# Work done is zero if an object moves with constant velocity? right?

Aug 8, 2018

Net work done is zero, but there still could be work done on an object

#### Explanation:

Unless the constant velocity is $0 \frac{m}{s}$, work is done when an object is moved a distance in the direction of the force.

A few scenarios to consider:

1. I am trying lifting a 20 N box that’s stationary on the ground with a 20 N force. Is work done? No, because the object is still on the ground with a constant velocity. The object will not move unless I apply a force that’s greater than the weight of the box.

2. I start dragging a 20 N cart with a force of 30 N, while the force of friction opposing my motion is 20 N. I reach constant velocity when I reduce my force applied to 20 N so that it’s equivalent to the 20 N force of friction. Since the forces are balanced, my cart now moves at a constant velocity. Am I doing work? Yes. Is the friction doing work? Yes. Is there any NET work being done on the cart? No, because the work done by friction cancels out the work done by you.

Aug 8, 2018

Both yes and no.

#### Explanation:

When an object is moving with constant velocity, it means that there is $0$ acceleration and hence no force and no work done.

But, this is only partly true. Generally an object, when it moves with constant velocity, is overcoming some friction and some force is being applied to balance it. Hence, when the object, though friction acting against it, is still moving with constant velocity, some work may be done.

Aug 8, 2018

It depends.

#### Explanation:

There are several details to consider:

• If the constant velocity is upward (lifting a book to a higher shelf) then work is done against gravity because the book's gravitational potential energy is increased.
• If the constant velocity is downward (moving a book to a lower shelf) then work is done by gravity (or negative work against gravity) because the book's gravitational potential energy is decreased.
• If the constant velocity is horizontal (sliding a book across a table) and there is friction, then work is done against friction. That is because a force in the direction of the motion, equal and opposite the force of the friction, was required to nullify the friction yielding a net force of zero. There is no change in the book's energy.
• In none of the above examples was there no work done. If you carry a book across the room, keeping its height above the floor constant, then the work done is zero. There was a force and a displacement. Work done is zero because the opposition of its weight is a vertical force and the displacement is horizontal. That is because $\text{work" = "force" xx "displacement} \times \cos \theta$ where $\theta$ is the angle between $\text{the force and the displacement} ,$ and in this case the angle is ${90}^{\circ}$.

I hope this helps,
Steve