Chapter 4, Problem 43P

An object of mass M is held in place by an applied force $\stackrel{\to }{\text{F}}$ and a pulley system as shown in Figure P4.43. The pulleys are massless and frictionless. (a) Draw diagrams showing the forces on each pulley. Find (b) the tension in each section of rope, T₁, T₂, T₃, T₄, and T₅ and (c) the magnitude of $\stackrel{\to }{\text{F}}$.

Figure P4.43

44. Any device that allows you to increase the force you exert is a kind of machine. Some machines, such as the prybar or the inclined plane, are very simple. Some machines do not even look like machines. For example, your car is stuck in the mud and you can’t pull hard enough to get it out. You do, however, have a long cable that you connect taut between your front bumper and the trunk of a stout tree. You now pull sideways on the cable at its midpoint, exerting a force f. Each half of the cable is displaced through a small angle θ from the straight line between the ends of the cable. (a) Deduce an expression for the force acting on the car. (b) Evaluate the cable tension for the case where θ = 7.00° and f = 100 N.