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### Newton’s Second Law

How the apple fell from the tree…

The second Law

F= m x a

History

- Isaac Newton was one of the world’s great scientists. He combined his ideas and the ideas of earlier scientists, such as Galileo, into a unified picture of how the universe works.
- Isaac Newton explained the workings of the universe through mathematics. He formulated laws of motion and gravitation. These laws are math formulas that explain how objects move when a force acts on them. Principia, his most famous book, explained three basic laws that govern the way objects move. These three laws are known as Newton’s Laws.

http://cascooscuro.files.wordpress.com/2007/08/sir_isaac_newton_1643-1727.jpg

What is a force?

A force is a push or a pull on any object with a mass.

The second law States that the sum of all the forces pushing or pulling the object is directly proportional to how fast the object is speeding up.

History

- Newton’s First law of Motion

I. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.

- Newton\'s Second Law of Motion:

II. The relationship between an object\'s mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (as indicated by their symbols being displayed in slant bold font); in this law the direction of the force vector is the same as the direction of the acceleration vector.

- Newton\'s Third Law of Motion:

III. For every action there is an equal and opposite reaction.

What is a Force?

- If an object is speeding up at a constant rate, then a force is being exerted on the object.

http://www.mirage-replicas.co.uk/img/Race.jpg

What is the net force?

This is the most powerful of Newton\'s three Laws, because it allows us to calculate how objects move: It allows us to relate what moves to why it moves.

It also answers how and why speeds change when forces are applied

How do we measure Force?

- Forces are measured using the units of mass and acceleration combined. The SI standard unit of force is the Newton, N. In America, the standard unit of measure of weight is pounds, or lbs.

Weight

- Weight is a force acting down on a mass
- Your weight is the force that the earth exerts on you to keep you on the ground. The Earth exerts gravity that pulls you down.

http://www.3dnworld.com/users/1/images/UltimateEarth.jpg

If a rope attached to an object pulls with a force of 24 newtons and the mass of the object is 6 kg, how fast is the object speeding up?

24 N = (6kg) x acceleration

24 / 6 = acceleration = 4 m/s2

6 Kg

Atwood’s Machine

Atwood’s machine is a simple machine allows us to calculate gravity and mass.

Concept of Atwood’s Machine

Greater weights will cause the machine to accelerate in the direction of that weight.

What forces are acting on each individual mass?

Tension in rope

Gravity is the only force “pulling” on the lager mass.

For the smaller mass, gravity pulls down and the rope pulls up.

Weight of smaller mass

Weight of larger mass

Concept of Atwood’s Machine

The system accelerates in the direction with the heaviest weight. Is this in concord with the laws of gravity and balance?

1 kg

2 kg

What about friction?

Friction is defined as the resistant force between two objects’ nonsmooth surfaces

It always acts against an object.

What about friction?

- Imagine a wooden brick tied to a weight on a horizontal table. If the weight is hung over the edge of the table, the wooden brick will accelerate in the direction the string is being pulled (horizontally).

String

Block

Table

What about friction?

In this scenereo, gravity is not the only force acting on the block-weight system. Friction is also exerting a force opposite that of gravity.

String

Block

Friction

Table

Weight exerted by gravity

What about friction?

- That means that friction is acting against the pull of the string and the direction of the motion.
- What can you conclude about the relationship between gravity and the net acceleration by adding in friction?

Practice Problems

- Try some problems on your own:

Practice Problems

- An apple that has a mass of 2 kg falls with a net acceleration of 2m/s2 from the largest tree in the world. Air resistance also acts on the apple. What is the total force acting on the apple? How does this compare to the apple’s weight on the ground? What if there was no air resistance?

Practice answers

- We can set up our equation using what we know from Newton’s second law

Force = mass x acceleration

So:

Force = (2kg) x (2m/s2)

Force = 4N

Practice answers

- The weight of the object on the ground is:

(mass) x (gravity)

This is equal to:

(2kg) x (9.81 m/s2)

We can conclude that the apple’s weight is greater than the force acting on the apple in the air

Practice answers

- If there was no air resistance, the apple would fall with an acceleration of gravity, 9.81 m/s2, and the force acting on the apple in the air would be equal to that of the apple’s weight on the ground.

Practice Problems

- Two monster dogs pull on an 80 kg rope. Monster dog #1, Pepe, pulls to the left with a force of 12 N. Jumbo, monster dog # 2, pulls to the right with a force of 6 N. How fast is the rope speeding up and in what direction?

Practice answers

First we must find the direction of each force.

One dog pulls to the left, the other dog pulls to the right.

Pepe

Jumbo

Practice answers

- Both dogs pull in opposite directs so the total force is the result of one force subtracted from the other

Practice answers

- We know the mass of the rope is 80 kg, so:

12N - 6N = (80kg) x a

6N = (80kg) x a

a=0.075 m/s2

_

+

6N

12N

80 kg

References

- http://csep10.phys.utk.edu/astr161/lect/history/newton3laws.html
- http://en.wikipedia.org/wiki/Image:Atwoodmachine.gif
- http://www.dictionary.com

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