Friction, Part 2
Friction in systems. How to decide the direction of friction when it is not obvious, the band of forces that hold a block on an incline, the angle of friction and the best angle to pull, block on block, a block on an incline tied to a hanging mass, and a box on a moving belt.
Why this chapter
Part 1 gave you friction on one block pushed along one surface. Real problems join bodies together. Think of a load on a truck, a block on a block, a sack tied over a pulley or a bag on a moving belt. In each of them the hard question comes first. Which way does friction point, and does anything slip at all? This chapter gives you one method for that question, the tendency test, and then uses it on every standard system of friction.
You will learn
- Decide the direction of friction from the tendency of relative motion, or by assuming a direction and testing the sign and the limit.
- Find the least and the greatest force that hold a block at rest on a rough incline.
- Define the angle of friction and show that a rope pulls a block with the least force when it is raised by that angle.
- Test whether two stacked blocks move together or slip, and find the acceleration of each in both cases.
- Decide whether a block on a rough incline tied to a hanging mass moves up, moves down or stays.
- Find the time and the slip of a box placed on a moving belt.
Before you begin
You should know the whole of Friction, Part 1. That means static friction that adjusts itself up to \(\mu_s N\), kinetic friction \(\mu_k N\), the angle of repose and the block on a rough incline. You should be able to draw a free-body diagram and resolve the weight on an incline. You should also apply Newton's second law to bodies joined by a string.
Lessons
Read in order. The small labels are the topics of each lesson. They take your colour as you answer the checks.
0%Glossary
The key words of this chapter, with the meaning this chapter gives them.
- angle of friction
- The angle between the normal reaction and the contact force when friction is limiting. Its tangent equals \(\mu_s\), so it equals the angle of repose.
- angle of repose
- The largest angle of an incline at which a block rests without sliding. Its tangent equals \(\mu_s\).
- contact force
- The single force a surface exerts on a body in contact, the vector sum of the normal reaction and friction.
- friction
- The force that a surface exerts on a body along the surface of contact. It opposes the motion of the body relative to the surface, or the tendency of that motion.
- kinetic friction
- Friction between two surfaces that slide on each other. Its size is \(\mu_k N\) and it opposes the relative sliding.
- limiting friction
- The largest value static friction can have, \(\mu_s N\), reached when the body is just about to slide.
- normal reaction
- The force that a surface exerts on a body perpendicular to the surface of contact. It is written \(N\).
- slip distance
- The distance a body slides relative to the surface it touches before the two move together, such as a box placed on a moving belt.
- static friction
- Friction between two surfaces that do not slide on each other. It takes whatever value is needed to prevent sliding, up to a limit of \(\mu_s N\).
- tendency of relative motion
- The direction in which a body would slip relative to a surface if the contact were perfectly smooth. Static friction points opposite to it.
- third-law pair
- Two forces that two bodies exert on each other, equal in size and opposite in direction, acting on different bodies. Friction between two touching bodies is one such pair.