Chapter U5, Problem 10RE

Interpretation Introduction

Interpretation: The term work needs to be defined. The joules of work done by a pulley needs to be determined, if it lifts 500 lb of piano.

Concept Introduction: The work done can be calculated using the following relation:

  $w=F\times d$

Here, F is force and d is displacement.

Also, force is calculated as follows:

  $F=ma$

Here, m is mass and a is acceleration.

Answer to Problem 10RE

  $44452.8\text{ J}$

Explanation of Solution

The work is said to be done, if a force is applied on an object and it displace from its initial position.

It is given that mass of piano is 500 lb and height to which it is lifted is 20 m.

Since, the force is applied on the piano against the gravity of earth, force can be calculated as follows:

  $F=m\times g$

Here, g is acceleration due to gravity with value 9.8 m/s².

Putting the values,

  $F=\left(500\text{ lb}\right)\left(9.8{\text{ m/s}}^2\right)=4900{\text{ lb m/s}}^2$

Now, work done can be calculated as follows:

  $w=F\times d$

Here, displacement is the height up to which the piano is lifted.

Putting the values,

  $w=\left(4900{\text{ lb m/s}}^{\text{2}}\right)\left(20\text{ m}\right)=98000{\text{ lb m}}^2{\text{/s}}^{\text{2}}$

Since,

  $1\text{ lb }=\text{0}\text{.4536 kg}$

Thus,

  $w=98000\text{ lb}\left(\frac{\text{0}\text{.4536 kg}}{1\text{ lb}}\right){\text{ m}}^2{\text{/s}}^{\text{2}}=44452.8{\text{ kg m}}^{\text{2}}{\text{/s}}^{\text{2}}$

Also,

  $\text{1 J}={\text{kg m}}^{\text{2}}{\text{/s}}^{\text{2}}$

Thus,

  $w=44452.8\text{ J}$

Conclusion

Thus, work done to lift the piano is $44452.8\text{ J}$ .