Work of Rope on Skier on 12° Incline: 900 J or 2,000 J?

[MIA6]

Homework Statement

A skier is pulled up by a towrope up a frictionless ski slope that makes an angle of 12 degrees with the horizontal. The rope moves parallel to the slope with a constant speed of 1.0 m/s. The force of the rope does 900 J of work on the skier as the skier moves a distance of 8m up the incline. If the rope moved with a constant speed of 2 m/s, how much work would the force of the rope do on the skier as the skier moved a distance of 8m up the incline?

Homework Equations

W=KE or W=KE+PE

The Attempt at a Solution

This is a rather conceptual problem in my opinion. So I know the work-kinetic energy theorem. change in K=W. However, my question is: Does it only apply to a system where there is only kinetic energy present or it can be applied to a system where both Kinetic energy and potential energy present. I didn't use K=W, I had W=KE+PE. KE is 0, so W=PE. Because in this case, clearly, there are both Kinetic energy and Potential energy (8m) on the skier. But my teacher still used change in K=W=0, and since the work includes the work from the rope and gravity, they must be same in magnitude and opposite in direction. I hope someone can clarify things for me. thanks.

 

[Pythagorean]

If you're carrying something up a hill, working against a force like gravity, your work is equal to the potential energy you have to overcome to move against the field. If you pushed something up a hill so hard that you increased the velocity of it, you'd have a kinetic term to add, because changing the velocity of something requires an acceleration (note that when you referenced your teacher you spoke of a change in velocity).

Remember Newton's First Law. It implies that keeping and object at a constant velocity does not require extra work theoretically (in the real world, we're constantly battling friction, so we have to put extra energy into things to keep them going).

 

[PhanthomJay]

Please be careful with your subscripts when takling about "Work". The Work-Energy theorem is W_{total} = W_{net} = \Delta KE, where
W_{total} = W_c + W_{nc}, and where W_c is the work done by conservative forces (like gravity), and W_{nc} is the work done by non-conservative forces (like friction or applied forces).
Now the general conservation of total energy principle can be written W_{nc} = \Delta KE + \Delta PE. You can use either formula, just be careful how you define your variables. The latter is a bit easier to work with in this case.

 

[MIA6]

Hi, Jay. So change in KE is the same as NET WORK. and the conservation of energy equation: W=change in KE+ change in PE that we often use is for W for non-conservative force like applied forces? Never realized this before. When I learned energy, I first learned change in KE equals to work, but then I learned W=KE+PE. So if there is PE in a problem, we can't just write W=change in KE, we have to include PE. According to you, if we don't have gravity, then W total=Wnc=change in KE? But if there is no gravitation, then there is no PE either?