A skier is pulled by a tow rope up a frictionless ski slope that makes an angel of 12 degree with the horizontal. The rope moves parallel to the slope with a constant speed of 1.0m/s. The force of the rope does 900J of work on the skier as the skier moves a distance of 8.0m up the incline. (a) If the rope moved with a constant speed of 2.0m/s, how much work would the force of the rope do on the skier as the skier moved a distance of 8.0 m up the incline? At what rate is the force of the rope doing work on the skier when the rope moves with a speed of (b)1.0m/s? and (c) 2.0m/s? Thanks.
Hello and thank you for posting your question to Brainmass.
Since energy must be conserved, all the work done by the rope must be converted into the potential energy gained by the skier.
The potential energy of the skier is
where m is the mass, g is the gravitational acceleration and h is the final height of the skier above the initial starting point.
As you can see, this value has nothing to do with the actual path (or speed) of the skier. as far as potential energy is concerned, the skier could have gone ...
The solution provided is a detailed explanation and step-by-step calculation for force a exerted on a skier who is being pulled by a rope up a frictionless ski slope.