Magnus has reached the finals of a strength competition. in the first round, he has to pull a city bus as far as he can. one end of a rope is attached to the bus and the other is tied around magnus's waist. if a force gauge placed halfway down the rope reads out a constant 2.500×10^3 newtons while magnus pulls the bus a distance of 2.312.31 meters, how much work does the tension force do on magnus? the rope is perfectly horizontal during the pull.

The total work that the rope does to Mangnus is - 5780 Jules.

Explanation:

By definition, the work is defined as:

Where F and d are the force and the total displacement. Note that in the definition the product is a scalar product since F and d are both vectors.  

Take into account that according to third Newton's law the force that the rope does to Magnus is opposite to the force that Magnus does to the rope, therefore the scalar product will be negative due the rope's force goes against to Magnus displacement.  

For calculating the work, we take 2500 N as the value for the force and 2.312 meters as the value for the displacement:

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west