Gravitational Potential Energy of a skateboard

[galtspeaking]

Homework Statement

[PLAIN]https://dl.dropbox.com/u/9215647/webassign%20s.JPG

Rank the slopes (greatest first) according to the work done on the skater by the gravitational force during the descent on each slope,

Homework Equations

work=change in potential energy, ie. delta U = mg*(delta)h

The Attempt at a Solution

since potential energy is greatest at slope 1, shouldn't the rank be 1,2,3? but that is wrong..what am I doing wrong in this question then?

 

[SammyS]

The change in height is the same for all three slopes. What does that tell you about the change in potential for each?

 

[galtspeaking]

ah, I see..so they are all the same, b/c mgh is the same for all of them,

i was considering the total hight each of the slopes from the origin, i think that's where i was wrong

 

[SammyS]

Correct!

 

[rwisz]

Your attempt at a solution is partially correct. The potential energy of the skateboard is indeed greatest at slope 1, but the question is asking about the work done on the skater by the gravitational force during the descent on each slope. This means that we need to consider the change in potential energy as the skater moves down the slope, not just the potential energy at the bottom of the slope.

To determine the work done on the skater by the gravitational force, we can use the equation W = ΔU = mgh, where m is the mass of the skater, g is the acceleration due to gravity, and h is the change in height (or the height of the slope).

Since the skater is moving down the slope, the change in height will be negative. This means that the work done on the skater will also be negative, indicating that the gravitational force is doing work to decrease the skater's potential energy.

So, the rank of the slopes in terms of the work done on the skater by the gravitational force during the descent will be 3, 2, 1. This is because the change in potential energy is greatest at slope 3 (the steepest slope), followed by slope 2, and then slope 1 (the least steep slope). This means that the work done by the gravitational force will also be greatest at slope 3, followed by slope 2, and then slope 1.