Newton’s Laws of Motion

Topic 4

Lecture Outline

• Force • Newton’s First Law of Motion• Newton’s Second Law of Motion• Newton’s Third Law of Motion

Force

A force is a push or pull. An object at rest needs a force to get it moving; a moving object needs a force to change its velocity.

Force is a vector, having both magnitude and direction.

The magnitude of a force can be measured using a spring scale.

Newton’s First Law of Motion

According to Aristotle, the natural state of an object was to be at rest, and if you got them moving, eventually they would come to rest again.

It may seem as though it takes a force to keep an object moving. Push your book across a table—when you stop pushing, it stops moving.

Galileo did experiments rolling balls down and up inclined planes, and realized that, in the absence of some kind of force, an object would keep moving forever once it got started.

For example, you throw a ball across the room. The ball keeps moving after you let it go, even though you are not pushing it any more. Why?

Galileo called this inertia:Inertia is the natural tendency of an object to maintain a state of rest or to remain in uniform motion in straight line (constant velocity)

Later, Newton realized that mass is a measure of inertia

Newton’s First Law

An object at rest will stay at rest, and an object in motion will stay in motion at constant velocity, unless acted upon by an unbalanced force.

This is Newton’s first law, which is also called the law of inertia

Why then, do we observe every day objects in motion slowing down and becoming motionless seemingly without an outside force?

It’s a force we sometimes cannot see – friction.

It doesn’t take a force to keep an object moving in a straight line—it takes a force to change its motion. Your book stops because the force of friction stops it.

Objects on earth, unlike the frictionless space the moon travels through, are under the influence of friction.

Slide a book across a table and watch it slide to a rest position. The book comes to a rest because of the presence of a force - that force being the force of friction - which brings the book to a rest position.

In the absence of a force of friction, the book would continue in motion with the same speed and direction - forever! (Or at least to the end of the table top.)

Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it.

Inertia in everyday life

Don’t let this be you. Wear seat belts.Because of inertia, objects (including you) resist changes in their motion. When the car going 80 km/hour is stopped by the brick wall, your body keeps moving at 80 km/hour.

Conceptual Example 4-1: Newton’s first law.

A school bus comes to a sudden stop, and all of the backpacks on the floor start to slide forward. What force causes them to do that?

Newton’s Second Law of Motion

The acceleration of an object is directed proportional to the net force acting on it and inversely proportional to its mass. The direction of the acceleration is in the direction of the applied net force.

m

Fa

net

• The unit of force are called newton (N)

• One newton is equal to the force required to accelerate one kilogram of mass at one meter/second/second.1 N = 1kg • ms-2

The net force of an object is equal to the product of its mass and acceleration.

amF net

Example 4-2: Force to accelerate a fast car.

Estimate the net force needed to accelerate (a) a 1000-kg car at ½ g; (b) a 200-g apple at the same rate.

Example 4-3: Force to stop a car.

What average net force is required to bring a 1500-kg car to rest from a speed of 100 km/h within a distance of 55 m?

Newton’s Third Law of Motion

For every force (action), there is an equal and opposite force (reaction).

According to Newton, whenever objects A and B interact with each other, they exert forces upon each other. When you sit in your chair, your body exerts a downward force on the chair and the chair exerts an upward force on your body.

• There are two forces resulting from this interaction - a force on the chair and a force on your body. These two forces are called action and reaction forces.

Newton’s third law:Whenever one object exerts a force on a second object, the second exerts an equal force in the opposite direction on the first.

Newton’s 3rd Law in Nature

• Consider the propulsion of a fish through the water. A fish uses its fins to push water backwards. In turn, the water reacts by pushing the fish forwards, propelling the fish through the water.

• The size of the force on the water equals the size of the force on the fish; the direction of the force on the water (backwards) is opposite the direction of the force on the fish (forwards).

The reaction of a rocket is an application of the third law of motion. Various fuels are burned in the engine, producing hot gases.

The hot gases push against the inside tube of the rocket and escape out the bottom of the tube. As the gases move downward, the rocket moves in the opposite direction.

Conceptual Example 4-4: What exerts the force to move a car?

Response: A common answer is that the engine makes the car move forward. But it is not so simple. The engine makes the wheels go around. But if the tires are on slick ice or deep mud, they just spin. Friction is needed. On firm ground, the tires push backward against the ground because of friction. By Newton’s third law, the ground pushes on the tires in the opposite direction, accelerating the car forward.

Helpful notation: the first subscript is the object that the force is being exerted on; the second is the source.

Conceptual Example 4-5: Third law clarification.

Michelangelo’s assistant has been assigned the task of moving a block of marble using a sled. He says to his boss, “When I exert a forward force on the sled, the sled exerts an equal and opposite force backward. So how can I ever start it moving? No matter how hard I pull, the backward reaction force always equals my forward force, so the net force must be zero. I’ll never be able to move this load.” Is he correct?

ConcepTest 4.1aConcepTest 4.1a Newton’s First Law INewton’s First Law I1) there is a net force but the book has too

much inertia

2) there are no forces acting on it at all

3) it does move, but too slowly to be seen

4) there is no net force on the book

5) there is a net force, but the book is too heavy to move

A book is lying at

rest on a table.

The book will

remain there at rest

because:

There are forces acting on the bookThere are forces acting on the book, but the only

forces acting are in the y-direction. Gravity acts

downward, but the table exerts an upward force

that is equally strong, so the two forces cancel,

leaving no net forceleaving no net force.

ConcepTest 4.1aConcepTest 4.1a Newton’s First Law INewton’s First Law I1) there is a net force but the book has too

much inertia

2) there are no forces acting on it at all

3) it does move, but too slowly to be seen

4) there is no net force on the book

5) there is a net force, but the book is too heavy to move

A book is lying at

rest on a table.

The book will

remain there at rest

because:

ConcepTest 4.1bConcepTest 4.1b Newton’s First Law IINewton’s First Law II

1) more than its weight

2) equal to its weight

3) less than its weight but more than zero

4) depends on the speed of the puck

5) zero

A hockey puck

slides on ice at

constant velocity.

What is the net

force acting on

the puck?

The puck is moving at a constant velocityconstant velocity, and

therefore it is not acceleratingnot accelerating. Thus, there must

be no net forceno net force acting on the puck.

ConcepTest 4.1bConcepTest 4.1b Newton’s First Law IINewton’s First Law II

1) more than its weight

2) equal to its weight

3) less than its weight but more than zero

4) depends on the speed of the puck

5) zero

A hockey puck

slides on ice at

constant velocity.

What is the net

force acting on

the puck?

Follow-up:Follow-up: Are there any forces acting on the puck? What are they? Are there any forces acting on the puck? What are they?

1) a net force acted on it

2) no net force acted on it

3) it remained at rest

4) it did not move, but only seemed to

5) gravity briefly stopped acting on it

ConcepTest 4.1cConcepTest 4.1c Newton’s First Law IIINewton’s First Law III

You put your book on

the bus seat next to

you. When the bus

stops suddenly, the

book slides forward off

the seat. Why?

1) a net force acted on it

2) no net force acted on it

3) it remained at rest

4) it did not move, but only seemed to

5) gravity briefly stopped acting on it

The book was initially moving forward (since it was on a moving

bus). When the bus stopped, the book continued moving forwardcontinued moving forward,

which was its initial state of motioninitial state of motion, and therefore it slid forward

off the seat.

ConcepTest 4.1cConcepTest 4.1c Newton’s First Law IIINewton’s First Law III

You put your book on

the bus seat next to

you. When the bus

stops suddenly, the

book slides forward off

the seat. Why?

Follow-up:Follow-up: What is the force that usually keeps the book on the seat? What is the force that usually keeps the book on the seat?

ConcepTest 4.1dConcepTest 4.1d Newton’s First Law IVNewton’s First Law IV1) the force pushing the stone forward

finally stopped pushing on it

2) no net force acted on the stone

3) a net force acted on it all along

4) the stone simply “ran out of steam”

5) the stone has a natural tendency to be at rest

You kick a smooth flat

stone out on a frozen

pond. The stone slides,

slows down and

eventually stops. You

conclude that:

After the stone was kicked, no force was pushing it along!

However, there must have been some forcesome force acting on the

stone to slow it down and stop itto slow it down and stop it. This would be friction!!

ConcepTest 4.1dConcepTest 4.1d Newton’s First Law IVNewton’s First Law IV1) the force pushing the stone forward

finally stopped pushing on it

2) no net force acted on the stone

3) a net force acted on it all along

4) the stone simply “ran out of steam”

5) the stone has a natural tendency to be at rest

You kick a smooth flat

stone out on a frozen

pond. The stone slides,

slows down and

eventually stops. You

conclude that:

Follow-up:Follow-up: What would you have to do to keep the stone moving? What would you have to do to keep the stone moving?

ConcepTest 4.2aConcepTest 4.2a Cart on Track ICart on Track I

1) slowly come to a stop

2) continue with constant acceleration

3) continue with decreasing acceleration

4) continue with constant velocity

5) immediately come to a stop

Consider a cart on a

horizontal frictionless

table. Once the cart has

been given a push and

released, what will

happen to the cart?

ConcepTest 4.2aConcepTest 4.2a Cart on Track ICart on Track I

1) slowly come to a stop

2) continue with constant acceleration

3) continue with decreasing acceleration

4) continue with constant velocity

5) immediately come to a stop

Consider a cart on a

horizontal frictionless

table. Once the cart has

been given a push and

released, what will

happen to the cart?

After the cart is released, there is no longer a forceno longer a force in

the x-direction. This does not mean that the cart stops This does not mean that the cart stops

moving!!moving!! It simply means that the cart will continuecontinue

moving with the same velocitymoving with the same velocity it had at the moment of

release. The initial push got the cart moving, but that

force is not needed to keep the cart in motion.

ConcepTest 4.2bConcepTest 4.2b Cart on Track IICart on Track IIWe just decided that the cart continues with constant velocity. What would have to be done in order to have the cart continue with constant acceleration?

1) push the cart harder before release

2) push the cart longer before release

3) push the cart continuously

4) change the mass of the cart

5) it is impossible to do that

In order to achieve a non-zero acceleration, it is necessary

to maintain the applied forcemaintain the applied force. The only way to do this would

be to continue pushingcontinue pushing the cart as it moves down the track.

This will lead us to a discussion of Newton’s Second Law.

ConcepTest 4.2bConcepTest 4.2b Cart on Track IICart on Track IIWe just decided that the cart continues with constant velocity. What would have to be done in order to have the cart continue with constant acceleration?

1) push the cart harder before release

2) push the cart longer before release

3) push the cart continuously

4) change the mass of the cart

5) it is impossible to do that

ConcepTest 4.3ConcepTest 4.3 Truck on Frozen LakeTruck on Frozen Lake

A very large truck sits on a frozen lake. Assume there is no friction between the tires and the ice. A fly suddenly smashes against the front window. What will happen to the truck?

1) it is too heavy, so it just sits there

2) it moves backward at const. speed

3) it accelerates backward

4) it moves forward at const. speed

5) it accelerates forward

When the fly hit the truck, it exerted a force on the truck (only for a

fraction of a second). So, in this time period, the truck accelerated

(backward) up to some speed. After the fly was squashed, it no

longer exerted a force, and the truck simply continued moving at

constant speed.

ConcepTest 4.3ConcepTest 4.3 Truck on Frozen LakeTruck on Frozen Lake

A very large truck sits on a frozen lake. Assume there is no friction between the tires and the ice. A fly suddenly smashes against the front window. What will happen to the truck?

1) it is too heavy, so it just sits there

2) it moves backward at const. speed

3) it accelerates backward

4) it moves forward at const. speed

5) it accelerates forward

Follow-up:Follow-up: What is the truck doing 5 minutes after the fly hit it? What is the truck doing 5 minutes after the fly hit it?