yells at her and she stops.

While Esther is pulling, draw a system schema and free-body diagrams for Molly and the skateboard that will allow you to identify the forces that each of them will feel. We will label the forces so as to identify the kind of force (normal = N, tension = T, friction = f, and weight = W) and the actors (the one feeling the force and the one causing it: Esther = E, Skateboard = S, Molly = M, the rope = R). You can ignore the sliding friction between the skateboard wheels and the floor.

(a) Given that we are viewing Esther and Molly so that Esther is pulling the rope and moving to the left, in which direction do the following forces point? Use the compass rose at the right to specify directions or choose "0" if the force is zero.

(a₁) f_S→M; (a₂) T_R→S; (a₃) f_M→S; (a₄)N_M→S

(b₁) While Esther is speeding up, what is the direction of the net force that is acting on the skateboard?

Photo courtesy Nikki Bass (with permission)

(b₂)  While Esther is running at a constant speed,, what is the direction of the net force that is acting on the skateboard?

(c) Molly weighs 20 lbs, the skateboard weighs 3 lbs, and Esther gets the skateboard up to a speed of 2 m/s after a time of 3 s and keeps running for another 3 s. Do you have enough information to figure out the force that Esther exerts between 0 and t₁? Between t₁ and t₂? If you don't explain what additional information you need. If your answer was yes, calculate both forces in Newtons (give 3 significant figures).