Post on 17-Mar-2018
Copyright © 2010 Pearson Education, Inc.
Copyright © 2010 Pearson Education, Inc.
Chapter 6Applications of Newton’s
Laws
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6-1 Frictional ForcesFriction has its basis in surfaces that are not completely smooth:
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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.
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6-1 Frictional ForcesThe kinetic frictional force is also independent of the relative speed of the surfaces, and of their area of contact.
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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,
6-1 Frictional Forces
depending on what is needed to keep the sum of forces zero.
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6-1 Frictional Forces
(6-2)
where
(6-3)
The static frictional force is also independent of the area of contact and the relative speed of the surfaces.
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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.
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6-2 Strings and Springs
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.
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6-2 Strings and Springs
An ideal pulley is one that simply changes the direction of the tension:
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6-2 Strings and Springs
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.
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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:
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6-4 Connected Objects
We treat each box as a separate system:
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6-4 Connected Objects
If there is a pulley, it is easiest to have the coordinate system follow the string:
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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.
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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)
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6-5 Circular Motion
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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: