Chapter 4

Newton’s Laws of Motion

Sir Isaac NewtonPhilosophiae Naturalis Principia Mathematica (1687)

Opticks (1704)"Nature and nature's laws lay hid in night;God said 'Let Newton be' and all was light."

Newton’s Three LawsInertia:

“Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by a force impressed on it.”

Force, Mass, Acceleration (F=ma):“The change in motion is proportional to the motive force

impressed; and is made in the direction of the right line in which that force is impressed.”

“Action = Reaction”:“To every action there is always opposed an equal reaction;

or, the mutual actions of two bodies are always equal, and directed to contrary parts.”

Newton’s Law Summary1. Velocity is zero or constant when net force is zero.

2. F=ma

3. Action = Reaction (in opposite direction)

Net ForceNet force (or total force) is the sum of all the forces applied to an object.

For example, if there are three people, A, B and C pushing the crazy kid. The net force on him is:

First Law and Net ForceThe First Law deals with cases when there is no net force.

“Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by a force impressed on it.”

Puck on iceIce has very little friction (so no net force), so the inertia keeps the puck moving once it is set in motion.

Mass or Inertia Inertia is the tendency of an object to

remain at rest or in motion with constant speed along a straight line.

Mass (m) is the quantitative measure of inertia. Mass is the property of an object that measures how hard it is to change its motion.

Units: kg

Mass vs. Weight

Mass is an intrinsic property of an object. A rock has same mass whether it is on the moon

or on Earth. Mass does not change

Weight is the force exerted on an object by gravity: W=mg This is different depending upon the strength of

the gravitational force. You weigh less on the Moon than on Earth.

ExampleWhat is the weight of a man of mass 70kg on Earth?

Weight is measured in N.(Pound: 1lb = 4.448N)

Same mass, different weight

Newton’s 1st LawThere are many forces act on the plane, including weight (gravity), drag (air resistance), the thrust of the engine, and the lift of the wings. At some point the velocity of the plane is 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 backward5. is zero

lift

weight

drag thrust

correct

Newton’s 1st LawNewton's first law states that if no net force acts on an object, then the velocity of the object remains constant. Since the velocity is constant, the total force on the plane must be zero, according to Newton's first law. lift

weight

drag thrust

Newton’s Second LawF = ma

Deals with the effect of a non-zero net force.Non-zero net force causes acceleration.

Unit: N (Newton)

Some Math

What does the vector symbol mean?

F = ma applies to each component independently.

F means NET FORCE!!!

The F in F = ma is the net force on the object. If you are careful, you may write instead:Fnet = ma

Always remember to find the net force first!

Simple Examples: Find a

m = 10kg

m = 10kg

F = 200N

F = 200NF = 150N

Find the magnitude of a

When the net force is zero

Zero Net Force on a Lamp

When Fnet is non-zero

When Fnet ≠ 0, since F=ma, we have a≠0.

No net force, no acceleration.Net force leads to acceleration.

If an object is accelerating, there must be a non-zero net force.

Example

The mass of m = 2kg is accelerating upward at 4m/s2. Find the tension.

ExampleThe mass of m = 2kg is accelerating downward at 4m/s2. Find the tension.

T-mg or mg-T ?In non-vector notation, we usually assume the variable a represents the magnitude of the acceleration, and is therefore positive whether it is up or down. In other words, unless stated otherwise, we will not use the up/positive, down/negative convention.

With this new convention, whenever you have opposing forces, the forces pointing in the same direction as a comes first, minus the forces in the opposite direction as a.

T-mg or mg-T ?

Another way to remember, if a > 0, you want:(big number) - (small number) = maor(same direction) - (opposite direction) = ma

Two forces

m = 10kgF1 = 200N F2 = 350N

a

Newton’s Third Law For every force, there is an equal and

opposite force every “action” has a “back-reaction” these are precisely equal and precisely

opposite

Newton’s Third Law

You cannot push without being pushed back just as hard

In tug-of-war, each side experiences the same force (opposite direction)

When you push on a brick wall, it pushes back on you!

Force Pairs Illustrated

Force on person by box

Force on floor by box Force on box by floor

Force on box by person

Force on personby floor

Force on floorby person

Not shown are the forces of gravity and the associated floor forces

Don’t all forces then cancel?

Force on boxby floor

Force on box by person

Net Forceon box

How does anything ever move (accelerate) if every force has an opposing pair?

Action and reaction force act on different objects.

Exercise: Action/Reaction Suppose a tennis ball (m= 0.1 kg) moving at a velocity v = 40

m/sec collides head-on with a truck (M = 500 kg) which is moving with velocity V = 10 m/sec. During the collision, the tennis ball exerts a force on the

truck which is smaller than the force which the truck exerts on the tennis ball. TRUE or FALSE ?

The tennis ball will suffer a larger acceleration during the collision than will the truck. TRUE or FALSE ?

Suppose the tennis ball bounces away from the truck after the collision. How fast is the truck moving after the collision?

< 10 m/sec = 10 m/sec > 10 m/sec ?

Exercise: Action/Reaction solution During the collision, the tennis ball exerts a force on the

truck which is smaller than the force which the truck exerts on the tennis ball. TRUE or FALSE ?

Equal and opposite forces!

The tennis ball will suffer a larger acceleration during the collision than will the truck. TRUE or FALSE ?

Acceleration = Force / mass

Suppose the tennis ball bounces away from the truck after the collision. How fast is the truck moving after the collision?

< 10 m/sec = 10 m/sec > 10 m/sec ?

Force from the ball causes deceleration.

Normal ForceForce from a solid surface (e.g. wall, ground) providing support for an object.“Normal” means “perpendicular”, Normal Force is always perpendicular to the solid surface.

Notations:FN, Fn, N or n

Example of Normal ForceSuppose the elevator is not accelerating.m=70kg, what does the scale read?

Example of Normal Force 2Suppose the elevator is accelerating up.m=70kg, a=5m/s2

Example of Normal Force 3Suppose the elevator is accelerating down.m=70kg, a=5m/s2

Be careful with the normal force

What is Fn now?