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Section06 - Physics 204A Class Notes Section 6 Applying...

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Physics 204A Class Notes 6-1 Section 6 – Applying Newton’s Laws Outline 1. Frictional Forces 2. Dealing with Ropes and Pulleys 3. Uniform Circular Motion 4. Non-uniform Circular Motion 5. Freefall with Air Resistance Why do objects do what they do? Because of the forces acting on them is one answer. In the last section we dealt mostly with constant forces that acted along one coordinate axis. In this section we will address forces that act along more than one axis and forces that change with time. Remember the big picture, once we know the forces that act on an object, we can use Newton’s Laws to find the acceleration of the object and from there find the complete description of the motion of the object. The general method is, 1. Find the forces acting on the object. 2. Use Newton’s Laws to find the acceleration. 3. Use the definitions of velocity and acceleration as well as the initial position and initial velocity to completely describe the motion. 1. The Frictional Force If you push on a crate to get it moving, it will quickly come to rest once you stop pushing. Newton’s Laws explain that the crate comes to rest not because rest is the natural state of motion, but because frictional forces cause the crate to slow down. The detailed behavior of the frictional force is quite complex. It is due to the molecular forces between two surfaces. Let’s simplify matters as much as possible by looking at the frictional force empirically. Let’s look at two cases: one where the crate is moving and the frictional force is said to be “kinetic friction” and one where the crate is at rest and the frictional force is said to be “static friction.” Looking at the kinetic case, suppose the crate is moving to the right at some speed v 0 , but skidding along so it will soon be at rest. The forces on the crate are shown at the left. The crate will accelerate to the left due to the frictional force and soon come to rest. Suppose, the crate is moving to the right at the same speed, but someone had put a second crate on top of it. What would be different? The weight of the one crate we are looking at would still be the same, but the normal force, and the frictional force would both be larger. The point is that you probably have the sense that things that weigh more “sort of have more friction.” However, from the point of view of Newton’s Laws, objects that feel more normal force feel more frictional force. We can say that the frictional force is proportional to the normal force or F kf = μ F n where μ is mathematically, the constant of proportionality. Physically, μ represents all the complex interactions between the molecules of the two surfaces. If the surfaces are rough, μ would be larger. If the surfaces are smooth, μ is smaller. Instead of defining μ in terms of the intermolecular forces, it is easier to define the coefficient of kinetic friction as the ration of the frictional force to the normal force.
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