Any device that allows you to increase the force you exert is a kind of machine.

Question

Any device that allows you to increase the force you exert is a kind of machine. Some machines, such as the pry bar or the inclined plane, are very simple. Some machines do not even look like machines. An example is the following. Your car is stuck in the mud, and you can't pull hard enough to get it out. However, you have a long cable which 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 force f. Each half of the cable is displaced through a small angle theta from the straight line between the ends of the cable. Show that the force exerted on the car is given by F = f / 2 sin theta.

Explanation / Answer

Here ,

as the angle of cable is theta

at the midpoint of the cable ,

balancing forces in the direction of force applied by person

F * sin(theta) + F * sin(theta) = f

F = f/(2 * sin(theta))

the force exerted on the car is f/(2 * sin(theta))

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