Newton’s Laws of Motion

Chapter 4

Changes in Motion

Section 4.1

• Force is simply a push or pull

• It is an interaction between two or more objects

• Force is a vector so it has magnitude and direction

• In the SI system, Force is measured in Newtons (N). In the English system, it is measured in pounds.

• 1 pound = 4.445 Newtons

• The total force (or net force) exerted on an object is the vector sum of all forces acting on it

Aristotle & Galileo

• Aristotle was a great philosopher but not such a good scientist.

• Aristotle’s theory of motion is wrong.

• Took 2000 years before Galileo got motion right.

Motion according to Aristotle (I)

• Every object has a “natural” state.

• In “natural motion”, “Earth” elements (stone, apple, you, etc.) are drawn to the Earth.

• Heavier objects are more strongly attracted so they fall faster (stone falls faster than a feather).

Aristotle

Reality

Important: These are Aristotle’s ideas, but he’s wrong!

Motion according to Aristotle (II)

• Pushing or pulling an object causes “unnatural” motion (or “violent” motion).

• If cause is removed (stop pushing) then object returns to “natural” state and stops moving.

BRICK BRICK

Pushed brick slides but then comes to a stop

Galileo’s Inclines (I)

Downhill: Speed increases

Uphill: Speed decreases

Flat surface: Speed increases, decreases, or constant?

Questions existence of “natural Earth” state of not moving.

Inertia section 4.2

• An object’s tendency to persist in its original state of motion

• This concept was first discovered by Galileo in the 1630’s.

• Objects will keep doing whatever they’re already doing unless something causes it to change.

Isaac Newton

• 1642-1727, Lincolnshire, England

• Professor and Scholar at the University of Cambridge

• One of the most influential scientists of all time

• Uncovered universal laws of motion and gravity among many other discoveries.

• Most famous work: Principia

Newton’s First Law of Motion also referred to as the “law of inertia”

An object at rest remains at rest & an object in motion remains in motion*,

unless an outside, unbalanced force acts on the object.

*Moving in a straight line with constant speed.

Newton’s First Law of Motion

• An object in motion can still maintain its state with a force acting on it.

• It’s only when the forces acting on it are unbalanced that an object can change its motion!

Newton’s First Law of Motion

• The Gare Montparnasse

in France crashed

through this wall in 1895,

why?

• Trains are difficult to stop

because they are so

massive

• There is a direct

relationship between

mass and inertia.

Mass

• Mass is a measure of the quantity of

matter in an object

• Mass also measures how difficult it is to

change the velocity of an object

• Or, how much an object resists changes in

its motion

Example: Riding the subway

When a moving train stops, you continue moving forward. When the stopped train starts moving again, you remain stationary and are thrown backwards

When the rocket engines on a spacecraft are suddenly

turned off, while traveling in empty space far away from

distant stars and planets, the starship will..

A)go faster and faster

B)slow down and then stop

C)stop immediately

D)move with constant speed

E)move perpendicular to velocity

Question

Inertia demonstrations

• Coin/notecard

• Tablecloth

• Hanging mass

• Hoop and battery

• Mallet and mass

• Rolling carts

Discussion topics of inertia

• Inertia videos

• Getting ketchup out

• When are you taller? AM or PM?

• Collisions: Front and rear

• Seatbelts work off inertia

• If you drop something on a moving vehicle, where does it land?

• How do you find your mass in space?

Conceptual Checkpoint

• The metal head of a hammer is loose. To

tighten it, you drop the hammer down onto

a table. Should you (a) drop the hammer

with the handle end down, (b) drop the

hammer with the head end down, or (c) do

you get the same result either way?

Conceptual Checkpoint

Tighten the Hammer Head

Net Force ( ∑ F)

same as

The Newton is metric unit of force (about 1/5 pound).

When several forces act on an object, the forces add together.

Sum of forces called net force or total force

BRICK

3 Newtons

5 Newtons 8 Newtons

Check Yourself

?

Equilibrium Rule

same as

If an object is at rest then the net force must be zero. Similarly if in uniform motion.

BRICK 3 Newtons 3 Newtons

Zero Newtons (No Force)

When this happens we say that forces “balance.”

What is. . .

• Mass

• Weight, w

Weight vs Mass

• Mass is the amount of matter in an object

• Weight is a measure of the pull of gravity on an object.

• Weight (Newtons) = mass (kg) x acceleration due to gravity (m/s2)

• Formula for weight: W = m g

• Q: How much does one kilogram weigh?

• A: 9.8 N

Question

Is it better to have 1 N of gold on the moon or on the Earth?

Example An astronaut with a mass of 75 kg travels to Mars.

A) What is his mass on Mars?

B) What is his weight on Mars where the acceleration due to gravity is 3.8 m/sec2?

C) What is the acceleration due to gravity on top of a mountain if he weighs 683 N?

Free Body Diagrams

• A free body diagram is a diagram showing

an object in free space along with all

external forces acting on it

Free Body Diagrams

• The usual steps in constructing a free-

body diagram are:

– Sketch the forces

– Isolate the object of interest

– Choose a convenient coordinate system

– Resolve the forces into components

• You can then apply Newton’s 2nd law for

each coordinate direction

Constructing and Using a Free-Body Diagram

Figure 5-5bc

Constructing and Using a Free-Body Diagram

Constructing and Using a Free-Body Diagram

A Book Supported in a Person’s Hand

Example

Find the magnitude and direction of the net force.

45 N 23N

Example

Find the magnitude and direction of the net force.

24 N 13 N

15 N

Example

Four forces act on an object. 210 N acts to the East. 305 N acts to the South. 413 N acts to the West. And, 139 N acts to the North. Find the magnitude and direction of the net force.

Example

Three forces act on an object. 71 N act at 24 degrees North of East. 62 N act at 51 degrees North of West. And, 85 N act at 60 degrees South of West. Find the magnitude and direction of the net force.

Example

• The following object is in equilibrium. How big does the missing force have to be to keep it in equilibrium?

16 N 16 N

F= ?

11 N

Example

• Find the size and direction of the missing force in order for this object to be in equilibrium.

F = ?

3.3 N

6.3 N

Example

• Find the size and direction of the missing force in order for this object to be in equilibrium.

F = ?

33 N at 60 degrees N of E

63 N at 15 degrees S of E

Example • This 1kg mass is suspended by two cables at 50

degrees. Find the size and direction of the tension force in each cable in order for this object to be in equilibrium.

T=? T=?

50° 50°

1 kg

Newton’s 2nd Law

Section 4.3

• When a net force acts on an object of mass m,

the acceleration of the object will be given by:

Σ𝐹 = 𝑚𝑎

• Or in terms of components:

yyxx maFmaF

Newton’s 2nd Law

• If the net force is zero, the acceleration is

zero, and the velocity of an object stays

constant, which is Newton’s 1st law

• Force is measured in newtons (N), and

from the second law,

2 m/s kg1N 1

Newton’s Second Law of Motion

4.45 N = 1 lb

• Fnet = ma

Example

What is the net force required to accelerate a 1.5 kg box at 2.0 m/sec2?

Example

What is the net force exerted on a 1500 kg car if it is accelerated from 5 m/sec to 10 m/sec in 3 sec?

Example

• A 0.34 kg softball is accelerated from rest to 22 m/s over a length of 0.88 meters. Find the net force that was applied to the ball that produced this acceleration.

Example

• The following forces act on the 4.6 kg object. A) Find the net force acting on it. B) Find the magnitude of its acceleration.

24 N 13 N

15 N

4 N

Example

• Find the acceleration of the apparatus below. Assume there is no friction.

3.3 kg

0.75 kg

Example

• A 2,360 kg pickup truck slows down to a complete stop with a frictional force of 14,500 N directed opposite its motion. If its initial velocity was + 14.2 m/s, how far did it travel while slowing down? How much time did this take?

Newton’s 3rd Law

Newton’s 3rd Law

• For every force that acts on an object,

there is a reaction force equal in

magnitude and opposite in direction.

• For every action there is an equal and

opposite reaction.

• An isolated force does not exist in nature,

so forces always occur in pairs

Newton’s 3rd Law

• Action−reaction forces act on two different

objects: hence they do not cancel

• Action−reaction forces generally produce

different accelerations, since the masses

of the objects are likely to be different

Examples of Action-Reaction Force Pairs

Apparent Weight

• When you are in an elevator accelerating

upward a scale would read a greater weight

• When you are in an elevator accelerating

downward a scale would read a lesser

weight

• Thus, your apparent weight in an

accelerator is different from your true weight

Apparent Weight

Apparent Weight

• If you are accelerating upward, your

apparent weight is

• If you are accelerating downward, your

apparent weight is

)( agmWa

)( agmWa

Normal Forces

• When an object rests on a surface, the

surface provides a force on the object in a

direction perpendicular to the surface

• This called the normal force, N

• In most cases, the normal force is equal to

the weight of the object; however it can be

greater or less than the weight of the

object

Support (Normal) Force

Solid surfaces exert a force, called a support force, on objects pressed against them.

100 Newton Gold Brick

100 Newton Support force (Normal Force)

Downward force (weight) balanced by upward force (support).

* The term “normal” means “perpendicular”. So the normal force is always perpendicular to the surfaces

The Normal Force

May Equal the Weight

Normal Forces

• When a box is pulled by a force F at an

angle θ across a smooth floor, the

magnitude of the normal force is

sinFWN

The Normal Force

May Differ from the

Weight in certain

circumstances

Normal Forces

• For an inclined plane, the normal forces

are still at right angles to the surface, but

not in the vertical direction

• It is convenient to choose the x axis

parallel to the incline surface and y axis

perpendicular

• Then normal force is:

cosWN

Components of the Weight on an Inclined

Surface

Example

• A child of mass 45 kg rides on a sled down an ice-covered hill (frictionless) inclined at an angle of 22 degrees with respect to the horizontal.

• A) What is the acceleration of the child?

• B) What is the normal force exerted on the child by the sled?

• Driving down the road you hit the brakes

suddenly. As a result, your body moves

toward the front of the car. Explain, using

Newton’s laws.

• A drag-racing car accelerates forward

because of the force exerted on it by the

road. Why, then, does it need an engine?

Explain.

• An astronaut on a space walk discovers

that his jet pack no longer works, leaving

him stranded 50 m from the spacecraft. If

the jet pack is removable, explain how the

astronaut can still use it to return to the

ship.

• Is it possible for an object to be in motion

and yet have zero net force acting on it?

Explain.

• You are dribbling a basketball, ready to

make your move to the hoop. What

produces the force that causes the ball to

return to your hand with each dribble?

• You jump out of an airplane and open your

parachute after a brief period of free fall.

To decelerate your fall, must the force

exerted on you by the parachute be less

than, equal to, or greater than your

weight? Explain.

• Is it possible for an object at rest to have

only a single force acting on it? If your

answer is yes, provide an example. If your

answer is no, explain why not.

• Since all objects are “weightless” for an

astronaut in orbit, is it possible for

astronauts to tell whether an object is

heavy or light? Explain.

Everyday Forces Section 4.4

Two types of Friction

•Static •Kinetic

Friction

• Friction is the force that opposes motion when two surfaces are in contact

• Opposes motion means that the force of friction is always in the opposite direction of the motion

• There are two different types of friction: static and kinetic (sliding)

Static Friction

• Static means stationary or not moving

• When a force is first applied to an object, static friction opposes the start of motion

• A force greater than that of static friction must be applied for the object to start moving

Kinetic Friction

• Kinetic means related to motion

• Kinetic friction opposes motion once an object is moving

• Kinetic friction in general is less than static friction

• This means you have to push harder to start an object moving than to keep an object moving

What Affects Friction?

• Speed of pull? (assuming v>0)

• Area in contact?

• Weight of object?

• Materials in contact?

Ff = FN

s > k is the coefficient of friction

What if . . . ?

• FA < Ff

• FA = Ff

• FA > Ff

• Ff is NOT an “applied” force!!

Question

It's more difficult to start moving a heavy carton from rest than it is to keep pushing it with constant velocity, because

A) the normal force (N) is greater when the carton is at rest.

B) s< k

C) initially, the normal force (N) is not perpendicular to the applied force.

D) k < s

Example • A 13.4 kg crate is pushed across a floor.

The respective coefficients of friction are µs = 0.85 and µk = 0.62. Find the pushing force necessary to get it moving from rest. And, find the force necessary to keep it moving at a constant velocity.

13.4 kg