Chapter 6 Applications of Newton’s Lawsnsmn1.uh.edu/rbellwied/classes/spring2013/ch6_notes.pdfTitle ch6-notes.ppt Author Rene Bellwied Created Date 9/22/2011 8:39:50 PM

Copyright © 2010 Pearson Education, Inc.

Chapter 6

Applications of Newton’sLaws


Units of Chapter 6• Frictional Forces

• Strings and Springs

• Translational Equilibrium

• Connected Objects

• Circular Motion


6-1 Frictional ForcesFriction has its basis in surfaces that are notcompletely smooth:


6-1 Frictional Forces

Kinetic friction: the friction experienced bysurfaces sliding against one another

The static frictional force depends on the normalforce:

(6-1)

The constant is called the coefficient ofkinetic friction.




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


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


depending on whatis needed to keepthe sum of forceszero.



(6-2)

where

(6-3)

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


6-2 Strings and Springs

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



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

Here, we will assume thatall ropes, strings, wires,etc. are massless unlessotherwise stated.



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



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

The constant k is called the springconstant.


6-3 Translational Equilibrium

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

(6-5)

This allows the calculation of unknown forces.


6-3 Translational 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 canfind the acceleration and the tension:



We treat each box as a separate system:



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


6-5 Circular MotionAn object moving in a circle must have a forceacting on it; otherwise it would move in a straightline.

The direction of theforce is towards thecenter of the circle.


6-5 Circular Motion

Some algebra gives us the magnitude of theacceleration, and therefore the force, requiredto keep an object of mass m moving in a circleof radius r.

The magnitude of the force is given by:

(6-15)


6-5 Circular Motion

This force may be provided by the tension in astring, the normal force, or friction, amongothers.


6-5 Circular Motion


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


Summary of Chapter 6• Friction is due to microscopic roughness.

• Kinetic friction:

• Static friction:

• Tension: the force transmitted through astring.

• Force exerted by an ideal spring:


Summary of Chapter 6

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

• Connected objects have the same acceleration.

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

Documents

Chapter 6 Applications of Newton’s Lawsnsmn1.uh.edu/rbellwied/classes/spring2013/ch6_notes.pdfTitle ch6-notes.ppt Author Rene Bellwied Created Date 9/22/2011 8:39:50 PM