Work-Energy Theorem: Determine Distance for 73kg Skier w/ 4.2m/s

[Physicsgeeks1]

Homework Statement

A 73kg skier coasts up a hill inclined at 9.3 degree's to the horizontal. Friction is negligible. Use work-energy theorm to determine how far along the hill the skier slides before stopping, if the intial speed at the bottom is 4.2m/s


To find the distance I know i need w=Force applied x distance, but I can't find out how to get Force applied? I also just used W=change in EK to find work but is that correct?

 

[Redbelly98]

Welcome to Physics Forums!

To find the distance I know i need w=Force applied x distance, but I can't find out how to get Force applied?

Try drawing a free-body diagram for the skier. What are the forces acting on the skier, and in what direction are they?

I also just used W=change in EK to find work but is that correct?

Yes, that is the idea.

 

[kerimek]

I would provide the following response:

The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. In this case, the skier's initial kinetic energy at the bottom of the hill is given by 1/2 * mass * initial velocity^2, or 1/2 * 73kg * (4.2m/s)^2 = 132.78 Joules. The skier's final kinetic energy at the top of the hill is zero, since they have come to a stop. Therefore, the work done on the skier is equal to the change in kinetic energy, or 132.78 Joules.

To find the distance the skier slides, we can use the work-energy equation: Work = Force * Distance. In this case, the work done on the skier is equal to the force of gravity (mg) multiplied by the distance the skier slides up the hill (d). We can set this equal to the work calculated above (132.78 Joules) and solve for d:

132.78 Joules = (73kg)(9.8m/s^2)(sin(9.3 degrees)) * d

Solving for d, we get d = 18.3 meters. This means that the skier slides 18.3 meters up the hill before coming to a stop.

It is important to note that the work-energy theorem assumes that there are no external forces acting on the object, such as friction. Since friction is negligible in this scenario, we can use this theorem to accurately determine the distance the skier slides. However, if friction was not negligible, we would need to take it into account in our calculations.