# A 337kg crate needs to be lifted to a height of 2.3m using a ramp that is 7.6m long. If a force of 1408N is used to push the crate up the ramp, what is the work done on the crate?

May 10, 2018

$\text{work done on the crate} = 7596 J$

#### Explanation:

Since 1408 N was applied over the 7.6m length of the ramp, the work done was
$F \cdot d = 1408 N \cdot 7.6 m = 10701 J$.

Since the 337 kg crate was lifted 2.3 m, the crate's gain in Gravitational Potential Energy was
$G P E = m \cdot g \cdot h = 337 k g \cdot 9.8 \frac{m}{s} ^ 2 \cdot 2.3 m = 7596 J$

Which value in Joules will be the correct answer? In asking for the work done on the crate, they are asking for Joules that the crate will be able to hold. The 7596 J of GPE will belong to the crate as long as it sits there at the top of the ramp. That is where part of the 10701 J went. The rest went to work done on friction and was then lost as heat.

I hope this helps,
Steve