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# Welcome back to Physics 211 - PowerPoint PPT Presentation

Welcome back to Physics 211. Today’s agenda: More on Newton’s Laws Free Body Diagrams. Static Friction. An object remains at rest as long as f s < f s max . The object slips when f s = f s max . A static friction force f s > f s max is not physically   possible.

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### Welcome back to Physics 211

Today’s agenda:

More on Newton’s Laws

Free Body Diagrams

PHY211 Fall 2011 Lecture 7-2

• An object remains at rest as long as fs < fs max.

• The object slips when fs = fs max.

• A static friction force fs > fs max is not physically   possible.

where the proportionality constant μs is called the coefficient of static friction.

PHY211 Fall 2011 Lecture 7-2

The kinetic friction force is proportional to the magnitude of the normal force.

where the proportionality constant μk is called the coefficient of kinetic friction.

PHY211 Fall 2011 Lecture 7-2

f

N

W

q

PHY211 Fall 2011 Lecture 7-2

The magnitude of the forceofkinetic friction between two objects

depends on the type of surfaces of the objects

depends on the normal force that the objects exert on each other

does not depend on the surface area where the two objects are touching

does not depend on the speed with which one object is moving relative to the other

What if  > tan-1ms ?

fk = μkn

PHY211 Fall 2011 Lecture 7-2

What if  > tan-1 μs ?

Block begins to slide

Resolve along plane:

μkWcosθ - Wsinθ= ma

Or:

a = g(μkcosθ - sinθ)

f

n

W

q

PHY211 Fall 2011 Lecture 7-2

A baggage handler drops your 10 kg suitcase onto a conveyor belt running at 2.0 m/s. The materials are such that μs=0.50 and μk=0.30. How far is your suitcase dragged before it is riding smoothly on the belt?

PHY211 Fall 2011 Lecture 7-2

• Sam, whose mass is 75 kg, takes off across level snow on his jet-powered skis. The skis have a thrust of 200 N and a coefficient of kinetic friction on snow of 0.10. Unfortunately, the skis run out of fuel after only 10s.

• What is Sam’s top speed?

• How far has Sam traveled when he finally coasts to a stop?

PHY211 Fall 2011 Lecture 7-2

• Topics:

• Interacting Objects

• Analyzing Interacting Objects

• Newton’s Third Law

• Ropes and Pulleys

• Examples of Interacting-Object Problems

PHY211 Fall 2011 Lecture 7-2

If object A exerts a force on object B, then object B exerts a force on object A. The pair of forces, as shown, is called an action/reaction pair.

PHY211 Fall 2011 Lecture 7-2

Newton’s 3rd Law

PHY211 Fall 2011 Lecture 7-2

fact that a large majority can “recite” Newton’s third law when they enter the class.

Halloun and Hestenes (1985b) have characterized student beliefs about interactions in terms of a dominance principle: the larger (or faster or more active) object exerts a larger force than the smaller (or slower or less active) object. Students tend to view an interaction as a “conflict” in which the stronger wins. It’s not hard to understand how this common-sense view comes about. After all, the effect of the collision on the compact car is much larger than its effect on the truck.

PHY211 Fall 2011 Lecture 7-2

• Some of the more specific difficulties students have with Newton’s third law and with interacting objects are:

• • Students don’t believe Newton’s third law. It’s too contrary to common sense.

• • Students have difficulty identifying action/reaction force pairs:

• They match two forces on the same object.

• They place forces on the wrong objects.

• They don’t believe that long-range forces (e.g., gravity) have reaction forces.

• • Students confuse equal force with equal acceleration.

PHY211 Fall 2011 Lecture 7-2

Students don’t understand tension: Newton’s third law and with interacting objects are:

• They think that tension is the sum of the forces exerted at the two ends of a string.

• They think that tension exerts a force only in the direction of motion.

• They think that tension can pass through an object to another string on the other side.

• Students often don’t recognize that objects connected by an inextensible string must have accelerations of equal magnitude.

PHY211 Fall 2011 Lecture 7-2

Demos Newton’s third law and with interacting objects are:

• Pasco cars

• Equal masses

• Unequal masses

• 1 student + cart + medicine ball

• 2 students + cart + rope

PHY211 Fall 2011 Lecture 7-2

Ropes, pulleys, strings and springs Newton’s third law and with interacting objects are:

• Unless otherwise stated, all of these are massless and frictionless.

• These automatically accelerate with the connecting objects.

• These can be ordered from special imaginary physics equipment catalogs.

PHY211 Fall 2011 Lecture 7-2

• Ta > Tb

• Ta < Tb

• Ta = Tb

• Not enough information

PHY211 Fall 2011 Lecture 7-2

• T (b)?1 > T2

• T1 < T2

• T1 = T2

• Not enough information

PHY211 Fall 2011 Lecture 7-2

Block A is held in place. How does the tension in the section of the string tied to block A compare to the section tied to block B?

Ta > Tb

Ta < Tb

Ta = Tb

Not enough information

PHY211 Fall 2011 Lecture 7-2

Block A is released. How does the magnitude of the acceleration of block A compare to that of block B?

• aa > ab

• aa < ab

• aa = ab

• Not enough information

PHY211 Fall 2011 Lecture 7-2

Block A is released. How does the tension in the string now (T2) compare to the tension (T1) when block A was held in place?

• T1 > T2

• T1 < T2

• T1 = T2

• Not enough information

PHY211 Fall 2011 Lecture 7-2

• Ch.7 #32 (T2) compare to the tension (T1) when block A was held in place?

• The 1 kg. block (m1) is tied to the wall with a rope. It sits on top of the 2 kg block. The lower block is pulled to the right with a tension force of 20 N. The coefficient of kinetic friction at both the lower and upper surfaces of the 2 kg block is μk = 0.40.

• What is the tension in the rope holding m1?

• What is the acceleration of m2?

m1

m2

PHY211 Fall 2011 Lecture 7-2

Demo: Pulleys (T2) compare to the tension (T1) when block A was held in place?

*2 pulleys

2T = W

F = T = W/2

T

F

*N pulleys

F = W/N!

W

PHY211 Fall 2011 Lecture 7-2