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GGGG FFF makenahn/11summer/lectures/L7.pdf · GGGG T fid ht lti d t dd ll f Various Forces Gravity...
Transcript of GGGG FFF makenahn/11summer/lectures/L7.pdf · GGGG T fid ht lti d t dd ll f Various Forces Gravity...
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Chapter 4. Laws of Motion
Force
Net force
Today…
Newton’s 1st, 2nd, 3rd laws
Various Forces
Circular Motion
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Circular Motion
Motivation
1 2 ...netF F F ma= + + =
T fi d th l ti d t dd ll f
Various ForcesGravity forceNormal forceTension
To find the acceleration, we need to add all forces applied to an object of mass m.
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TensionFriction forces (static, kinetic)
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Gravitational Force (Weight):
Magnitude:F h 9 8 / 2
Weight: From the Earth on objects near Earth Surface
F = mg, where g = 9.8 m/s2
•Weight: The force that the Earth is pulling the object with near the surface of the Earth.
Direction: Pointing downward
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Direction:Direction:
Magnitude:Determined by analyzing forces
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Determined by analyzing forces
From surface on objects in contact
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Example: Person in an elevatorExample: Person in an elevator
A person with a mass 50 Kg in an elevator is moving upward with an upward acceleration 21.1 /a m s=
Identify all forces on the person and find magnitude and direction for each.
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A B
Direction: pulls along the rope
From the rope on objects at both ends
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Direction: pulls along the ropeMagnitude : Constant along a single rope,
determined by analyzing forces
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Tension force = 50 N
RopeiClicker
M=10 kg
Horizontal surfaceNormal force from surface on block is _______
(a)98 N
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(b) less then 98 N(c) greater than 98 N
A block of mass m is pulled along a frictionless horizontal floor by an applied force T as shown. The normal force on the block by the floor is
A) mgB) Less than mgc) Grater than mg
iClicker quiz:
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Example: m=10 kg, theta=30 degree, T=60 N.Find the normal force and acceleration.
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Name the forces on the block.What is the direction of the gravity force?What is the direction of the normal force on the block?What is the direction of acceleration?
(a)
A block of mass m is on a frictionless inclined surface as below.
θ
m
(a)
(b)
(c)
Example: m=10 kg, theta=30 degree. Find the normal force and acceleration.
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θ
(d)(e)
Friction force
Friction forces are good:You need friction force to walk.
Force from surface on objects in contact with [parallel to surface, against (attempted) motions]
Frictional forces are bad:~20% of gasoline in automobile is used to counteract friction in the used to counteract friction in the engine and drive train.
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Static Friction Kinetic Friction
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Static and Kinetic Friction
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Object Not sliding on surfaceStatic friction : Max
S S S Nf f Fμ< =
NF = (normal force)
Object sliding on surface
k k Nf Fμ=F
Kinetic friction : ( l f )
Sμ = (coefficient of static friction)
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kμNF = (normal force)
= (coefficient of kinetic friction)
Example: Pushing a bookcase
Bookcase
M=500 kg
0.5sμ =0.2kμ =
(a) Find the magnitude of the force you need to apply to start motion
Rough horizontal surface
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(a) Find the magnitude of the force you need to apply to start motion.
(b) Find the magnitude of the force to maintain a constant accelerationof 2 m/s^2.
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A block of mass m is pulled along a rough horizontal floor by an applied force T as shown. Coefficient of kinetic friction is 0.1.
m=10 kg, theta=30 degree, T=60 N.
A) Find the normal force on the block by the floor.B) Find the friction forceC) Find the acceleration
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C) Find the acceleration
(a)
A block of mass m is on a rough inclined surface as below. The coefficient of static friction is 0.2, and coefficient of static friction is 0.1.m=10 kg, theta=30 degree. The block is initially at rest. Would the block slide? If it slides, find its acceleration.
θ
m
(a)
(b)
(c)
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θ
(d)(e)
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m2=6 kg m1=4 kgF=20 N
Example: Multiple objects moving together.
Find the acceleration.
Find the tension in the rope between the two blocks.
Frictionless surface
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Why do we study circular motions?Circular motions are everywhere around us!!!
CD
Circular Motion
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Why do we study circular motions?Circular motions are everywhere around us!!!
Questions:
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How can we describe a circular motion?
What causes a circular motion?
First, uniform circular motion
Uniform circular motion ice
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Constant speed, or,“constant magnitude” of velocity
Motion along a circle:“changing direction” of velocity
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Does the velocity change in uniform circular motion?iClicker Quiz
(a) Yes
(b) No
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Acceleration is NOT zero!
Direction of velocity: changingYes, velocity changes
F
Does the velocity change in uniform circular motion?
Net force acting on the object is NOT zero.
The “net” force in circular motion is called “Centripetal force”.
amFnet =
C t i t l f i i l t f th t i i t
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Centripetal force is simply a net force that gives rise to a circular motion, NOT a new type of force.
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Acceleration
Magnitude:
Di ti n: t d nt f i l
Uniform circular motion
netF netF
Direction: toward center of circle
Magnitude:
Direction: toward center of circle
Net force (“Centripetal force”)2
netmvF
r=
netF
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Derivations of the above relations (see textbook)
Example: Circular motion of a hanging ball
iClicker Quiz: What is the direction of acceleration when the ball is at the position in the figure?
(a) (b) (c)
m=4.8 kg
2m 22 deg
Find the tension in the rope and the speed of the ball.
(d) Out of plane (e) into plane
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Non-Uniform circular motion
Changing speed, or,changing magnitude of velocity
Motion along a circle:Changing direction of velocity
Why do we study non-uniform circular motion?
Some exciting motions are non-uniform circular motions!
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Example
Radial component of acceleration2
rva =
Even for Non-Uniform circular motion,
r r
Radial component of net force2
rvF mr
=
Radial components follow the same relations
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Radial components follow the same relations as uniform circular motions!
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iClicker QuizFor the roller coaster,the magnitude of normal force at A is _______ mg.
(a) equal to(b) less than(c) greater than
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ExampleA roller coaster of mass m=1000 kg is passing point A at 30 m/s.Find the magnitude of normal force.
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iClicker QuizFor the roller coaster,the magnitude of normal force at B is _______ mg.
(a) equal to(b) less than(c) greater than
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ExampleA roller coaster of mass m=1000 kg is passing point B.Find the maximum speed it can have without losing contact with the track.
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Example: A ball of mass 0.5 kg attached to a rope is rotating in a vertical plane. What is the minimum speed the ball should have at the top to prevent the rope from becoming loose?
iClicker Quiz: At the bottom, the tension is ____ mg
(a) equal to(b) less than(c) greater than(d) not enough information !!!
2m
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(d) not enough information !!!