How Much Work Does a Child Do Pulling a Toboggan Up a Hill?

[x86]

Homework Statement

A 25.6 kg child pulls a 4.81kg toboggan up a hill inclined at 25.7 degrees to the horizontal. The vertical height of the hill is 27.3 m. Friction is negligible.

Determine the amount of work the child must do on the toboggan to pull it at a constant velocity up the hill.

Homework Equations

W = F * D

The Attempt at a Solution

ag = gravity component of acceleration
ap = acceleration applied

ag - ap = 0
ag = 9.81 m/s^2 * cos(25.7 deg) = 8.8 m/s/s

F = 8.8 m/s/s * 4.81 kg = 42.5 N

W = F * D = 42.5 N * (27.3 m / (sin(25.8 deg)) = 2 665.82513 joules

This answer is completely wrong. The book got 1.3 * 10 ^ 3 J.

Not sure what I can do, I thought about setting W = Eg2 - Eg1. But I remember my teacher said that only works for kinetic energy (honestly, sometimes I think she doesn't know what she's talking about. It should work for gravitational energy too)

But if I do that,

W = 4.8 kg * 9.8 m/s^2 * 27.3 m I get the right answer which is 1 284.192 joules

This is confusing for me. Shouldn't I have gotten the same answers for both questions? How come my answers are different? Does it have something to do with vectors? Does work only count in one direction in this case (vertical), shouldn't the work done be how I calculated it in step 1?

More importantly, can I set W = change in energy, even if that energy is NOT kinetic?

 

[Dewgale]

Both methods would work. Your math is off in the first one, though: It should be sin(25.7°), not cos(25.7°). You're looking for the parallel part of a_g, not the perpindicular part.

 

[PhanthomJay]

More importantly, can I set W = change in energy, even if that energy is NOT kinetic?

you may have misunderstood your teacher. The TOTAL work done by ALL forces is equal to the change in kinetic energy. This includes work done by conservative forces (like gravity) and non conservative forces (like applied forces). The work done by only nonconservative forces is equal to the change in kinetic plus potential energy.