Chapter 10, Problem 78A

To determine

The one that requires more work-carrying a $420\text{N}$ backpack up a hill for $200\text{m}$ distance or carrying a $210\text{N}$ backpack up a hill for $400\text{m}$ distance.

Answer to Problem 78A

Work required will be same for both cases.

Explanation of Solution

Introduction:

Work done is given by,

  $W=Fd\cos \theta$

Where $F$ is the force done, $d$ is the distance, and $\theta$ is the angle between the distance and force.

The force required to the carry the backpack will be equal to the weight of the backpack. Then, the angle between the force and the displacement of the backpack will be $0°$ .

Thus, the work done for the given cases will be,

  $W=Fd$

As can be seen from above, the work done will be equal to the force multiplied by the displacement, and for both the given cases the product of the force and the displacement of the backpack will be same.

Thus, the work required will be same for both the cases.

Conclusion:

Since the work required to be done is given by the product of the force and the displacement of the backpack, it will be same for both the cases - carrying a $420\text{N}$ backpack up a hill for $200\text{m}$ distance or carrying a $210\text{N}$ backpack up a hill for $400\text{m}$ distance.