Question

The frictional force acting on the drum set does negative work. Does friction always do negative work? If yes, explain why. If no, give an example of friction doing positive work.

Short answer

No, friction can do positive work, such as when helping a car accelerate.

Step-by-step solution

Understanding Negative Work by Friction

Friction often opposes the direction of motion. Since work is defined as the force applied times the distance over which it acts in the direction of the force, when friction opposes motion, the angle between the force of friction and the direction of motion is 180 degrees. The cosine of 180 degrees is -1, meaning that friction typically does negative work.

Is Negative Work by Friction Always the Case?

Friction does not always perform negative work. For example, consider someone walking forward. The friction between their shoes and the ground actually acts in the same direction as the motion of the body because it prevents slipping and allows forward movement. Here, the frictional force contributes positively to the work done on the person.

Example of Positive Work Done by Friction

Think about a situation where an object, like a car, accelerates. The static friction between the car's tires and the road acts in the direction of the car's acceleration. In such cases, this static friction force does positive work on the car by helping it speed up.

Key concepts

Negative Work

Negative work occurs when a force acts in the opposite direction to the motion. This usually happens when friction is involved. Imagine trying to slide a book across a table. As you apply force to move it in one direction, friction acts in the opposite direction, resisting the motion.
The formula for work is \( W = F \cdot d \cdot \cos(\theta) \), where \( F \) is the force, \( d \) is the displacement, and \( \theta \) is the angle between the force and displacement directions. In the case of friction, this angle is typically 180 degrees. The cosine of 180 degrees is -1, meaning the work done by friction is calculated as negative.

• Friction often does negative work by slowing down or stopping objects.
• Even when you stop pushing, friction continues to reduce an object's speed until it comes to a stop.

In these cases, friction is counterproductive to the object's motion, hence performing negative work.

Positive Work

While it's common to associate friction with negative outcomes, friction can sometimes perform positive work. An excellent example is when a person walks forward. Consider how your feet push off the ground. The friction between your shoes and the ground prevents slipping, allowing you to walk forward effectively. This frictional force acts in the direction of your movement.

• Frictional force in this scenario is crucial as it helps in maintaining balance and gaining speed.
• The work is positive because the force is aiding movement, not opposing it.

Similarly, when a car accelerates, the static friction between the tires and the road facilitates this acceleration. By acting in the same direction as the car's movement, friction is doing positive work, contributing to an increase in speed.
In these cases, friction is not a hindrance but an enabler of motion.

Force

Force is a fundamental concept in physics, defined as any interaction that, when unopposed, will change the motion of an object. It can cause an object to start moving, stop moving, or change direction. Friction is a particular type of force that resists motion between two surfaces in contact.

• When a force causes movement in the same direction as its application, it does positive work.
• Conversely, when it opposes movement, like friction often does, it performs negative work.
• Understanding the vector nature of force (having both magnitude and direction) is crucial to determining the type of work done.

Forces can be visible, like pushing a door, or invisible, like gravity holding you to Earth. Recognizing these interactions in daily life helps appreciate how forces govern the physical world, influencing whether an object speeds up, slows down, or remains at rest.