Example: Applying Newton's 2nd law - complex case

Understanding the situation

Applying Newton's second law to a complex system can be quite tricky. Often there are many forces and many different principles have to be called on to work through an answer. Here's a typical problem.

Presenting a sample problem

Two students have just finished analyzing the forces on a passenger and the parts of an accelerating automobile. But in this problem they treated the car and the wheels as a single object. Snooki says, “But if we were stopping we would have to consider the brakes.” Ronnie knows that his motorbike has disc brakes. A clamp, when open, allows the wheel to spin freely through it. But when he brakes, the clamp squeezes tightly together and creates a strong frictional force of the clamp on the wheel. He says, “I think we can work it out how the bike stops.” Let’s help them fill in their reasoning.

A. Consider the motorbike (= “the rest of the bike not including the clamp or wheel”), the clamp, and the wheel. While the brake is being squeezed to slow down the bike, draw a system schema and free body diagrams for the horizontal and vertical forces on the clamp and on the wheel. Be sure to label each force with the type of force it is, what is causing the force and what is feeling the force. Only show the forces in the plane of the wheel. (Don’t bother showing the forces perpendicular to that plane such as e.g. the normal forces the clamp exerts on the wheel.)

B. Ronnie says, “It’s the frictional force of the clamp on the wheel that slows the car.” Snooki disagrees. She thinks that the friction force of the road is what slows the car. Are either of them correct or is it something else? Explain your reasoning.

C. Snooki recalls that lots of times when Ronnie has made quick stops, he has left a track of rubber behind the bike. Does this fact support her claim or his? Explain your reasoning.

Solving this problem

A. The system schema must include the clamp, the wheel, the rest of the bike, the ground, and the earth (to provide gravity). The clamp touches the rest of the bike and the wheel, and it feels the pulls of gravity. The wheel touches the clamp and the ground, and the rest of the bike to connect the wheel to the bike, and it feels the pulls of gravity. We don’t need to consider the other interactions. 

For our free body diagram, consider the clamp. The clamp feels the pull of gravity so it must also be held up be a normal force through its connection to the rest of the bike. When it squeezes the clockwise turning wheel, it will feel a frictional force from the wheel trying to pull it along with the wheel – upward. Since it is slowing down, there must be a backwards force from something. The only plausible force is from the rest of the bike.

The wheel feels the pull of gravity so it must also be held up be a normal force through its connection to the rest of the bike. When it is being squeezed by the clamp, it will feel a frictional force from the clamp trying to stop it from rotating. Since it is slowing down, there must be a backwards force from something. This is from the friction of the wheel with the ground. There also has to be a force from the bike to the wheel since the slowing wheel is exerting a force on the bike.

B. Snooki is right from the point of view of the physics framework. An object (the car) cannot slow itself down, it can only do so through interactions with an external object. If the bike were on a slick patch of ice the clamp could grab the wheel so the wheel stopped spinning entirely, but the wheel would continue to slide. From a mechanism point of view Ronnie is correct but he is not giving the full chain of reasoning. The wheel would not start sliding along the ground and feeling an external frictional force unless the clamp slowed its rotation.

C. It supports her claim since it shows that there is significant friction between the wheel and the ground that rubs some of the rubber off the wheel.

Joe Redish 8/14/15