Newton’s Laws of Motion

FORCES

Forces are: Pushes or Pulls on an object.

Forces cause objects to: START, STOP, or Change Direction

Two forces we are familiar with: Gravity Friction

The symbol for Force is a capital F: F

Forces are vectors – they have both magnitude and direction.

Raymond J. FonashRadnor High School, 2011-2012

May the FORCE be with you . . .

Use the force, you

will.

Who’s Who in the Forces Game . . .

• Back around 350 bc, Aristotle believed that forces were needed to make objects MOVE and to keep an object in motion.

• Around 1500 ac, Galileo believed that a force was NOT needed to keep an object in motion. He believed that moving was just as natural a state for an object as being at rest.

• Around 1687, Sir Isaac Newton studied forces and how they effect objects, both at rest and in motion. He developed Three Laws of Motion.

Newton came to the Dark Side. I know more about the Force than he does.

An example of this is the Waiter andthe tablecloth trick. When you yank out the tablecloth, the dinnerware Remains in place. WHY????

INERTIA !

• When we push an object across the floor, we see that it does NOT stay in motion. It will eventually stop. Was Newton wrong ??????

• NO! On Earth, two forces are acting on that object. Gravity pulls it down toward the center of the Earth. This causes Friction (a rubbing between two surfaces). Friction acts to slow the object down (negative acceleration) causing it to stop. Friction is an external force acting on the object

• What would happen to an object set in motion in Outer Space where there is NO air or friction? Think about it!

Newton’s Second Law of MotionNewton looked at the relationship between the force exerted on

an object and what happened to the object.

Here’s what he saw:

EMPT

Y

FULL

If you exert a force on an object with a small mass, it begins to move quickly

If you exert the same force on an object with a large mass, it doesn’t move very quickly.

m ma aF F

Then Newton went grocery shopping one day (he wanted Fig Newtons)

and he saw another relationship between the force exerted on anobject and what happened to the object.Here’s what he saw:

It takes a little Force to push an empty cart (little mass).

It takes a great ForceTo push a full cart. (big mass)

F F

Most people accelerate at the same rate in shopping aisles.

m mAcceleration a Acceleration a

So, here’s what Newton decided:

For an object to accelerate (not just move), a force must be applied to it.

Bottom Line . . . .

Forces do NOT cause objects to MOVE.

Forces cause objects to ACCELERATE !

This means: move

Solving Problems withAccelerating Objects

F = 100N

m = 50kg

You push a box with a horizontal force. How fast does it accelerate?

Given:F = 100Nm = 50kga= ?

F = m*a100 = 50 (a)

a = 2 m/s2

Newton said:

What happens when more than one force is exerted on an object?

Question:

Answer:

We need to find the Net Force. - The Net Force is the vector sum of all the forces

acting on the object.

you need to add up both the magnitude AND the directionof every force to make ONE Resultant force.

The forces add up as vectors. The net force Fnet = 5The Fnet makes the box accelerate to the right.20 15

10 10

The Forces cancel each other out. Fnet = 0The box will not accelerate.

If the Net Force = o then neither team accelerates.

Net Force = FNet

Calculate the Fnet on the box.

Click for answer:

3.6N @ 56.3 degrees to the right of up

F = m a∙

My mass is 80 kg

My weight is 800 N

F = m a∙F = 80kg 9.81m/s∙ 2

F = 784.8 kg m/s∙ 2

F ≈ 800 N

mass

weightmass

Solving Problems with Newton’s 1st and 2nd Laws of Motion

2nd Law – Accelerating Bodies

F1 F2

m

Forces in a straight line Fnet = m a∙

1st Law – Non-Accelerating Bodies

Off-setting forces ina straight line

Fnet = 0

(@ rest or in motion)

Newton’s 2nd Law of Motion for accelerating bodies in 1 Dimension (all forces acting along a straight line)

F2F1

When forces are put on an object with mass, (remember that ALL objects have mass) the object will accelerate. (This means it will start, stop, or change direction.)

Remember, when there are two or more forces, you must compute the net force.

Newton’s Law should be more precisely stated as: FNet = m a∙

Newton’s 1st Law – Non-Accelerating Bodies @ rest in 1 Dimension (all forces acting along a straight line)

Consider an object hanging from a single rope suspended from a ceiling . . . (@ rest)

The box’s downward Force is called Weight. - Weight is caused by the effect of gravity pulling downward.

Since the object is not accelerating in any direction, Fnet = 0- Fnet = 0 means that all the forces cancel each other out.

The weight (downward Force) = mass a∙ g

- It is easier to use ag = 10m/s2 as an rough estimate.

Since the forces cancel out, the magnitude of the upward force of the rope pulling must equal that of the downward force. The direction will be opposite.- Fup = Fdown

Force in ropes/strings/chain/cable, etc. is called TENSION

This is called a system in Equilibrium (all forces are equal both horizontally and vertically)

Fup

Fdown

Fup

Fdown

Suppose the box is suspended from two vertical ropes instead of one.

What do we know ?

• The Fnet = 0 if the box is not accelerating. • The system is in equilibrium.• The ∑ Forces = 0• All forces up = All forces down ( F = F)

• If the mass of the box is 5kg, the weight is approximately 50N• The total Fdown = 50N so the total Fup = 50N• The force (or Tension) in each rope is 50/2 = 25N

m=5kg

Here’s a question for you:

You go mountain climbing. You bring a very long rope (Be careful, you bought it at the dollar store!) and 20kg of climbing equipment. Your mass is 80kg. The ropehas a breaking force of 400N.

How can you safely climb the mountain?

Here’s a thought experiment ( a Gedanken experiment )

Image two window cleaners on a scaffold as shown:

T1 T2

m1=100kg m2=100kg

What is the tension in each rope?

What is the tension in each rope ifPainter #2 moves to the center of the plank?

What is the tension in each rope ifPainter #2 stands next to Painter #1?

What would happen in each case if the rope’s breaking force is 1600N ?

- You can try this @ home with two bathroom scales . . . .

Newton’s 1st Law – Non-Accelerating Bodies in Motion in 1 Dimension (all forces acting along a straight line)

Remember it was believed by Aristotle that if an object was in motion, there was a net force on it. Galileo and Newton said he was WRONG !!!

If an object is in motion, but traveling with constant velocity, there is NO acceleration and hence NO Net Force !

Any forces acting on it will cancel each other out. ∑ Forces = 0

A 10,000kg plane travels at a constant velocity through the air. It’s engines put out 1200N of thrust.

• How much air resistance does the plane experience?

• What happens to the plane if it increases thrust to 1300N ?• Give me details . . .

Question: Are moving objects accelerating objects?

Consider this . . .

You push a lawnmower with 60N of force. It moves horizontally across your lawn with constant velocity.

• Is the lawnmower moving?

• Is the lawnmower accelerating?- what does this mean?

Q: what is the resisting horizontal force of friction on the lawnmower by the grass?

I Love to cut grass !

A: the exact same as the horizontal force applied to the mower, just in the opposite direction.

Newton’s Third Law of Motion

Lex III: Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi.

”

“ To every action there is always an equal and opposite reaction: or the forces of two bodies on each other are always equal and are directed in opposite directions.

The Law of Action / Reaction Pairs

Let’s start with the easy part . . . To every action there is always an equaland opposite reaction.

If you want to go forward, Newton said you have to push backward.

If you want to go up, you need to push down.

Very simply stated:

Forces always come in pairs - known as "action-reaction force pairs." Identifying and describing action-reaction force pairs is a simple matter of identifying the two interacting objects and making two statements describing who is pushing on whom and in what direction. For example, consider the interaction between a baseball bat and a baseball. The baseball forces the bat to the left; the bat forces the ball to the right. Together, these two forces form the action-reaction force pair.

Action-Reaction Pairs – no force acts alone.

You place a book on a table. The action is the force (weight) of the book pushing down on the table. The reaction is the force of the table pushing back up on the book.

FYI: This upward reaction force perpendicular to the plane of contact between two bodies is called the Normal Force. FN

You pull with 500 N on a rope tied to a brick wall. The action is the pulling force of 500N on the wall. The reaction is the pulling force of 500N back on you.

(Yes, the wall actually pulls back on you!)

What about the second part of the 3rd Law of Motion?

The forces of two bodies on each other are always equal and are directed in opposite directions.

Imagine two ice skaters pushing off from each other.

The force exerted on each other is identical except for direction. This means that each skater can only push the other with the same magnitude of force.

When you fire a rifle, the blast pushes the bullet forward with the same amount of force as the recoil pushes you back. The bullet just accelerates at a faster rate than you because of its smaller mass. Don’t forget Newton’s 2nd Law: F = m a∙

Only forces on you accelerate you. Forces you exert on other objects accelerate the other objects.

So then how does anything ever move if there are always equal and opposite forces?

Let’s consider a classic Physics example:

1. A hammer hits a nail into a block of wood. (Let’s say with a force of 50 N) the action force: the hammer exerts a force on the nail. the reaction force: the nail exerts an equal and opposite force on the hammer.

Let’s look at the forces ON each object involved . . .

50N Force on hammer by nail.

Fnet (hammer) = 50N causes hammer to stop.

5N Force on nail 50N Force on nailby wood. by hammer.

Fnet(nail) = 45N causes nail to accelerate into wood.

5N Force on wood by nail.

Fnet(wood) = 5N causes wood to accelerate.

Here’s another classic Physics Example of Newton’s 3rd Law of Motion:

Question: If the horse pulls on the cart with the same force that the cart pulls on the horse,How does they EVER move?

Answer: Again, look at each object alone and identify the forces ON that object.

Action Force: the horse pulls on the cart with 100N of Force.Reaction Force: the cart pulls on the horse with 100N of Force

Action Force: the horse pushes on the earth with 150N of Force.Reaction Force: the earth pushes on the horse with 150N of Force.

Earth Horse Cart150N on earth by horse. 150N on horse by ground 100N on cart by horse.

100N on horse by cart

Fnet = 150N Fnet = 50N Fnet = 100NEffect: earth accelerates Effect: horse accelerates Effect: cart accelerates

Aristotle believed that space travel was NOT possible because there were no air molecules to push against. Understanding Newton’s 3rd Law of Motion and the idea of equal and opposite forces, state how rockets can travel through space.

You are standing at the middle of an ice rink (very slippery) and cannot walk to the edge of the rink. You are holding a fire extinguisher. How could you get to the edge of the rink.

What happens when you punch a brick wall? How do you know?

How does a starting block work for track runners?

What happens when you hit an empty box of tissues. Describe the action/reaction force pairs.

Look at the picture below. Describe in your own words how the puller and toboggan can accelerate even with action/reaction pairs of forces.

Force Diagrams are also called Free Body Diagrams. They replace drawings with concise coordinate vectors.

Friction and the coefficient of Friction