A car stuck in a mudhole. in order to move the car, the driverattaches one end o

Question

A car stuck in a mudhole. in order to move the car, the driverattaches one end of a rope to the car and the other end to a tree10m away, strecthing the rpoe as much as possible. the driver thenapplies a horizontal force of 4.00 X 10^2N perpendicular to therope at its midpoint. The rope streches, with its center pointmoving 50cm to the side as a result of the applied force. the carbegins to move slowly. what is the tension in the rope?

I understand how to find the tension of both sides of the ropewithout the car moving, but i'm unsure how the 50cm shift in centerpoint affects the problem.

Explanation / Answer

If the rope did not stretch (remained in a straight line) thetension would be infinite due to the applied force sin = .5 / 5 = .1 F = 2 T sin          thesideways component(s) of the tension equals the applied force T = F / ( 2 sin ) = 400 / (2 * .1) = 2000 N (afterthe rope has stretched .5 m

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