Motion & ForcesMotion & ForcesLesson 3Lesson 3

Action and ReactionAction and Reaction Newton’s Third LawNewton’s Third Law MomentumMomentum Conservation of MomentumConservation of Momentum

Newton’s Third LawNewton’s Third Law Newton’s Third Law of MotionNewton’s Third Law of Motion

When one object exerts a When one object exerts a forceforce on a second object, the second on a second object, the second object exerts an object exerts an equalequal but but oppositeopposite force on the first. force on the first.

Newton’s Third LawNewton’s Third Law Problem:Problem:

How can a horse How can a horse pull a cart if the cart pull a cart if the cart is pulling back on is pulling back on the horse with an the horse with an equalequal but but oppositeopposite force? force?

NO!!!

Aren’t these “Aren’t these “balancedbalanced forces” resulting in no forces” resulting in no acceleration?acceleration?

Newton’s Third LawNewton’s Third Law

forces are equal and opposite forces are equal and opposite but act on but act on differentdifferent objects objects

they are they are notnot “balanced forces” “balanced forces” the the movementmovement of the horse of the horse

depends on the depends on the forcesforces acting acting on the horse

Explanation:Explanation:

Action and Reaction Action and Reaction

When a When a forceforce is applied in nature, a is applied in nature, a reaction force occurs at the same reaction force occurs at the same time.time.

When you jump on a trampoline, for When you jump on a trampoline, for example, you exert a example, you exert a downwarddownward force on the trampoline.force on the trampoline.

Simultaneously, the trampoline Simultaneously, the trampoline exerts an equal force exerts an equal force upwardupward, , sending you high into the air. sending you high into the air.

Action and Reaction Action and Reaction Forces Don’t Cancel Forces Don’t Cancel

According to the third law of motion, According to the third law of motion, action and reaction forces act on action and reaction forces act on differentdifferent objects. objects.

Thus, even though the forces are Thus, even though the forces are equalequal, they are not balanced , they are not balanced because they act on different because they act on different objects.objects.

Action and Reaction Action and Reaction Forces Don’t Cancel Forces Don’t Cancel

For example, a swimmer “For example, a swimmer “actsacts” on ” on the water, the “the water, the “reactionreaction” of the ” of the water pushes the swimmer forward. water pushes the swimmer forward.

Thus, a net force, or Thus, a net force, or unbalancedunbalanced force, acts on the swimmer so a force, acts on the swimmer so a change in his or her motion occurs. change in his or her motion occurs.

Rocket PropulsionRocket Propulsion

In a rocket engine, burning fuel In a rocket engine, burning fuel produces hot gases. The rocket produces hot gases. The rocket engine exerts a force on these gases engine exerts a force on these gases and causes them to and causes them to escapeescape out the out the back of the rocket.back of the rocket.

By Newton’s third law, the By Newton’s third law, the

gases exert a force on the gases exert a force on the

rocket and rocket and pushpush it forward. it forward.

Newton’s Third LawNewton’s Third Law

Action-Reaction PairsAction-Reaction PairsThe hammer The hammer exertsexerts a force a force on the nail to on the nail to the right.the right.

The nail exerts The nail exerts an equal but an equal but oppositeopposite force force on the hammer on the hammer to the left.to the left.

MomentumMomentum

A moving object has a property A moving object has a property called momentum that is related to called momentum that is related to how much force is needed to change how much force is needed to change its its motionmotion..

The The momentummomentum of an object is the of an object is the product of its mass and velocityproduct of its mass and velocity

Momentum is given the symbolMomentum is given the symbol pp and and can be calculated with the following can be calculated with the following equation: equation:

MomentumMomentum

MomentumMomentum quantityquantity of motion of motionp = mv

p: momentum (kg·m/s)m: mass (kg)v: velocity (m/s)m

p

v

• Use the unit Use the unit kg·m/skg·m/s

Force and Changing Force and Changing Momentum Momentum

By By combiningcombining these two these two relationships, Newton’s second law relationships, Newton’s second law can be written in this way: can be written in this way:

In this equation In this equation mvmvff is the final is the final momentum and momentum and mvmvii is the initial is the initial momentummomentum

Law of Conservation of Law of Conservation of Momentum Momentum

The momentum of an object doesn’t The momentum of an object doesn’t change unless its mass, change unless its mass, velocityvelocity, or , or both change.both change.

Momentum, however, can be Momentum, however, can be transferredtransferred from one object to another. from one object to another.

The law of conservation of momentum The law of conservation of momentum states that if a group of objects exerts states that if a group of objects exerts forces only on each other, their total forces only on each other, their total momentum momentum doesn’tdoesn’t change. change.

Law of Conservation of Law of Conservation of MomentumMomentum

• The results of a collision depend on The results of a collision depend on the the momentummomentum of each object. of each object.

When the first puck hits the second When the first puck hits the second puck from behind, it gives the second puck from behind, it gives the second puck momentum in the same puck momentum in the same directiondirection..

When Objects CollideWhen Objects Collide • If the pucks are speeding toward If the pucks are speeding toward

each other with the same speed, each other with the same speed, the total momentum is the total momentum is zerozero..

Newton’s Third LawNewton’s Third Law

Action-Reaction PairsAction-Reaction Pairs Both objects Both objects accelerateaccelerate.. The amount of acceleration depends The amount of acceleration depends

on the on the massmass of the object. of the object.

a Fm

Small mass Small mass more acceleration more acceleration Large mass Large mass less acceleration less acceleration

Conservation of MomentumConservation of Momentum

Law of Conservation of Law of Conservation of MomentumMomentum The total momentum in a group The total momentum in a group

of objects doesn’t change unless of objects doesn’t change unless outside outside forcesforces act on the objects. act on the objects.

pbefore = pafter

Conservation of MomentumConservation of Momentum ElasticElastic Collision Collision

KE is conservedKE is conserved

InelasticInelastic Collision CollisionKE is not conservedKE is not conserved

MomentumMomentum Find the momentum of a bumper car if it Find the momentum of a bumper car if it

has a total mass of 280 kg and a velocity of has a total mass of 280 kg and a velocity of 3.2 m/s. 3.2 m/s.

GIVEN:

p = ?m = 280 kgv = 3.2 m/s

WORK:p = mv

p = (280 kg)(3.2 m/s)

p = 896 kg·m/s

m

p

v

MomentumMomentum The momentum of a second bumper car is The momentum of a second bumper car is

675 kg·m/s. What is its velocity if its total 675 kg·m/s. What is its velocity if its total mass is 300 kg? mass is 300 kg?

GIVEN:

p = 675 kg·m/sm = 300 kgv = ?

WORK:v = p ÷ m

v = (675 kg·m/s)÷(300 kg)

v = 2.25 m/sm

p

v

Conservation of MomentumConservation of Momentum A 5-kg cart traveling at 1.2 m/s strikes a A 5-kg cart traveling at 1.2 m/s strikes a

stationary 2-kg cart and they connect. Find stationary 2-kg cart and they connect. Find their speed after the collision. their speed after the collision.

BEFORECart 1:m = 5 kgv = 4.2 m/s

Cart 2 :m = 2 kgv = 0 m/s

AFTERCart 1 + 2:m = 7 kgv = ?

p = 21 kg·m/s

p = 0

pbefore = 21 kg·m/s pafter = 21 kg·m/s

m

p

vv = p ÷ mv = (21 kg·m/s) ÷ (7 kg)v = 3 m/s

Conservation of MomentumConservation of Momentum A 50-kg clown is shot out of a 250-kg A 50-kg clown is shot out of a 250-kg

cannon at a speed of 20 m/s. What is the cannon at a speed of 20 m/s. What is the recoil speed of the cannon? recoil speed of the cannon?

BEFOREClown:m = 50 kgv = 0 m/s

Cannon:m = 250 kgv = 0 m/s

AFTERClown:m = 50 kgv = 20 m/s

Cannon:m = 250 kgv = ? m/s

p = 0

p = 0

pbefore = 0

p = 1000 kg·m/s

pafter = 0

p = -1000 kg·m/s

Conservation of MomentumConservation of Momentum So…now we can solve for velocity. So…now we can solve for velocity.

GIVEN:

p = -1000 kg·m/sm = 250 kgv = ?

WORK:v = p ÷ m

v = (-1000

kg·m/s)÷(250 kg)

v = - 4 m/s (4 m/s backwards)

m

p

v

Rocket ChallengeRocket Challenge

After I check your fill in the blank After I check your fill in the blank notes. Come and get the instructions notes. Come and get the instructions for the paper rockets. Depending on for the paper rockets. Depending on time you might have time to do all 3. time you might have time to do all 3. If not you will complete them on If not you will complete them on Tuesday.Tuesday.

You will use the best design and You will use the best design and make it for your larger one we will do make it for your larger one we will do next week.next week.