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Chapter 6Applications of Newton’s

Laws


6-1 Frictional ForcesFriction has its basis in surfaces that are not completely smooth:


6-1 Frictional Forces

Kinetic friction: the friction experienced by surfaces sliding against one anotherThe static frictional force depends on the normal force:

(6-1)

The constant is called the coefficient of kinetic friction.


6-1 Frictional ForcesThe kinetic frictional force is also independent of the relative speed of the surfaces, and of their area of contact.


The static frictional force keeps an object from starting to move when a force is applied. The static frictional force has a maximum value, but may take on any value from zero to the maximum,


depending on what is needed to keep the sum of forces zero.



(6-2)

where

(6-3)

The static frictional force is also independent of the area of contact and the relative speed of the surfaces.


6-2 Strings and Springs

When you pull on a string or rope, it becomes taut. We say that there is tension in the string.



The tension in a real rope will vary along its length, due to the weight of the rope.

Here, we will assume that all ropes, strings, wires, etc. are massless unless otherwise stated.



An ideal pulley is one that simply changes the direction of the tension:



Hooke’s law for springs states that the force increases with the amount the spring is stretched or compressed:

The constant k is called the spring constant.


6-4 Connected Objects

When forces are exerted on connected objects, their accelerations are the same. If there are two objects connected by a string, and we know the force and the masses, we can find the acceleration and the tension:



We treat each box as a separate system:



If there is a pulley, it is easiest to have the coordinate system follow the string:


6-5 Circular MotionAn object moving in a circle must have a force acting on it; otherwise it would move in a straight line.

The direction of the force is towards the center of the circle.


6-5 Circular Motion

Some algebra gives us the magnitude of the acceleration, and therefore the force, required to keep an object of mass m moving in a circle of radius r.The magnitude of the force is given by:

(6-15)


6-5 Circular Motion


6-5 Circular MotionAn object may be changing its speed as it moves in a circle; in that case, there is a tangential acceleration as well:

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