application of newton’s lawsnsmn1.uh.edu/cratti/phy1301-spring2015_files/ch6_claudia.pdf ·...

APPLICATION OF NEWTON’S LAWS Chapter 6

Copyright © 2010 Pearson Education, Inc.

•  Frictional forces

• Strings and springs

•  Translational Equilibrium

• Connected objects

• Circular Motion

Units of Chapter 6


6-1 Frictional forces


•  Friction has its basis in surfaces that are not completely smooth:



• Types of frictional forces:

•  Kinetic friction: the friction experienced by surfaces sliding against one another (object is moving)

•  Static friction: the friction experienced by surfaces when the object is not in motion (object is not moving)



• Kinetic friction:

•  Is a vector;

•  Occurs between two objects;

•  One or both objects are in motion;

•  Occurs at the point of contact between surfaces;

•  Opposes motion, i.e. if object is sliding to the right, kinetic friction points to the left



• Kinetic friction:

•  The kinetic frictional force depends on the normal force:

•  The constant is called the coefficient of kinetic friction.



•  The kinetic frictional force is independent of the relative speed of the surfaces, and of their area of contact.



• Static friction:

•  Is a vector;

•  Occurs between two objects;

•  Objects are NOT in motion;

•  Occurs at the point of contact between surfaces;

•  Opposes direction motion would occur, i.e. if a force is applied to the right of an object but it does not move, static friction points to the left (opposite direction object would move)



•  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.



where

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.

Example Copyright © 2010 Pearson Education, Inc.

•  (a) If forces of 5.0 N applied to each end of a spring cause the spring to stretch 3.5 cm from its relaxed length, how far does a force of 7.0 N cause the same spring to stretch?

Example continued Copyright © 2010 Pearson Education, Inc.

•  (b) What is the spring constant of this spring?

6-3 Translational equilibrium


• When an object is in translational equilibrium, the net force on it is zero:

•  This allows the calculation of unknown forces.

(6-5)

6-3 Transational equilibrium


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 motion


•  An 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:

6-5 Circular motion


•  This force may be provided by the tension in a string, the normal force, or friction, among others.

6-5 Circular motion


6-5 Circular motion


•  An object may be changing its speed as it moves in a circle; in that case, there is a tangential acceleration as well:

Summary of Chapter 6 Copyright © 2010 Pearson Education, Inc.

•  Friction is due to microscopic roughness.

•  Kinetic friction:

•  Static friction:

•  Tension: the force transmitted through a string.

•  Force exerted by an ideal spring:

Summary of Chapter 6 Copyright © 2010 Pearson Education, Inc.

• An object is in translational equilibrium if the net force acting on it is zero.

•  Connected objects have the same acceleration.

•  The force required to move an object of mass m in a circle of radius r is:

application of newton’s lawsnsmn1.uh.edu/cratti/phy1301-spring2015_files/ch6_claudia.pdf ·...

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