Question

You are planning to build a log cabin and will need to pull the logs up a hill to the building site by means of a rope attached to a winch. In order to buy the rope, you need to know how strong the rope must be and decide to do a quick calculation for this. The logs weigh 500 lbs at most, and the hill is at an angle of 30 degrees with respect to the horizontal. You estimate that the coefficient of kinetic friction between a log and the hill is 0.9. When pulling a log up the hill, you will make sure that the rope stays parallel to the surface of the hill and the acceleration of the log is never more than 0.8 m/s/s

Answer 1

Consider the free body diagram of the log.
the sin component of mg would be acting downwards and so will be the friction , The only force in the upwards direction that is , towards you is the Tension
So T - {mgsin (Theta) + Friction} = ma

The normal would be equal to cos component of mg
So N = mgcos(theta)
Friction = coefficient of dynamic friction * Normal

Friction = 0.9* 500*9.8*cos(30) = 3819.2N

And mgsin(theta) = 500*9.8*sin(30) = 2450 N

So T -{ 6269.2} = 500 *a

Tension will be max when a will be max = 0.8m/sec²

T -{6269.2 } = 500 * 0.8
T = 6669.2Newton ==> Max Tension