Question

A skier is pulled by a tow rope up a frictionless ski slope that makes an angle of 7.0° with the horizontal. The rope moves parallel to the slope with a constant speed of 1.4 m/s. The force of the rope does 750 J of work on the skier as the skier moves a distance of 3.5 m up the incline. (a) If the rope moved with a constant speed of 2.1 m/s, how much work would the force of the rope do on the skier as the skier moved a distance of 3.5 m up the incline?

Answer 1

From the given data, we have:

- Initial Speed = 1.4 m/s
- Initial Work = 750 J
- Distance = 3.5 m
- New Speed = 2.1 m/s

Our aim is to find the New Work done when the Speed of the rope changes.

According to the problem, the Work done is proportional to the speed of the rope. The Work done by a force on an object is equal to the product of the force and the distance. As the Force exerted by the rope, the Distance, and Angle of the slope are all constants, the equation that represents the relation between Work done and speed of movement can be written as:

Work_initial / Speed_initial = Work_new / Speed_new

This setup allows us to solve for the new Work ('Work_new') done by the Force. By multiplying both sides of this equation by Speed_new, we can isolate 'Work_new'. This computation lets us determine how much work would be done at the new speed.

So, moving things around, we get the following equation to solve for the new work done:

Work_new = (Work_initial / Speed_initial) * Speed_new

Substituting the given values, we get:

Work_new = (750 J / 1.4 m/s) * 2.1 m/s = 1125 J

So, if the rope moved with a constant speed of 2.1 m/s, the work done by the Force of the rope on the skier as the skier moved a distance of 3.5 m up the incline would be 1125 Joules.