A person would like to pull a car out of a ditch. This person ties one end of a chain to the car's bumper and wraps the other end around a tree so that the chain is taut. The person then pulls on the chain perpendicular to its length. If the distance between the car and tree is 5.0 m and the length of the chain between the car and the tree is 5.2 m and the person can pull with 100LB of force, what force can the chain exert on the car?
The Attempt at a Solution
Let d_1, d_2 be 5.0 m and 5.2 m respectively. Let F_1 be 100 LB.
Draw a pair of congruent triangles by connecting a line from the person to the ground. This gives two right triangles with base (1/2)d_1 and hypotenuse (1/2)d_2. You can calculate the angle between the base and hypotenuse to be about 15.94 degrees which we may call theta. Then F_T = csc(theta) * F_1 = 364 N. The book gets about half of that at 180 N.