Example
The following question involves a situation where work is being done and energy is being transformed. It will test your ability to use the terms, The amount of energy it takes to do a task. Measured in joules (J). For example, the work done in raising a mass through 10 m would be equal to the gain in potential energy of the mass. and gravitational potential energy.
Question
A crane operator on a building site slowly raises a loaded crate of mass 1500kg at a steady speed.
a) What is the weight \(W\) of the crate?
b) What is the upwards pull \(P\) on the crate?
c) How much work is done by \(P\) in raising the crate to a height of \(4 m\)?
d) What is the gain in gravitational potential energy of the crate when it is at a height of \(4m\).
e) What is the gravitational potential energy of the crate when it is a height of \(9 m\)?
The weight of the crate is calculated using \(W = mg\), where \(g= 9.8 Nkg^{-1}\)
\(W = mg = 1500 \times 9.8 = 14700N\)
Weight of loaded crate = \(14700N\)
b) Upwards pull \(P = \) weight of crate \(= 14700N\)
c) Work done by \(P\) in raising crate to a height of \(4 m =\) force applied to crate \(\times\) distance moved
\(=14700 \times 4 = 58800 J\)
d) Work done by \(P\) in raising crate to a height of \(4 m\) = gain in gravitational potential energy
So, gain in gravitational potential energy \(= 58800 J\)
e) Gravitational potential energy, \(E_{p}= mgh\)
\(= 1500 \times 9.8 \times 9 = 132300 J\)
Gravitational potential energy of the crate at a height of \(9m = 132300 J\)
