Newton's Laws of Motion

Newton’s First Law

  An object at rest tends to stay at rest and an object in motion tends to stay in motion unless acted upon by an unbalanced force. 

What does this mean?

An object will “keep doing what it was doing” unless acted on by an unbalanced force.

If the object was sitting still, it will remain stationary.  If it was moving at a constant velocity, it will keep moving.

It takes force to change the motion of an object.

What is meant by unbalanced force?

If the forces on an object are equal and opposite, they are said to be balanced, and the object experiences no change in motion.  If they are not equal and opposite, then the forces are unbalanced and the motion of the object changes.

Some Examples from Real Life for the first law of motion

1. A soccer ball is sitting at rest. It takes an unbalanced force of a kick to change its motion.

2. Two teams are playing tug of war. They are both exerting equal force on the rope in opposite directions. This balanced force results in no change of motion.

Newton’s First Law is also called the Law of Inertia

Inertia: the tendency of an object to resist changes in its state of motion.

The First Law states that all objects have inertia.  The more mass an object has, the more inertia it has (and the harder it is to change its motion).

If objects in motion tend to stay in motion, why don’t moving objects keep moving forever?

Things don’t keep moving forever because there’s almost always an unbalanced force acting upon it, especially on Earth.

1. A book sliding across a table slows down and stops because of the force of friction.

2. If you throw a ball upwards it will eventually slow down and fall because of the force of gravity.

Newton’s Second Law

Force equals mass times acceleration.

F = ma

Force: the push or pull on an object

Acceleration: a measurement of how quickly an object is changing speed or direction

Mass: the amount of matter in an object

What does F = m * a mean?

F = m * means that the force of an object comes from its mass and acceleration. 

Something massive (m) that’s changing speed slowly (a), like a glacier, can still have great force (F).

Something of little mass (m) that’s changing speed quickly (a), like a bullet, can still have a great force (F). 

A low-mass object (m) changing speed slowly (a) will have very little force (F).

How do the components of F = m * a relate?

Force is directly proportional to mass and acceleration.

Imagine a ball of a certain mass moving at a certain

acceleration. This ball has a certain force.  

Next, imagine we make the ball twice as big (double the mass) but keep the acceleration constant.

Finally, imagine the original ball moving at twice the original acceleration.  

How they relate: F = m * a

If you double the mass, you double the force. 

If you double the acceleration, you double the force.

What if you double the mass and the acceleration?

Doubling the mass and the acceleration quadruples the force.

(2m)(2a) = 4F

What if you decrease the mass by half? How much force would the object have now?

(½ m) (a) = ½F

Algebra and the 2nd Law

You can rewrite the formula like this:

a = F/m

Acceleration of an object produced by a net force is directly proportional to the magnitude of the net force and in the same direction.

Acceleration is inversely proportional to the mass of an object.

Newton’s Third Law

For every action there is an equal and opposite reaction.

What does this mean about the third law?

For every force acting on an object, there is an equal force acting in the opposite direction. Right now, gravity is pulling you down in your seat, but Newton’s Third Law says your seat is pushing up against you with equal force. This is why you are not moving. There is a balanced force acting on you– gravity pulling down, your seat pushing up.

Momentum Formula

p = m * v

p = momentum

m = mass

v = velocity

Momentum Units

p = kg * m/s

m = kg
v = m/s (in a given direction)

Momentum Question

p = ?

m = 10 kg
v = 5 m/s south

Momentum Answer

p = 50 kg * m/s, south

Review of the Three Laws

Newton’s First Law:

1. Objects in motion tend to stay in motion and objects at rest tend to stay at rest unless acted upon by an unbalanced force.

Newton’s Second Law:

1. Force equals mass times acceleration F = m * a

Newton’s Third Law:

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

Weight versus Mass

• Weight is the measure of the force of gravity on an object

• Mass is the amount of matter in an object

• Your weight will change depending on the force of gravity

  • On the Moon, you weigh less

  • On Jupiter, you weigh more

• Your mass does not change. It would be the same on both the Moon and Jupiter.

Weight versus Mass

• f you weigh 60 kg (~ 132 lb) on Earth, what would you weigh on Jupiter?

• On Earth the formula is F = m * 9.8 m/s²

• On Jupiter the formula is F = m *  24.5 m/s²

• To calculate your weight:

• 60 kg/9.8 m/s² * 24.5 m/s²

Weight

60 kg (~ 132 lb) on Earth = 150 kg (~ 330 lb) on Jupiter

Vocabulary

Force: push or pull on an object

Friction: the force that opposes motion

Mass: how much matter is in an object

Weight: the measure of the force of gravity on an object

Velocity: speed in a given direction

Acceleration: a change in speed or direction or both