Newton’s Third Law of Motion

Momentum and The Conservation of Momentum

Newton’s Third lawMomentum

For every action there is an equal and opposite reaction.

Forces always come in pairs:

Action force

Reaction force

The Third Law: Action/Reaction

Newton’s Third Law states that every action force creates a reaction force that is equal in strength and opposite in direction.

There can never be a single force, alone, without its action-reaction partner.

Action/reaction pairs

Identifying Action and Reaction Pairs

Both are always there when a force appears

They always have the exact same strength

They always act in opposite directions

They always act on different objects

Both are real forces and either can cause acceleration

Momentum

Newton’s third law tells us that any time two objects hit each other, they exert equal and opposite forces on each other.

The effect of the force is not always the same.

Momentum

If two kids on skateboards are moving toward you and each one has a mass of 40 kg.

One is moving at 10 m/sec and the other is moving at 20 m/sec, which one is harder to stop? Why?

Momentum

Momentum is the mass of an object multiplied by its velocity.

This explains why faster moving objects are harder to stop.

It also explains/illustrates why objects with more mass are harder to stop.

Explain how inertia is related to Newton’s Third Law and Momentum. Use complete sentences!

Momentum; formula and units

Note the units for momentum are kg m/sec which is quite different that what we are used to!!

Impulse

Impulse

Momentum of an object can change

That happens when the velocity of the object changes

Since force is what changes an object’s velocity, that means that force is ALSO responsible for changing momentum.

A change in momentum is created by a force exerted over time which is called an impulse

Impulse

Impulse is = Force x timeImpulse = Ft (Nsec)

Impulse = change in momentumThis is a conservation of

energy law

Momentum and Impulse

Note that the momentum before she hits the ball is -3 kg m/sec

The impulse is the force applied for .1 sec

The new momentum is 3 kg m/sec because

The change in momentum is 6 N sec

The change in momentum MUST equal the impulse

If a 500 kg car is traveling at 45 m/sec, what is the momentum of the car?

If a 15 N force is applied to a baseball for .3 seconds, what is the impulse applied to that ball?

Change in Momentum

Change in Momentum =

Final Momentum – Initial Momentum

or

-

Impulse is equal to change in momentum

Impulse

The change in momentum is often referred to as impulse.

We can use this relationship to solve equations using changes in mass or velocity.

How do you find the change in momentum of an object? Explain in your own words.

If an impulse of 2 N sec is applied to an object, what is its change in momentum?

Momentum and the third law

If we combine Newton’s third law with the relationship between force and momentum, the result is a powerful new tool for understanding motion.

If you stand on a skateboard and throw a 5 kg ball, with a velocity of 4 m/s, you apply a force to the ball.

That force changes the momentum of the ball.

If the ball gains +20 kg·m/s of forward momentum, you must gain –20 kg·m/s of backward momentum assuming there is no friction.

1. Looking for: …the velocity of the astronaut after throwing the hammer.

2. Given: … the mass of the hammer (2 kg) and the velocity of the hammer (15 m/s) and the mass of the astronaut (60 kg).

3. Relationships: The total momentum before the hammer is thrown must be the same as the total momentum after it is thrown.

momentum (p) = mass (m) × velocity (v)

A negative sign indicates the velocity is to the left.

An astronaut floating in space throws a 2-kilogram hammer to the left at 15 m/s. If the astronaut’s mass is 60 kilograms, how fast does the astronaut move to the right after throwing the hammer?

Solution: Both the astronaut and hammer were initially at rest, so the initial momentum was zero. Use subscripts a and h to distinguish between the astronaut and the hammer.

momentum after + momentum before = 0mava + mhvh = 0

Substitute the known quantities:(60 kg)(va) + (2 kg)(–15 m/s) = 0

Solve:(60 kg)(va) = +30 kg·m/s

va = +0.5 m/s

The astronaut moves to the right at a velocity of 0.5 m/s.

Solve these Problems

1. You throw a basketball in one direction with 20 Newtons of force. Newton’s Third Law states that there is an equal and opposite force. If there are two equal forces applied, how is it that the ball “accelerates”?

2. If a hockey player has a mass of 60 kg and is moving with a velocity of 3 m/sec, what is his momentum?

3. If the same hockey player experiences an impulse of 2 N sec, what will his “change in momentum” be?

Problems continued

If there is a hockey player with a mass of 60 kg and he experiences a force of 2 N for .2 seconds, what will his change in momentum be?

Using the information from above, what is the initial velocity of the player if his final velocity is 5 m/sec?

Problems continued

1. If a 15 N force is applied, for 10 seconds, to a 1 kg ball that is initially at rest, what is the ball’s final momentum?

(hint, you need to consider the ball’s change in momentum and impulse)

2. How much time should a 100 N force be applied to increase a 10 kg car’s velocity from 10 m/sec to 100 m/sec?

Units of energy

Pushing a 1-kilogram object with a force of one newton for a distance of one meter uses one joule of energy.

n A joule (J) is the S.I. unit of measurement for energy.

Potential energy

Systems or objects with potential energy are able to exert forces (exchange energy) as they change.

Potential energy is energy due to position.

Potential energy

A stretched spring has potential energy.

If released, the spring will use this energy to move itself and anything attached to it back to its original length.

Kinetic energy

Energy of motion is called kinetic energy.

A skateboard and rider have kinetic energy because they can hit other objects and cause change.

The amount of kinetic energy is equal to the amount of work the moving board and rider do as they come to a stop.

Kinetic Energy

EK = ½ mv2

mass of object (kg)

velocity (m/sec)

KE (joules)

Conservation of Energy

The law of energy conservation says the total energy before the change equals the total energy after it.

A 2-kg car moving with a speed of 2 m/s starts up a hill. How high does the car roll before it stops?

Potential and kinetic energy

1. Looking for: … the height.

2. Given: …the car’s mass (2 kg), and initial speed (2 m/s)

3. Relationships: The law of conservation of energy states that the sum of the kinetic and potential energy is constant. The ball keeps going uphill until all of its kinetic energy has been turned into potential energy.

Potential and kinetic energy

Solution:

Find the kinetic energy at the start:

EK = (½)(2 kg)(2 m/s)2 = 4 J

Use the potential energy to find the height:

EP = 4 J = mgh

Therefore:

h = (4 J) ÷ (2 kg)(9.8 N/kg) = 0.2 m

The car rolls to a height of 0.2 m above where it started.

CollisionsThere are two

main types of collisions, elastic and inelastic.

When an elastic collision occurs, objects bounce off each other with no loss in the total kinetic energy of the system.

Collisions

In an inelastic collision, objects change shape or stick together, and the total kinetic energy of the system decreases.

An egg hitting the floor is one example of an inelastic collision.

An 8,000-kg train car moves to the right at 10 m/s. It collides with a 2,000-kg parked train car. The cars get stuck together and roll along the track. How fast do they move after the collision?

Momentum and collisions

1. Looking for: … the velocity of the train cars after the collision.

2. Given: … both masses (m1= 8,000 kg; m2= 2000 kg) and the initial velocity of the moving car (10 m/s). You know the collision is inelastic because the cars are stuck together.

Momentum and collisions

Relationships: Apply the law of conservation of momentum. Because the two cars are stuck together, consider them to be a single larger train car after the collision (m3). The final mass is the sum of the two individual masses: initial momentum of car1 + initial momentum of car2 = final momentum of combined cars.

m1v1 + m2v2 = (m1+ m2)v3

Solution: (8,000 kg)(10 m/s) + (2,000 kg)(0 m/s) = (8,000 kg + 2,000

kg)v3

v3 = 8 m/s.

The train cars move together to the right at 8 m/s.

Newton’s 2nd law and circular motion

An object moving in a circle at a constant speed accelerates because its direction changes.

How quickly an object changes direction depends on its speed and the radius of the circle.

Centripetal acceleration increases with speed and decreases as the radius gets larger.

Centripetal Acceleration

Acceleration is the rate at which an object’s velocity changes as the result of a force.

Centripetal acceleration is the acceleration of an object whose direction and velocity changes.

Newton’s 2nd law and circular motion

Newton’s second law relates force, mass, and acceleration.

The strength of the centripetal force needed to move an object in a circle depends on its mass, speed, and the radius of the circle.

1. Centripetal force is directly proportional to the mass. A 2-kg object needs twice the force to have the same circular motion as a 1-kg object.

Newton’s 2nd law and circular motion

Centripetal force is inversely proportional to the radius of its circle.

The smaller the circle’s radius, the greater the force.

An object moving in a 1 m circle needs twice the force it does when it moves in a 2 m circle at the same speed.

Universal Gravitation and Orbital Motion

Sir Isaac Newton first deduced that the force responsible for making objects fall on Earth is the same force that keeps the moon in orbit.

This idea is known as the law of universal gravitation.

Gravitational force exists between all objects that have mass.

The strength of the gravitational force depends on the mass of the objects and the distance between them.

Gravitational force

The force of gravity between Earth and the Sun keeps Earth in orbit.

Gravitational force

You notice the force of gravity between you and Earth because the planet’s mass is huge.

Gravitational forces tend to be important only when one of the objects has an extremely large mass, such as a moon, star, or planet.

The gravitational force

The force of gravity between two objects is proportional to the mass of each object.

The distance between objects, measured from center to center, is also important when calculating gravitational force.

Law of universal gravitation

Newton’s law of universal gravitation gives the relationship between gravitational force, mass, and distance.

The gravitational constant (G) is the same everywhere in the universe (6.67 × 10–11 N·m2/kg2)

Law of universal gravitation

The gravitational force of Earth on the Moon has the same strength as the gravitational force of the Moon on Earth.