Chapter 6 Applications of Newton’s...
Transcript of Chapter 6 Applications of Newton’s...
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Chapter 6
Applications of Newton’sLaws
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Units of Chapter 6• Frictional Forces
• Strings and Springs
• Translational Equilibrium
• Connected Objects
• Circular Motion
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6-1 Frictional ForcesFriction has its basis in surfaces that are notcompletely smooth:
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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.
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6-1 Frictional Forces
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6-1 Frictional ForcesThe kinetic frictional force is also independent ofthe relative speed of the surfaces, and of theirarea of contact.
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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,
6-1 Frictional Forces
depending on whatis needed to keepthe sum of forceszero.
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6-1 Frictional Forces
(6-2)
where
(6-3)
The static frictional force is also independentof the area of contact and the relative speed ofthe surfaces.
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6-2 Strings and Springs
When you pull on a string or rope, it becomestaut. 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 itslength, due to the weight of the rope.
Here, we will assume thatall ropes, strings, wires,etc. are massless unlessotherwise stated.
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6-2 Strings and Springs
An ideal pulley is one that simply changes thedirection of the tension:
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6-2 Strings and Springs
Hooke’s law for springs states that theforce increases with the amount thespring is stretched or compressed:
The constant k is called the springconstant.
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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.
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6-3 Translational Equilibrium
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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 canfind 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 thecoordinate system follow the string:
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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.
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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)
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6-5 Circular Motion
This force may be provided by the tension in astring, the normal force, or friction, amongothers.
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6-5 Circular Motion
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6-5 Circular MotionAn object may be changing its speed as itmoves in a circle; in that case, there is atangential acceleration as well:
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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:
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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: