University:
Boston University
Course:
CAS PY 521 | Electromagnetic Theory I
Academic year:

2023
Views:

216

Pages:

2
Author:

Lafuentedqri

Physics Challenge Question 8: Solutions Part 1 The trailer is not moving, so the forces acting on it must sum to 0, by Newton’s first law. The only forces acting on it are gravity and the ground’s normal force. FN = mg Fg = mg Part 2 The free-body diagram is the same as before with two new forces added to it. The net force is no longer 0. FN = mg Ff Fpull Fg = mg Part 3 Looking at our free-body diagram from the previous part, we see that the vertical forces cancel. (The trailer is not accelerating into the ground or off the Earth!) So let’s write down Newton’s second law for the horizontal direction: ma = F pull + F f m= 7,000 N − 1,000 N 6,000 kg = 2,000kg = 3 3 sm2 Since the rope broke, the trailer must have had a mass of at least 2,000 kg. (We used 7,000 N in our calculations, because that was the smallest force that could break the rope. We don’t know for sure that it wasn’t in fact larger!) Part 4 The vertical forces (gravity and the normal force) still cancel. Note that the 2,000 N is the net force, i.e. the force of the pulling minus friction. As the wind pushes it sideways, we can draw the following free-body diagram, now viewed from above: Fwind = ? Fnet = 2,500 N Fpull = 2,000 N Since these two forces are pointing in different directions (one is left/right, and the other is forward/backward), we have to be careful when adding them. Since they form a right-angled triangle, let’s use the Pythagorean theorem: 2 2 2 Fnet = Fwind + F pull 2 2 Fwind = Fnet − F pull = (2,500 N ) 2 + (2,000 N ) 2 = 1,500 N