Carrying a box along

The idea

A force acting perpendicular to an object's displacement does zero work on it, because there is no displacement in the direction of the force.

A girl carries a box

A girl holds a box in her hands and walks across the room. She keeps pushing up on the box to hold it up.

How much work do you think her upward force does on the box as she walks along?

• Some work, because she is holding the box
• No work
• A lot of work, because the box is heavy

Look at the directions

Open each tab and compare the force with the displacement.

Right angles, no work

When she lifted the box, the force and the displacement were in the same direction. When she walked along, the box moved sideways while the force stayed upward. Work needs displacement in the direction of the force, so this force did none. In higher grades you will learn how to find the work when the force and the displacement are at an angle to each other.

A force acting perpendicular to the displacement of an object does zero work on it, because there is no displacement in the direction of the force.

Notes

A force perpendicular to the displacement does zero work: there is no displacement in the direction of the force.

Check yourself

A girl carries a box while walking along level ground. The upward force she applies to hold the box does…

Why does the upward force do no work on the carried box?

Which case has a force perpendicular to the displacement?

A constant force is perpendicular to the displacement of an object. The work done by that force is…

• positive work on the box, because the box moves. The box does move, but sideways, not in the direction of the upward force.
• negative work on the box, because it is heavy. Work depends on displacement along the force, not on how heavy the box is. Here that displacement is zero.
• zero work on the box — correct. Yes!
• The box has no displacement in the direction of the force — correct. Yes!
• The force is too small to move the box. The force holds up the weight of the box. Work is zero because the displacement is at right angles to the force.
• The girl is not moving. She is walking. The box is displaced, but not in the direction of the upward force.
• The force is to the right and the object moves to the right. These are in the same direction, not at right angles.
• The force is upward and the object moves horizontally — correct. Yes!
• The force is upward and the object moves upward. These are in the same direction, not at right angles.
• equal to force × displacement. The displacement along the force is what counts, and it is zero.
• positive and large. With no displacement in the direction of the force, the work is zero, not large.
• zero — correct. Yes!