Work Done by Gravity on 265kg Load: 6.24x10^4 J

[PeachBanana]

Homework Statement

A 265-kg load is lifted 24.0 m vertically with an acceleration =0.190 g by a single cable.

Determine the work done by gravity on the load.

Homework Equations

Force of Gravity = mg
W = F * d * cos (theta)

The Attempt at a Solution

I think I know why I did this incorrectly but I want to make sure.

First attempt: Force gravity = (265 kg)(9.8 m/s^2) = 2.6 * 10^3 N.
W = (2.6 x 10^3 N) (24.0 m) * cos (0°)
W = 6.24 x 10^4 J.

The correct answer is the same magnitude but the opposite sign. Is that because the angle should have been 180° because gravity always points down? The displacement is up so therefore the angle between the net force and the displacement would have been 180°, not 0°?

 

[SammyS]

Homework Statement

A 265-kg load is lifted 24.0 m vertically with an acceleration =0.190 g by a single cable.

Determine the work done by gravity on the load.

Homework Equations

Force of Gravity = mg
W = F * d * cos (theta)

The Attempt at a Solution

I think I know why I did this incorrectly but I want to make sure.

First attempt: Force gravity = (265 kg)(9.8 m/s^2) = 2.6 * 10^3 N.
W = (2.6 x 10^3 N) (24.0 m) * cos (0°)
W = 6.24 x 10^4 J.

The correct answer is the same magnitude but the opposite sign. Is that because the angle should have been 180° because gravity always points down? The displacement is up so therefore the angle between the net force and the displacement would have been 180°, not 0°?

That looks fine. What's your question?

 

[PeachBanana]

I did it incorrectly the first time but I wanted to make sure I knew why it was wrong.

 

[Ericv_91]

Yes, if your displacement is in the positive direction, then in this case gravity must be in the opposite direction (180 degrees from positive direction).

 

[asteriatic]

Yes, you are correct. The angle should be 180° because gravity always acts in the opposite direction of the displacement. Therefore, the work done by gravity in this situation would be -6.24x10^4 J, indicating that gravity is doing negative work on the load as it is being lifted. This is because the force of gravity is acting in the opposite direction of the displacement, resulting in the negative sign in the work equation. It is important to pay attention to the direction of forces and displacement when calculating work done by a force.