Transcript Lecture 8

Physics I
95.141
LECTURE 8
9/29/10
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
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? B
A
θ =30°
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
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).
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
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?
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
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?
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
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?
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
Common Mistakes
• Orientation of
mass on plane.
• Direction of
Normal Force.
• Confusing sin and
cos.
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
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.
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
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
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
Review Problem
50m
250m
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
Solve for acceleration, velocity
• Geometry
• Free-body diagram
• Forces
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
Zip-Line problem
• a, vf
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
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?
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
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.
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
Coefficient of Kinetic Friction
• Sliding Friction
• Force acting against sliding motion of object on
a surface
F fr   k FN
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
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
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
A
C
B
-FH
FFR
vo
FFR
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
+FH
vo
FFR
vo
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?
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
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
FSfr   s FN
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
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 20N. What is
acceleration?
• I push a little harder (F=40N)…Does it move?
• I push with a Force of 60N. What is acceleration now?
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
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?
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
Demo: Static Friction
• Case 1: only a couple of pages overlap
• 10 pages overlap
• Every other page
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
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
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
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
F  F  mg cos  0  Fx  mg sin   Ffr  mg sin   s FN

y
N
 mg sin    s mg cos 
 max  27 
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
Die Hard with a Physics Vengeance
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
Die Hard with a Physics Vengeance
40º
 S  1.0
k  0.8
What is acceleration with
a) wheels spinning?
b) wheels locked?
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
Die Hard with a Physics Vengeance
k  0.8
40º
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
Die Hard with a Physics Vengeance
 s  1.0
40º
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
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.
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
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:
FD  bv 2
FD  bv
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
Terminal Velocity
• If we assume drag force is: FD  bv
• What is terminal velocity of a skydiver?
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
Terminal Velocity II
2
F


bv
• If we assume drag force is: D
• What is terminal velocity of a skydiver?
95.141, F2010, Lecture 8
Department of Physics and Applied Physics
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
95.141, F2010, Lecture 8
Department of Physics and Applied Physics