4.1.2.P20

Little Nathan’s dad has hooked together two boxes with ropes to make a train for him as shown in the picture. Nathan has put one of his twin sisters in each box and is pulling them along the rug as shown.

(a) Draw a system schema for considering the problem of the motion of the two boxes.

(b) If Nathan is pulling on rope 1 (the one he's holding) with a constant force T and the boxes are moving draw free body diagrams for each of the boxes, identify all the forces on it, being sure to specify the kind of force each one is and what object is exerting it.

(c) Draw a free-body diagram for rope 2 (the one connecting the two boxes). Assume the rope is very light so that you can ignore its weight.

(d) For the first 5 seconds (t = 0s to 5s), Nathan is pulling his train with a constant force so it is slowly speeding up. If any of the forces in your three diagrams are equal, identify them and say how you know.

(e) For the next 10 seconds (t = 5s to 15s), Nathan is pulling his train with a constant force so it is moving at a constant speed. If any of the forces in your three diagrams are equal, identify them and say how you know.

(f) Sketch graphs of the following variables for the time from 0s to 15s being careful to indicate when the graph is straight (horizontal or at an angle) and to show at what times changes in the graph take place. Take the starting position of box A as the origin and the direction of motion as positive.

• Position of box A
• Velocity of box A
• Acceleration of box A
• Net force on box A
• Force of friction between the floor and box A 
• Magnitude of the force T exerted on box A by rope 1

Joe Redish 8/26/15