Newton’s Laws

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F. Newton’s Laws of Motion

Kinematics is the study of how objects move, but not why they move.

Sir Isaac Newton turned his attention to Dynamics

Dynamics is the study of why an object moves the way that it does. Includes such concepts as: mass, force, momentum, kinetic force, etc.

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Newton’s First Law of Motion

also known as the Law of Inertia

“A body continues in its state of rest or uniform motion unless an external unbalanced force acts on it.”

In order to fully understand, we must look at force, inertia, and friction.

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Force

a force is a push or a pull exerted on an object.

This could result in starting, stopping, speeding up, slowing down, or changing direction.

A force depends on magnitude and direction, therefore it is a vector quantity.

often, there are several forces acting on a single object. The motion of the object is determined by the net effect of all forces.

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Inertia the property of a body that tends to resist a change in

its state if in rest or motion.Ex. If you are standing in a bus and it stops, you are

thrown forward. If the bus turns, you will be thrown to the side. A table cloth can be pulled from beneath a pile of plates.

In the first two situations, inertia wants to keep you moving at the same speed and direction. In the last situation, the plates are at rest, so they want to stay at rest.

Due to the inertia of matter, a moving body continues to move unless external forces stop it. This external force is usually friction.

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Unbalanced Force

most objects usually undergo several different forces

ex. Gravity, friction, normal, push/pull (external)

in order to study this, we need to review how to find the resultant force also known as the net force.

The symbol used is: Fnet

the rules for vector addition apply here!

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Sample Problems

1.Two forces of 5N [E] and 10N [E] are acting upon an object. Find the net force.

5N [E]

10N [E]

Fnet = F1 + F2

= 5N [E] + 10N [E]

= 15 N [E]

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2. Two boys pull in opposite directions on a toy. One pulls with a force of 15N [E] and the other with 5N [W]. Find the net force.

5N [W] 15N [E]

Fnet = F1 + F2

= 15N [E] + 5N [W]

= 10 N [E]

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3. For each case below, determine the net force and state its value (with a direction).

a. 12N 16N b. 8N

12N

8N

c. 15N 12N

8N

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Friction

is the extra force that is usually present when an object is moving on or through something.

If we can find out how large friction is, we can add it to the other forces.

The easiest type of friction to understand is when something slides over something else. (book over a desk)

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This type of friction is nearly constant.

Does not depend on speed

Does depend on the surface

Does depend on the force pushing them together

the rougher the surface and the larger the force pushing them together, the larger the force of friction.

friction always slows down an object, therefore as a vector, it should always be drawn opposite to the velocity vector.

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Newton’s Second Law of Motion

“ If an unbalanced force acts upon an object, then the object accelerates in the direction of the force and the acceleration so produced varies directly with the unbalanced force and inversely with the mass of the object.”

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Summary:

1) a F this means that if a stronger force is applied, the acceleration will be greater.

if the force weakens, the acceleration isn’t as great.

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2) a 1/m

this means that a heavier object will not accelerate as fast.

If acceleration increases, mass decreases (assuming that the force is constant).

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3)Putting these two proportions together, we get:

a F/m OR F = m a

Units F = m a

= (kg)(m/s2)

= 1 Newton

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Sample Problems

1. A mass of 4kg on a frictionless surface is given an acceleration of 3.8m/s2. What force was given to the object?

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2. A 12kg body falls at a downward acceleration of 9.8 m/s2. What force does the earth exert on the body?

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3. A car has a mass of 2000kg. When standing from rest, the motor can exert a force of 4.0 103N, which pushes the car forward. How quickly can the car accelerate?

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4. A worker applies a force of 400N [E] on an object with a mass of 50kg. If the frictional opposing force is 340N, what is the resulting acceleration of the object?

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Newton’s Third Law of Motion

States that to every action there is an equal and opposite reaction force.

Ex. 1) If a hand pushes on a table, the table exerts an equal force on the hand.

2) A person pushing off a boat causes the boat to accelerate away from the shore.

3) When a package is tossed by someone, the package exerts a force on the person which pushes the boat back slightly.

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