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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 !!!