Question

A mass m=15.0 kg is pulled along a horizontal floor, with a coefficient of kinetic friction μk =0.06, for a distance d=8.5 m. Then the mass is continued to be pulled up a frictionless incline that makes an angle θ=35.0° with the horizontal. The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of θ=35.0° (thus on the incline it is parallel to the surface) and has a tension T=45.0 N.1) What is the work done by tension before the block gets to the incline?2) What is the work done by friction as the block slides on the flat horizontal surface?

Answer 1

1. The work done by tension before the block gets to the incline is 382.5 J.

2. The work done by friction as the block slides on the flat horizontal surface is -69.6 J.

When the block is on the horizontal surface, the only forces acting on it are the tension in the rope and friction. The tension pulls the block forward, while friction opposes its motion. The work done by tension is positive, since it is in the direction of the block's motion. The work done by friction is negative, since it is in the opposite direction of the block's motion.

Part 1: Before the block gets to the incline, the only force acting on it is the tension in the rope. The work done by tension is given by:

W_t = Td = 45.0 N * 8.5 m = 382.5 J

Part 2: The work done by friction is given by:

W_f = -μ_k FN

where F_N is the normal force on the block. The normal force is equal to the weight of the block, mg, since the block is not accelerating vertically. Therefore:

W_f = -μ_k mgd = -0.06 * 15.0 kg * 9.81 m/s^2 * 8.5 m = -69.6 J

Answer 2

Base on your question where as a mass m is 15kg is pulled along a horizontal floor, with a coefficient of kinetic friction 0.06 and for a distance of D = 8.5 so the ask of the problem is to calculate the work done by tension before the bock. Base on my calculation and through step by step procedure and with the guidance of the theories and by the use of formulas, I came up with an answer of 313 joules.