Notes

Units	Newton's First Law of Motion	Mass and Weight	Friction
Frames of Reference Discussion	Newton's Second Law of Motion	g and the Normal Force	Videos
Inertial Reference Frames	Newton's Third Law of Motion	Free Body Diagrams

Units

Item	Units
Mas (quantity of matter)	kilogram (kg)
Force (push or pull on an object)	newton (N) kg · m/s²
Weight (pull of gravity on an object)	newton

Notes

n A newton is the force required to impart an acceleration of 1 m/s² to a mass of 1 kg

n Weight = mg, so the weight of a 1 kg mass on Earth would b 1 kg(9.80 m/s²) = 9.80 kg m/s² = 1 N

n Weight is a force

n The mass of an object does not depend on g (it is the quantity of matter, which is not affected by g)

n The weight of an object does depend on g - you would weight less on the Moon even though your mass remains constant

Newton's First Law of Motion

Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it.

This law is often called the law of inertia, where inertia is the tendency of an object to maintain its state of rest or uniform motion in a straight line.

Inertial Reference Frames

A reference frame or coordinate system in which there are no accelerations, only zero or uniform motion in a straight line – in other words, in which the first of Newton's laws of motion is valid. According to the special theory of relativity, it is impossible to distinguish between such frames by means of any internal measurement. For example, no measurements made inside a spaceship traveling at high speed (even close to the speed of light) relative to some locally agreed stationary frame, such as the Earth, can show different results from similar measurements made when the ship is at rest relative to the local stationary frame.

Newton viewed the first law as valid in any reference frame moving with uniform velocity relative to the fixed stars;that is, neither rotating nor accelerating relative to the stars.

Today the notion of "absolute space" is abandoned, and an inertial frame is defined as

One in which the motion of a particle not subject to forces is a straight line.

This can be interpreted to be one in which Newton's' first law applies.

A reference frame in an accelerating car, for example, is not an inertial reference frame.

A reference frame attached to one of the seats on the left is also not an inertial reference frame.

Newton's Second Law of Motion

The acceleration of an object is directly proportional to the net force acting on it, and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object. This can be written as an equation as follows.

Newton's Third Law of Motion

Whenever one object exerts a force on a second object, the second object exerts an equal for in the opposite direction on the first.

Said another way, for every action there is an equal and opposite reaction.

Consider the flying motion of birds. A bird flies by use of its wings. The wings of a bird push air downwards.

Since forces result from mutual interactions, the air must also be pushing the bird upwards. The size of the force on the air equals the size of the force on the bird; the direction of the force on the air (downwards) is opposite the direction of the force on the bird (upwards).

For every action, there is an equal (in size) and opposite (in direction) reaction.

Action-reaction force pairs make it possible for birds to fly.

Questions answers

First Question

A rifle recoils when fired. This recoil is the result of action-reaction force pairs. A gunpowder explosion creates hot gases which expand outward allowing the rifle to push forward on the bullet. Consistent with Newton's third law of motion, the bullet pushes backwards upon the rifle. The acceleration of the recoiling rifle is ...

a. greater than the acceleration of the bullet

b. smaller than the acceleration of the bullet

c. the same size as the acceleration of the bullet

Second Question

While driving down the road, a firefly strikes the windshield of a bus and makes a quite obvious mess in front of the face of the driver. This is a clear case of Newton's third law of motion. The firefly hit the bus and the bus hits the firefly.

Which of the two forces is greater: the force on the firefly or the force on the bus?

Mass and Weight

Mass is a measure of the inertia of an object. It is the quantity of matter contained in the object.

Mass is sometimes confused with weight. Your mass is the same wherever you are--on Earth, on the moon, floating in space--because the amount of stuff you're made of doesn't change. But your weight depends on how much gravity is acting on you at the moment; you'd weigh less on the moon than on Earth, and in interstellar space you'd weigh almost nothing at all.

The SI unit of mass is the kilogram (kg).

Weight = massxgravity

Normal Force and g

When a contact force acts perpendicular to a common surface of contact, it is referred to a s normal force.

For example, an object resting on a table would be subjected to g, directed downward. The normal force, supplied by the table on the object, is directed up.

Free Body Diagrams

When solving problems involving Newton's laws and force, it is often very useful to draw a diagram showing all fores acting on each object. Such a diatgram is called a free-body diagram.

Drawing

n Select an object or group of objects to focus on as the "body", i.e. the system.

n Sketch the body by itself, "free" of its surroundings. The body could be represented by a single point located at the body's center of mass.

n Draw only those forces that are acting directly on the body. Include both the magnitude and the direction of these forces.

n Except for rotational problems, you can normally sketch the forces as though they were acting through a single point at the center of mass of the body.

It is useful to draw the force-vectors with their tails at the center of mass.

n Do not include any forces that the body exerts on it surroundings, they do not act on the body. However, there is always an equal reaction force acting on

the body.

n For a compound body you do not need to include any internal acting between the body's subparts, since these internal forces come in action-reaction pairs

which cancel each other out because of Newton's Third Law.

n Choose a coordinate system and sketch it on the free-body diagram. If you choose one of the axes to be parallel to the object's acceleration, it can

sometimes simplify the equations you have to solve.

Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation. A free-body diagram is a special example of the vector diagrams discussed earlier.

The size of the arrow in a free-body diagram is reflects the magnitude of the force. The direction of the arrow shows the direction which the force is acting.

Each force arrow in the diagram is labeled to indicate the exact type of force. It is generally customary in a free-body diagram to represent the object by a box and to draw the force arrow from the center of the box outward in the direction which the force is acting.

An example of a free-body diagram is shown at the right.

The free-body diagram above depicts four forces acting upon the object. Objects do not necessarily always have four forces acting upon them. There will be cases in which the number of forces depicted by a free-body diagram will be one, two, or three. There is no hard and fast rule about the number of forces which must be drawn in a free-body diagram. The only rule for drawing free-body diagrams is to depict all the forces which exist for that object in the given situation.

Friction

There are two forms of friction, kinetic and static.

If you try to slide two objects past each other, a small amount of force will result in no motion.

The force of friction is greater than the applied force. This is static friction.

If you apply a little more force, the object "breaks free" and slides, although you still need to apply force to keep the object sliding. This is kinetic friction.

You do not need to apply quite as much force to keep the object sliding as you needed to originally break free of static friction.

m_s = coefficient of static friction

m_k = coefficient of kinetic friction

Some typical coefficients are listed below

Surfaces	µ (static)	µ (kinetic)
Steel on steel	0.74	0.57
Glass on glass	0.94	0.40
Metal on Metal (lubricated)	0.15	0.06
Ice on ice	0.10	0.03
Teflon on Teflon	0.04	0.04
Tire on concrete	1.00	0.80
Tire on wet road	0.60	0.40
Tire on snow	0.30	0.20

Videos

Newton's Third Law: http://www.scienceforamerica.com/technology-integration/video-demo-newtons-3rd-law.html

Newton's Three Laws: http://teachertech.rice.edu/Participants/louviere/Newton/law1.html (no video - animated)

Answers Return

1. The force on the rifle equals the force on the bullet. Yet, acceleration depends on both force and mass. The bullet has a greater acceleration due to the fact that

it has a smaller mass. Acceleration and mass are inversely proportional. Acceleration = F/m

2. Each force is the same size. For every action, there is an equal ... (equal!). The fact that the firefly splatters only means that with its smaller mass, it is less

able to withstand the larger acceleration resulting from the interaction.