Question
Tue March 08, 2011 By: Akanksha Gupta

dear sir/mam, it seems confusing to me what is suppose to be the sign- negative or positive...when it comes to the amount of work done. And what is it suppose to be when a man is walking a horizontal plane. Thanking you, akanksha:-).

Expert Reply
Tue March 08, 2011

 Work done can  be positive or negative. When 0o <= θ < 90o, work done is positive as  Cos θ is positive. Work done by a force is positive if the applied force has a component in the direction of the displacement. When a body is falling down, the force of gravitation is acting in the downward direction. The displacement is also in the downward direction. Thus the work done by the gravitational force on the body is positive. Consider the same body being lifted in the upward direction. In this case, the force of gravity is acting in the downward direction. But, the displacement of the body is in the upward direction. Since the angle between the force and displacement is 180o, the work done by the gravitational force on the body is negative.

 

When object A transfers energy to object B, we say that A does positive work on B. B is said to do negativework on A. This use of the plus and minus signs relates in a logical and consistent way to their use in indicating the directions of force and motion in one dimension

Suppose that a ball is moving with some velocity from right side to left side on a horizontal table. The ball possesses some kinetic energy (1/2 mv^2)
It strikes a spring on the table and compresses it to some distance.

The ball does positive work on the spring. It imparts some energy to the spring.
The force exerted by the ball on the spring and the displacement are in the direction of the force.
On the other hand, the spring also exerts a force on the ball (resistive force).
But the displacement of the spring is opposite to the direction of the force of the spring on the ball. The spring does negative work on the ball. The ball’s energy decreases.

Ask the Expert