Textbook Problem

Calculate the work performed by a person who exerts a force of 30 N(N =  newtons) to move a box 30 meters if the force were (a) exactly parallel to the direction of movement, and (b)45° to the direction of movement. Do the relative magnitudes make sense?

Interpretation Introduction

(a)

Interpretation

To calculate the work performed by a person who exerts a force of 30N to move a box 30 meters if the force were exactly parallel to the direction of movement.

Concept introduction

The work is performed on an object when an object moves a certain distance s due to the force F. Mathematically, it is indicated by the dot product of the force vector F and the distance vector s. The mathematical equation is given below,

Work = F.s = |F||s| cos Ѳ

Where Ѳ is the angle between the vectors F and s. The unit of work is joules. Work is a way to transfer the energy. The energy is defined as the ability to do work and so energy and work are described using the same unit in joules.

Answer to Problem 2.1E

Work exactly parallel to the direction of movement = 900 J

Explanation of Solution

The work is defined as force x displacement [distance].

In the given question

work = 30N

distance = 30m

Work = F.s

Therefore work = 30 N.30 m= 900 J

Conclusion

Thus the Work exactly parallel to the direction of movement = 900 J

Interpretation Introduction

(b)

Interpretation

To calculate the work performed by a person who exerts a force of 30N to move a box 30 meters if the force were 45° to the direction of movement.

Concept introduction

The work is performed on an object when an object moves a certain distance s due to the force F. Mathematically, it is indicated by the dot product of the force vector F and the distance vector s. The mathematical equation is given below,

Work = F.s = |F||s| cos Ѳ

Where Ѳ is the angle between the vectors F and s. The unit of work is joules. Work is a way to transfer the energy. The energy is defined as the ability to do work and so energy and work are described using the same unit in joules.

Answer to Problem 2.1E

Work were 45° to the direction of movement = 640 J

Explanation of Solution

The work is defined as force x displacement [distance].

In the given question

work = 30N

degree = 45°

Work = F.s = |F||s| cos Ѳ

Therefore work = 30 N. 30m cos 45°

= 30 x 30 x0.71

Work = 640 J

Conclusion

Thus the work at 45° to the direction of movement = 640 J