I know that when the net force and displacement are in opposite directions (such as only a frictional force on a moving object) the work is negative. However, if net force is positive, can an opposing force still do negative work? As an example, if I lift a box from the ground, I do positive work. But does gravity still do negative work, even though I am resisting that force and net force is positive?
Work is measured as the force multiplied by the displacement in the direction of the force.
Whenever there is a net force, the object will move only in the direction of the net force.
When the net force is zero, the object will be either in rest or in uniform velocity.
Work is measured by the product of the force and displacement in the direction of the force.
Positive and negative work
When object A transfers energy to object B, we say that A does positive work on B. B is said to do negative work 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.
When the balls’ energy is completely lost, it comes to rest. But now the spring begins to elongate and still continues to exert a force on the ball and ball begins to go to the right.
Now the motion is in the direction of the spring’s force.
The spring does positive work on the ball. (The one which does positive work will loose its energy)
The ball also resists the elongation of the spring. It exerts a force on the spring. But the motion is in the opposite direction of this force. The ball does negative work. (The one which does negative work will gain energy). The ball’s kinetic energy now increases.
When you lift an object, you are doing positive work. The force is moved in the direction of the motion of the object. This means you are loosing energy.
The gravitational force opposes this action. It is pulling the object down ward, but the motion is upward. The gravitational force does negative work on the object. The earth gains energy. (Note that the potential energy of the object increases)
When an object is pulled along a horizontal road, the force pulling the object in its direction is doing positive work. It looses its energy. But frictional force acts in the opposite direction of the motion. Frictional force does negative work. The friction causing objects gain energy.
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