Question

Which requires more work to do, using a force to lift a 50 kg. rock, 2 meters or lifting a 25 kg. rock, 4 meters? (1 kilogram=10 newtons)

Answer 1

Given data:

Mass of rock 1;

`m_1=50\text{ kg}`

Height rock 1 lifted;

`h_1=2\text{ m}`

Mass of rock 2;

`m_2=25\text{ kg}`

Height rock 2 lifted;

`h_2=4\text{ m}`

The work done in lifting the rock is given as,

`W=mgh`

Here, m is the mass of the rock, g is the acceleration due to gravity (g=10 m/s²) and h is the height the rock lifted.

The work done in lifting rock 1 is given as,

`W_1=m_1gh_1`

Substituting all known values,

`\begin{gathered} W_1=(50\text{ kg})*(10\text{ m/s}^2)*(2\text{ m}) \\ =1000\text{ J} \end{gathered}`

The work done in lifting rock 2 is given as,

`W_2=m_2gh_2`

Substituting all known values,

`\begin{gathered} W_2=(25\text{ kg})*(10\text{ m/s}^2)*(4\text{ m}) \\ =1000\text{ J} \end{gathered}`

On comparing the work done in lifting rock 1 and 2 we conclude that,

`W_1=W_2=1000\text{ J}`

Therefore, the same amount of work is done in lifting a 50 kg rock by 2 meters and lifting a 25 kg rock by 4 meters.