Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Physics I 95.141 LECTURE 8...

Department of Physics and Applied Physics95.141, F2010, Lecture 8

Physics I95.141

LECTURE 89/29/10


Exam Prep Problem

• A 5kg block (A) sits on an inclined plane tilted at an angle of 30º. It is attached via a massless cord to a block of mass 2kg (B) lying on a flat surface. Ignore friction.– (10pts) Draw a free body diagram for each block (include

coordinate system).– (8pts) What are the magnitude of the Normal Forces on each

block?– (10pts) What is the acceleration of the blocks?– (7pts) What is the tension in the cord?

A

B

θ =30°


Exam Prep Problem

• A 5kg block (A) sits on an inclined plane tilted at an angle of 30º. It is attached via a massless cord to a block of mass 2kg (B) lying on a flat surface. Ignore friction.– (10pts) Draw a free body diagram for each block (include coordinate

system).


Exam Prep Problem

• A 5kg block (A) sits on an inclined plane tilted at an angle of 30º. It is attached via a massless cord to a block of mass 2kg (B) lying on a flat surface. Ignore friction.– (8pts) What are the magnitude of the Normal Forces on each block?


Exam Prep Problem

• A 5kg block (A) sits on an inclined plane tilted at an angle of 30º. It is attached via a massless cord to a block of mass 2kg (B) lying on a flat surface. Ignore friction.– (5pts) What is the acceleration of the blocks?


Exam Prep Problem

• A 5kg block (A) sits on an inclined plane tilted at an angle of 30º. It is attached via a massless cord to a block of mass 2kg (B) lying on a flat surface. Ignore friction.– (4pts) What is the tension in the cord?


Common Mistakes

• Orientation of mass on plane.

• Direction of Normal Force.

• Confusing sin and cos.


Administrative Issues

• EXAM 1: Monday, IN CLASS!– Equation sheet given

• If you rely on this, you will run out of time!!

– Wait outside class– Practice Exams– Pens/Pencils and Calculators are all that are allowed!– No iPods/mp3 players

• Exam Review session– Thursday evening, OH218, 6:30 pm. – Come with questions!! I will work out whatever you ask,

but session ends when you run out of questions.


Outline

• Friction • Velocity dependent Forces

• What do we know?– Units– Kinematic equations– Freely falling objects– Vectors– Kinematics + Vectors = Vector Kinematics– Relative motion– Projectile motion– Uniform circular motion– Newton’s Laws– Force of Gravity and Normal Force– Free Body Diagrams– Problem Solving


Review Problem

50m

250m


Solve for acceleration, velocity

• Geometry

• Free-body diagram

• Forces


Zip-Line problem

• a, vf


Up to now…

• We have worked with frictionless surfaces and no air resistance.

• Not particularly realistic!

• If I apply a Force to an object on this table, does it keep moving forever?


Friction

• Friction is actually a microscopic effect.– The roughness of two surfaces sliding against one

another provides a Force opposite to the direction of motion.

– The magnitude of this force depends on two things:• The properties of the two surfaces• The Normal Force between the two surfaces.


Coefficient of Kinetic Friction

• Sliding Friction• Force acting against sliding motion of object on

a surface

Nkfr FF

k Coefficient of kinetic friction

Depends on surfaces

Magnitude of Ffr depends on FN, but direction is ALWAYS against direction of motion.

Not a fundamental law Experimental Result


Friction Example

• Suppose we consider the 3 examples from last lecture. Let’s rank the Frictional Forces for a mass sliding on a surface with coefficient of static friction k

ov ov ov

-FH +FH

FFR FFR FFR

A B C


In Class Demo

• Pull on book from rest

– What is Force required to start book moving?

– What is Force required to keep book moving once it has started?

– What happens to the magnitude of this Force if I press down on the book?


Two Types of Friction

• Kinetic Friction: associated with movement• Static Friction: Friction at rest

– If I push on an object on the ground and it doesn’t move, I am exerting a Force, and since the object isn’t moving, there must be a second Force opposing my Force. This Force is the Force of Static Friction

• The expression for Static Friction is slightly different than for Kinetic Friction.

• Still depends on FN

NsSfr FF


Static Friction

• I push a little harder (F=40N)…Does it move?

• Imagine a 10.2kg box on the ground, at rest. The system has a coefficients friction μs=0.5, and μk=0.3.

• I push (horizontally) with a Force 20N. What is acceleration?

• I push with a Force of 60N. What is acceleration now?


Static Friction• Imagine a 10.2kg box on the ground, at rest. The system

has a coefficients friction μs=0.5, and μk=0.3. • I push (horizontally) with a Force 50N. Does it move?

What is acceleration?

• I push with a Force of 60N. What is acceleration now?


Demo: Static Friction

• Case 1: only a couple of pages overlap

• 10 pages overlap

• Every other page


Example I (Kinetic and Static Friction)

• A block lies on an inclined plane (μk=0.3, μs=0.5). At what angle do you see the block start to move? What is the acceleration when θ=45º?

• Choose coordinate system• Draw Free Body Diagram


Example I (Kinetic and Static Friction)• A block lies on an inclined plane (μk=0.3, μs=0.5). At

what angle do you see the block start to move? • Write out Force components

27max

0cos mgFF Ny

cossin

sinsin

mgmg

FmgFmgF

s

Nsfrx


Die Hard with a Physics Vengeance



40º

0.1S8.0k

What is acceleration with a) wheels spinning?b) wheels locked?



40º

8.0k



40º

0.1s


Velocity-Dependent Forces

• Friction is relatively easy, it just has two values, depending on whether the object is moving or at rest.

• Friction does not depend on the velocity of the object!

• Some forces, however, do depend on the velocity of the object.


Drag Forces

• Force acting on an object as it moves through a Fluid or Gas.– Boat in water– Any motion in air

• Cars• Skydivers• Projectile motion

• Mathematics of velocity dependent Forces is tricky, but a good approximations are:

bvFD 2bvFD


Terminal Velocity

• If we assume drag force is:• What is terminal velocity of a skydiver?

bvFD


Terminal Velocity II

• If we assume drag force is:• What is terminal velocity of a skydiver?

2bvFD


Now we Know

• Force problems with friction– Draw diagram– Draw free body diagram– Divide Forces into components– Obtain equations of motion for each dimension

• Velocity Dependent Forces– Terminal Velocity

Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Physics I 95.141 LECTURE 8...

Documents

Transcript of Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Physics I 95.141 LECTURE 8...