Question

A person is able to do 4.5 x 10^5 J of work in 6 hours. Working at this rate, how long will it take this person to lift 1000 kg of bricks up a 0.80 m high platform?

Answer 1

1st option: 6.3 min

Explanation:

Given:

Work (W) = 4.5x10^5 J

Mass (m) = 1000 kg

Height (h) = 0.8 m

Time (t) = 6 h

1 hour is equal 3600 sec, therefore:

`6\text{ h}\cdot\frac{3600\text{ sec}}{1\text{ h}}=21600\text{ sec}`

Time (t) =21600 sec

We have the following formula (Power):

`P=(W)/(t)^{}`

We replace the values of this case:

`\begin{gathered} P=(4.5\cdot10^5)/(21600) \\ P\: =20.83\text{ W} \end{gathered}`

Now we calculate the work in the form of potential energy needed to lift the bricks:

`\begin{gathered} W=m\cdot g\cdot h \\ \text{ we replacing} \\ W=1000\cdot9.8\cdot0.8 \\ W=7840\text{ J} \end{gathered}`

Now, we can calculate the time by calculating the ratio between the work and the power, like this:

`\begin{gathered} P=(W)/(t) \\ t=(W)/(P) \\ \text{ we replacing} \\ W=(7840)/(20.83) \\ W=376.4\text{ sec} \end{gathered}`

This is the time in seconds, to convert it to minutes, we must take into account that 1 minute is equal to 60 seconds, therefore:

`376.4\text{ sec}\cdot\frac{1\text{ min}}{60\text{ sec}}=6.27\cong6.3\text{ min}`

The time it would take is 6.3 minutes