In physics, work is done when a force causes an object to move in the direction of the force.

Positive Work

Positive work happens when the force and the movement (displacement) are in the same direction. When you push a shopping cart forward, you are applying force in the direction the cart is moving. Because your force helps the cart go faster or move further, this is positive work. The mathematical formula for work is Work = Force × Displacement × cos(θ). When the angle (θ) is 0 degrees, the work is positive because cos(0) equals 1.

Negative Work

Negative work occurs when the force acts in the opposite direction of the movement. Imagine a car applying its brakes. The car is still moving forward, but the friction from the brakes creates a force pulling backward. This backward force tries to slow the car down. Because the force and the movement are pulling against each other, the work done by the braking force is negative. In this case, the angle is 180 degrees, and cos(180) equals -1.

Zero Work

Zero work happens in two main situations. First, if you apply force to an object but it does not move, you have done zero work. For example, pushing against a solid concrete wall results in zero work because the wall stays in place. Second, zero work occurs if the force is applied at a 90-degree angle to the direction of movement. If you carry a heavy school bag and walk horizontally, your upward force (holding the bag) is at a right angle to your forward movement. Therefore, gravity or your hand is doing zero work on the bag in the direction of your walk.

• Positive: Force and movement go the same way.
• Negative: Force and movement go opposite ways.
• Zero: No movement happens, or force is at a right angle to movement.