chapter 4 lec newton

8/10/2019 Chapter 4 Lec Newton

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Newtons Laws


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what have been discussed so far

Everything about kinematics In 1D

In 2D (such as projectile motion)

Circular motion -> later

Chapter 3


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Sir Isaac Newton, English Physicist, 1643-1727


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What are they and what do they

do?

A Force is a pull(an attraction)


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Or, a push (a repulsion)

What are they and what do they

do?


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Forces can also cancel each other out!


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The Meaning of Force

To a layman:

A forceis a push or pull upon an object

To a physics student:

A forceis that which causes the velocity of an

object to change

Chapter 4


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Force

It is a vector quantity(with both magnitudeanddirection)

The combined effect of all forceson an objectdetermines its acceleration.

To combine forces means to add vectors, i.e.

Superposition of Forces

Chapter 4


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Principle of Superposition

The sum of the x-components of forces Fxaffects only ax

The sum of the y-components of forces Fyaffects only ay

The sum of the z-components of forces Fzaffects only az

x

y

F1xF2x

F1yF2y

F1F2

1 2F F F

1 2

1 2

22

x x x

y y y

x y

F F F

F F F

F F F

Chapter 4


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SI Unit of Force

Newton (N)

1 N is the required force to accelerate a 1kg object by 1

m/s2, i.e.

21 1 1

mN kg

s

Typical Force Magnitudes

Suns gravitational force on the Earth

Weight of a large blue whaleWeight of a medium-sized apple

Electric attraction between the proton

and the electron in a hydrogen atom

3.5 x 1022N

1.9 x 106

N1 N

8.2 x 10-8N

Chapter 4


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Thought Experiment

If an object sitting on a level surface is given a swiftkick, how will you describe its motion?

The Big Misconception:

The object will start to move but will eventually slow

down or stop because there is no more force to sustain

its motion.

Newtonian Mechanics Explain:

The slowing down of an object is caused by other forces

(i.e. frictional force exerted by the surface on the moving

object).

Chapter 4


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Newtons First Law

0F ma

Consider a body on which NOnet force acts. If the bodyis at rest, it will remain at rest. If the body is moving, it willcontinue to move with constant velocity.

This is also called the Law of Inertia

A constant velocity implies that its acceleration is zero.Hence, the body is in equilibrium.

Chapter 4


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The motion of an object does not change unless it is acted upon by a net

force.

If v=0 it remains 0

If v is some value it stays at that value

Another way to say the same thing:

No net force

velocity is constant

acceleration is zero

no change of direction of motion

Newtons First Law


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Law of Inertia


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An airplane is flying from Buffalo airport to O'Hare. Many forces act

on the plane, including weight (gravity), drag (air resistance), the

trust of the engine, and the lift of the wings. At some point during its

trip the velocity of the plane is measured to be constant (which

means its altitude is also constant). At this time, the total (or net)

force on the plane:

1. is pointing upward2. is pointing downward

3. is pointing forward

4. is pointing backward

5. is zero

lift

weight

drag thrust

correct

Newtons First Law


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Newton's first law states that if no net force acts on anobject, then the velocity of the object remains

unchanged. Since at some point during the trip, the

velocity is constant, then the total force on the plane

must be zero, according to Newton's first law.

lift

weight

drag thrustF= ma = m0 = 0

Newtons First Law


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Newtons Second Law

Fa

m

If a NETexternal forceacts on an object, it willcause that object to accelerate in the same direction

as the net force.

The amount of acceleration is given by the force

divided by the objects mass.

F ma

Chapter 4


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Ch t 4


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Newtons Second Law

Fa

m

F ma

Chapter 4


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F = ma


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the bigger the mass, the

greater the inertia, loweracceleration


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Newtons 2ndLaw in Multiple Dimensions

Forces (or its components) in perpendiculardimensions are independent and separable.

Fx = max along the x-axis

Fy = may

Fz = maz

along the y-axis

along the z-axis

Ch t 4


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Example #1

What acceleration will result when a 12-N net forceapplied to a 3-kg object? A 6-kg object?

A net force of 16 N causes a mass to accelerate at a

rate of 4 m/s2. Determine the mass.

a

=4 m/s2 ; 2 m/s2

m=4 kg

Chapter 4


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Example #2

Three forces act on a particle that moves withunchanging velocity v = (2 m/s)i (7 m/s)j.Two

of the forces are FA= (2N) i +(3 N)jand F

B= (-

5N) i +(8 N)j. What is the third force?

FC=(3 N)i + (-11 N)j

Chapter 4


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Defining the Mass

Mass is a quantitative measure of inertia The greater the mass, the more a body resists at

being accelerated

SI Unit kilogram

Gravitational Mass : based on the gravitational interaction of

the earth to an object

1 kg is the mass of a platinum-iridium alloy kept in a vault inParis

Inertial mass: based on the 1N amount of force that gives an

acceleration of 1 m/s2

Chapter 4

Chapter 4


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Mass vs. Weight

Massis an inertial property of a body

Does not change with location

Measured in kilograms (SI)

Weightis a force due to local gravitational attraction

exerted by the Earth or some other massive

astronomical object (such as the moon) on the body

Measured in newton May vary with location W mg

Chapter 4

Chapter 4


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Newtons Third Law

If one object is exerting a force on a second object,then the second object is also exerting a force back

on the first object. The two forces have exactly the

same magnitude but act in opposite directions.

A B B AF F

Chapter 4

Chapter 4


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Types of Forces

Contact Forces Long-range/Non-contact

Normal force

Tension

Frictional force

Air resistance

Spring force

Applied force

Weight

Electrical/Coulomb Force

Magnetic Force

Chapter 4


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Interaction of Forces

WEIGHT

FRICTION

APPLIED FORCE

NORMAL

FORCE


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What is the Normal Force?

Comes from the Latin word norma whichmeansperpendicular

When an object exerts a force with a component thatis perpendicular to the surface of another object, that

object deforms and pushes back on the first object

with an opposing force that is perpendicular to the

surfaces in contact.


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Frictional force

When an object exerts a force to a surface ofanother object, that object deforms and

pushes back on the first object with opposing

force that is parallel to the surfaces in contact.

Static friction

Kinetic friction

Chapter 4


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Action-Reaction Pairs in Nature

The propulsion of a fish through the water.

The flying motion of birds.

The motion of vehicles.

The propulsion of rockets.

Chapter 4

Chapter 4


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Free-body Diagram

1. These are diagrams used to show the relativemagnitudeand directionof all forces acting uponan object, free of its surrounding.

2. The size of the arrow in a free-body diagram isreflective of the magnitude of the force. Itsdirection reveals the direction which the force isacting.

3. Each force arrow in the diagram is labeled toindicate the exact type of force.

Chapter 4


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Chapter 4


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Example

A loaded elevator has a total mass of 2500 kg, andthat it can accelerate upwards or downwards at2.5m/s2.

Find the Tension of the elevator

(a) if it is at rest

(b) if it is accelerating upwards at a = 2.5 m/s2.

(c) if it is accelerating downwards at a = -2.5 m/s2.

Chapter 4

Chapter 4


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Example

A loaded elevator with very worn cables has a totalmass of 1800 kg, and the cables can withstand amaximum tension of 28,000 N.

(a) What is the maximum upward acceleration for theelevator if the cables are not to break?

(b) How would the answer differ if the elevator is to betaken to the moon where g = 1.62 m/s2.

Chapter 4

Chapter 4


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Example

Two blocks are connected by a heavy rope with a massof 4.00 kg. The upper box has a mass of 6.00 kg and thelower box of mass 5.00 kg. An upward force of 200 N isapplied.

(a) Draw a free-body/force diagram for the upper box,rope, and the lower box.

(b) What is the acceleration of the system?

(c) What is the acceleration of the boxes and rope?

(d) What is the tension at the top of the heavy rope?

Chapter 4

chapter 4 lec newton

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