Physics chapter 4 1

Newton’s Laws

Chapter 4

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Newton’s Laws

Dynamics – causes of motion

Fundamental – from data, not other principles

Newtonian or classical mechanicsValid for most familiar kinds of motion

Not at very high speeds or very small sizes

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Force

A push or a pull

Contact force – involves direct contact between the two bodies

Done by your hand, a rope, friction, etc.

Long-range force – acts even when the bodies are separated by empty space

Done by gravity, magnets, etc.

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Force

A vector – has direction and magnitude – how much or how hard the force pushes or pulls

The SI unit of force is the newton, abbreviated N

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Newton’s 1st Law

A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration.Every body continues in its state of rest, or of uniform motion in a straight line, unless acted upon by an outside force.Inertia – property that causes this tendency

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Newton’s 1st law

Note that it is the net force that is important. Something with no net force acting on it can still have forces acting on it.If these forces cancel each other out, there is no net force.Example – book sitting on table

Weight and normal force

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Adding Forces

We use vector addition to add forces.

We can also split forces into their x and y components to make them easier to add.

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Example

Three boys are fighting over a ball at recess. They apply the following forces, as seen from above. Find the net force on the ball.

N 0.31 F

12

N 0.42 F

45

N 7.33 F

75

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On your own

If a fourth boy were to join in the fight, how hard and in what direction would he have to pull in order for the net force on the ball to be zero?

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Coordinate plane

You can set it wherever you want.

Often, when doing problems with ramps or inclines, you want to tilt the coordinate plane.

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Newton’s 2nd Law

What happens when the net force is not zero?

Acceleration

For a given body, the ratio of the magnitude of the net force to the magnitude of the acceleration is constant.

constanta

Fnetmass

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Newton’s 2nd law

maFnet

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Mass and force

Greater mass has greater inertia – it resists being accelerated more.

One N is the amount of force required to accelerate one kg of mass at 1 m/s2.

2s

m11kgN 1

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Mass and weight

Weight is the force of the earth’s gravitational attraction for a body.

Mass is a measure of inertia, weight is a measure of the force of gravity.

Objects with large mass also have large weight.

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Mass and weight

Weight acts on a body all the time, whether it is in free fall or not.

Example – book on table

mgw

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Weight variation by location

Your weight can vary by location, but your mass does not.

On the moon, g = 1.6 m/s2.

On the moon, astronauts weigh less, but have the same mass.

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Example

A given force produces an acceleration of 5 m/s2 on an object with mass of 1 kg.

When an equal force is applied to a carton of ice cream, it produces an acceleration of 11 m/s2. What is the mass of the carton of ice cream?

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On your own

You’re stranded in space away from your spaceship. Fortunately, you have a propulsion unit that provides a constant force F for 3 s. After 3 s you have moved 2.25 m. If your mass is 68 kg, find F.

Hint: you need to use a kinematics equation to find acceleration

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Example

A person in an elevator is holding a 10-kg block by a cord rated to withstand a tension of 150 N. When the elevator starts up, the cord breaks. What was the minimum acceleration in of the elevator?

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On your own

An object of mass m is suspended from the ceiling of an elevator that is descending with an acceleration of a. What is the tension in the string?

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Newton’s 3rd law

When two objects interact, the two forces they exert on each other are always equal in magnitude and opposite in direction.

Note – the two forces act on different objects

Aon BBon A FF

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Example

A horse refuses to pull a cart. The horse reasons, “according to Newton’s 3rd law, whatever force I exert on the cart, the cart will exert an equal and opposite force on me, so the net force will be zero and I will have no chance of accelerating the cart.” What is wrong with this reasoning?

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On your own

An advertisement claims that a particular automobile can “stop on a dime”. What net force would actually be necessary to stop a 850-kg automobile traveling initially at 45.0 km/h in a distance equal to the diameter of a dime, which is 1.8 cm?

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Normal force

Exerted by a surface

Perpendicular to the surface

Reaction force

For objects resting on horizontal surfaces, it is equal in magnitude to gravitational force.

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Gravity

The Earth exerts a gravitational force on you.

This makes you move towards the Earth

You exert an equal and opposite gravitational force on the Earth.

The Earth doesn’t move towards you because it is so big.

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Frame of reference

An observer with coordinate axes and instruments to measure distance and time

On a plane vs. on the ground

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Inertial frames of reference

Ones where Newton’s laws work

Ones that are not acceleratingNonexample - Force felt on a plane

Attached to the Earth (for simplicity)