Newton’s Laws

El Paso Independent High School

Newton’s First LawNewton’s First Law: An object at rest or an object in motion at constant speed will remain at rest or at constant speed in the absence of a resultant force.

Newton’s First Law: An object at rest or an object in motion at constant speed will remain at rest or at constant speed in the absence of a resultant force.

A glass is placed on a board and the board is jerked quickly to the right. The glass tends to remain at rest while the board is removed.

A glass is placed on a board and the board is jerked quickly to the right. The glass tends to remain at rest while the board is removed.

Newton’s First Law (Cont.)Newton’s First Law: An object at rest or an object in motion at constant speed will remain at rest or at constant speed in the absence of a resultant force.

Newton’s First Law: An object at rest or an object in motion at constant speed will remain at rest or at constant speed in the absence of a resultant force.

Assume glass and board move together at constant speed. If the board stops suddenly, the glass tends to maintain its constant speed.

Assume glass and board move together at constant speed. If the board stops suddenly, the glass tends to maintain its constant speed.

Inertia

• Newton's first law is often referred to as the law of inertia.

• Inertia is the resistance or unwillingness of an object to accelerate (speed up, slow down, or change directions).

• The more mass an object has, the harder it is to accelerate. Thus, more mass equals more inertia.

Understanding the First Law

(a) The driver is forced to move forward. An object at rest tends to remain at rest.

Discuss what the driver experiences when a car accelerates from rest and then applies the brakes.

(b) Driver must resist the forward motion as brakes are applied. A moving object tends to remain in motion.

Newton’s Second Law

• Second Law: Whenever a resultant force acts on an object, it produces an acceleration that is directly proportional to the force and inversely proportional to the mass.

• Second Law: Whenever a resultant force acts on an object, it produces an acceleration that is directly proportional to the force and inversely proportional to the mass.

m

Fa maF

Force Units: Newton’s or N

Acceleration and Force

Pushing a cart with twice the force produces twice the acceleration. Three times the force triples the acceleration.

Newton: The Unit of ForceOne newton is the force required to give an

acceleration of 1 m/s2 to a mass of 1 kg.

F (N) = m (kg) a (m/s2)

What resultant force will give a 3 kg mass an acceleration of 4 m/s2?

F = 12 N

F = ?

a = 4 m/s2

3 kg )/4()3( 2smkgmaF

Example A 40 N resultant force causes a block to accelerate at 5 m/s2. What is the mass?

F = 40 Nm=?

a = 5 m/s2

kgsm

N

a

Fm

maF

8/5

402

Example A net force of 4.2 x 104 N acts on a 3.2 x 104 kg airplane during takeoff. What is the force on the plane’s

75-kg pilot?

F = 4.2 x 104 N

m = 3.2 x 104 kg

+F = ma

a = 1.31 m/s2

To find the force on the pilot, assume same acceleration:

First we find the acceleration of the plane.

kgx

Nx

m

Fa

4

4

102.3

102.4

NsmkgmaF 4.98)/31.1)(75( 2

Example A 54-g tennis ball is in contact with the racket for a distance of 40 cm as it leaves with a velocity of 48 m/s. What is

the average force on the ball?

Given: vo = 0; vf = 48 m/s x = 0.40 m; m = 0.0540 kg; a = ?

First, draw sketch and list given quantities:

Given: vo = 0; vf = 48 m/s x = 40 cm; m = 54 g a = ?

Consistent units require converting grams to kilograms and centimeters to meters:

Cont. . .

Example (Cont). A 54-g tennis ball is in contact with the racket for a distance of 40 cm as it leaves with a

velocity of 48 m/s. What is the average force on the ball?

F= (0.054 kg)(2880 m/s2) F = 156 N

2

2fv

ax

Knowing that F = m a, we need first to find acceleration a:

22222

22

/2880)4(.2

048

2

2

smx

vva

axvv

of

of

Weight and Mass• Weight is the force an object applies as a

result of gravity pulling it downward. It is directed downward and it varies with gravity.

• Mass is a universal constant which is a measure of the matter that makes up an object. It is always constant regardless of location

mgW

maF

Because weight is a force

created by the downward acceleration of gravity, we can make this substitution.

Weight and Mass: ExamplesWhat is the weight of a 10-kg block?

9.8 m/s2 W

m10 kg

W = mg = (10 kg)(9.8 m/s2)

W = 98 N

The weight of an object is the force it causes as a

result of gravity.

The weight of an object is also referred to as the force of gravity

Always Remember!!In Physics, the use of Newton’s second law and many other applications makes it absolutely necessary to distinguish between mass and weight. Use the correct units!Metric SI units: Mass is in kg; weight is in N.

Always give preference to the SI units.

Pounds should never be used!!!

Example A resultant force of 40 N gives a block an acceleration of 8 m/s2. What is the weight of the block near the surface of the

Earth?

W=?

F = 40 Na 8

m/s2

To find weight, we must first find the mass of the block:

Now find weight of a 5-kg mass on earth.

Now find weight of a 5-kg mass on earth.

W = mg

= (5 kg)(9.8 m/s2)

W = 49.0 NW = 49.0 N

a

FmmaF ;

kgsm

N

a

Fm 5

/8

402

Newton’s Third Law

• Third Law: For every action force, there must be an equal and opposite reaction force. Forces occur in pairs.

• Third Law: For every action force, there must be an equal and opposite reaction force. Forces occur in pairs.

Action

Reaction

ActionReaction

Action and Reaction ForcesUse the words by and on to study action/reaction forces below as they relate to the hand and the bar:

Use the words by and on to study action/reaction forces below as they relate to the hand and the bar:

The action force is exerted by the _____ on the _____.

The reaction force is exerted by the _____ on the _____.

bar

hands

bar

hands

Action

Reaction

m= 1 kg

ForcesIf a bar of gold that has a mass of 1 kg is sitting at rest on a table, what forces are acting on it and to what magnitude?

FN= 9.8 N

The normal force of an object pushes up with a force equal to the bar’s downward force. Because both forces are present, the bar remains at

equilibrium.

Gravity acts on the object in the downward

direction. However, because the bar is

not moving downward, there must be another

force counteracting it.

Fg= 9.8 N

Free-body Diagrams

• A free body diagram is a diagram that shows all of the forces present on a given object.

• When drawing a free body diagram, objects are always represented as points or dots and forces are drawn as arrows pointing away from the object.

• For now the only forces we will consider are gravity, tension, normal, applied, and friction.

Free-body Diagrams

• Gravitational Force: This is the only force that will always be present and will always point straight down.

• Tension Force: This type of force is caused by a rope, chain, string, etc. and goes in the direction of the rope, chain, string, etc.

• Normal Force: This type of force is present when the object is in contact with a surface. It always points perpendicular to the surface.

Free-body Diagrams

• Applied Force: This type of force is used when an outside agent is acting on the object such as a person.

• Frictional Force: This type of force is the result of two surfaces being drug across each other, creating friction. It always points in the direction opposite of the movement.

The size of the arrow should be proportional to the size of the force. Larger forces should

have larger arrows!!!

ExamplesFa

FN

FF

Fg

Fa

FT

Fg

FT

Friction acts parallel to the surface but opposite the direction of travel.

There is no normal force present because the object is not resting on a surface.

Example A cart and driver have a mass of 120 kg. What force F is required to give an acceleration of 6 m/s2 with

no friction?

1. Read problem and draw a sketch.

2. Draw a free body diagram and label forces.

Diagram for Cart:FN

Fg

Fa

3. Choose x-axis along motion and indicate the right direction as positive (+).

x+

Example What force F is required to give an acceleration of 6 m/s2?

SFy = 0; FN - Fg = 0

The normal force FN is equal to weight Fg

SFx = max; Fa = ma

Fa = (120 kg)(6 m/s2)

Fa = 720 N

m = 120 kg

4. Write Newton's Law equation for both axes.

ay = 0

Diagram for Cart:FN

Fg

Fa

Example What is the tension FT in the rope below if the block accelerates upward at 4 m/s2? (Draw sketch and free-body)

10 kg

a = +4 m/s2

FT a

FT

Fg

+

SFx = m ax = 0SFy = m ay = m

aFT- Fg = m a

Fg=mg = (10 kg)(9.8 m/s) = 98 N

m a= (10 kg)(4 m/s) = 40 N

FT - 98 N = 40 N

FT = 138 N

Example Find the acceleration of the blocks if there is no friction on the surfaces.

2 kg

4 kg12 N

First apply F = ma to entire system (both masses).

12 NFN

Fg=(m2 + m4)g

SFx = (m2 + m4) a

12 N = (6 kg) a

2/26

12sm

kg

Na

Because the blocks are tied together and move together, we can treat

them as one object

Now find the tension force in the rope connecting the two blocks.

2 kg

4 kg12 N Now find tension

T in connecting cord.

Apply F = m a to the 2 kg mass where a = 2 m/s2.

FT

FN

m2 g

SFx = m2 a

FT = (2 kg)(2 m/s2)

FT= 4 N

Example (Cont.) The two-body problem.

2 kg

4 kg12 N Same answer for FT

results from focusing on 4-kg by itself.Apply F = m a to the 4 kg mass where a = 2

m/s2.

SFx = m4 a12 N - FT = (4 kg)(2

m/s2)

T = 4 N

Fa

FT

m4g

FT