momentum and its conservation

MOMENTUM & ITS CONSERVATION

Chapter 9

The inertia of motion

Momentum Every moving object has momentum.

- Measure of HOW HARD IT WILL BE ABLE TO STOP A MOVING OBJECT.

Momentum = Mass x Velocity•Equation: p = m x v• Unit: kg*m/s

What is the relationship of momentum to mass and

velocity of objects?

• Mass and velocity are both directly proportional to the momentum.

If the boulder and the boyhave the same momentum,will the boulder crush the boy?

Hint:  think about the momentum formula!

p = mv

IMPULSE CHANGES MOMENTUM

• TO STOP/SLOW DOWN A MOVING OBJECT - apply force to an object

• IMPULSE – average net force exerted on the object multiplied by the time interval over which the force acts (application of force over a period of time)

• Equation: Impulse = FΔt• Unit: N.s

Impulse-momentum Theorem

The force in the baseball increases then it decreases with collision

FΔt = pf − pi

PROBLEM SOLVING, page 237

• Under the curve is about 15N.s• Suppose the batter hits the ball. Assume that the

positive direction is toward the pitcher.• Before collision of the ball and the bat, the ball with a

mass of 0.145kg, has velocity of -47m/s. Therefore, the baseball’s momentum is -6.8kg.m/s. What is the momentum of the ball after the collision?

pf = (-6.8kg.m/s) + (15kg.m/s) = +8.2 kg.m/s

Impulse and MomentumImpulse-Momentum Theorem (Cont.)

• Solve the impulse-momentum theorem for the final momentum. pf = pi + FΔt

What is the baseball’s final velocity? Because pf = mvf, solving for vf yields the following:

• = = +57m/s

Why it’s better for a falling tightrope-walker to hit a surface that will stretch and give (like a net), rather than a rigid

surface (like the concrete floor)?

Mass of tightrope walker = 50 kgSpeed before impact = 20 m/sMomentum before contact = 1, 000 kg·m/sMomentum after impact = 0 kg · m/s

Time of impact:A. concrete floor = 0.0001 sB. net = 1 s

Force = Δ momentum / timea. Concrete Floor

Force = 1,000 kg · m/s ÷ 0.0001 s = 10,000,000 kg · m/s2

b. NetForce = 1,000 kg · m/s ÷ 1 s =

1,000 kg · m/s2

Philippe Petit • a French high-wire artist

 who gained fame for his high-wire walk between the Twin Towers of the World Trade Center in New York City, New York, on 7 August 1974. 

• He used a 450-pound (200-kilogram) cable and a custom-made 26-foot (8-metre) long, 55-pound (25-kilogram) balancing pole.

Example of producing large impulse in a short amount of time:

• a martial art expert breaking a stack of bricks using only his bare hands

• Snap motions

Before the space shuttle lands, why does it take giant S curves?

To increase landing time and decrease the force of the landing

Impulse-momentum can save livesThe airbag increases time interval during which the force acts on passenger. Therefore, the required force is less. It also spreads the force over a larger area of the person’s body, therefore, reducing injuries.

Page 238

Date: January 12, 2016Topic: Angular Momentum and Moment of Inertia (Chapter 9)Objective (s): To observe how conservation of momentum and changes in moment of inertia affect angular velocity.NGSS Standard:PS2.A – Forces and Motion

Changing moment of inertia DemoMaterials: rotating stools, two heavy objectsProcedure:1. sit on the stool holding the heavy object close to your body.2. Gently spin the student seated on the stool3. To the student seated on the stool, extend your arms and bring them back in.

Changing moment of inertia DemoMaterials: rotating stools, two heavy objectsProcedure:4. Do it again, this time, have your arms extended first before spinning, then while spinning, hold the heavy object close to your body.

Observation:What did you observe as you spin and the heavy object is close to your body?

What happened when you extended your arms?

Getting familiar with terminologies…

• Rotation action of rotating about an axis or center

• Torque a force that can cause the object to rotate

• Angular momentum

Getting to our topic…page 240-241• Observe the ball’s movement? Is it rotating

or going on a linear movement?

• Can angular momentum be observed in this situation?

Getting to our topic…page 240-241

What is Angular momentum?- the product of a rotating object’s moment of inertia and angular velocity.

Angular Momentum L = Iω• Angular momentum is

measured in kg·m2/s.

Angular impulse – angular momentum theorem

Can angular momentum be changed? In what way?• It can be changed when angular

impulse acts on it.

Angular Impulse-Angular Momentum Theorem τΔt = Lf − Li

Relating to the rotating stool demo:How does the extending and tucking the arm affects conservation of angular momentum and changes in moment of inertia?

How does the extending and tucking the arm affects affect angular velocity

Decrease of moment of inertia = increase in angular velocity

Decrease of moment of inertia = increase in angular velocity

Relating to the rotating stool demo:Note: • If the net force of the object is zero, its linear

momentum is constant (coz mass of object cannot change).

• If the net torque acting on the object is zero, its angular momentum is also constant. But this can change if the shape of the object changes thus increasing its velocity.

Relating to the rotating stool demo:Why?Moment of inertia depends on the object’s mass and the way it is distributed about the axis of rotation or revolution, so angular velocity can change even if no torque acts on it.

Angular Momentum: Practical Applications

Decrease of moment of inertia = increase in angular velocity

Practical Applications:- In what way the knowledge on Angular

impulse – angular momentum theorem be useful to your everyday life?

Problem solving, page 242

Problem solving, page 242

Conservation of Momentum

CONSERVATION OF MOMENTUM

• a total momentum of a closed system can never increase or decrease (conserved property).

• The increase of momentum in one part of the system means a decrease in momentum in another part.

• So, if you want to change the momentum of an object, it must be with an outside force (similar to Newton’s 2nd law).

Two particle Collision

closed system - a system, which does not gain or lose massisolated system - When the net external force on a closed system is zeroLaw of conservation of momentum – momentum of any closed, isolated system does not change.

Dale Earnhardt Sr.• While driving in the 2001 Daytona 500, Earnhardt died

 of basilar skull fracture in a last-lap crash at Daytona International Speedway on February 18, 2001

• The apparatus below consists of 5 suspended balls of equal masses. If one of the ball was lifted and made to swing towards the 4 other stationary balls, what will happen? Explain how this is an example of the conservation of momentum.

ANALYSIS2. There is something wrong with this scenario.

What is it? Explain your answer.

BEFORE COLLISION 2 m/s 0 m/s

A B C

A B C

AFTER COLLISION

0 m/s 1 m/s 1m/s

A B C

Problem solving, page 246A 1875-kg car going 23 m/s rear-ends a 1025-kg compact car going 17 m/s on ice in the same direction. The two cars stick together. How fast do the two cars move together immediately after the collision?

Known:mC = 1875 kgvCi = +23 m/smD = 1025 kgvDi = +17 m/sUnknown:vf = ?

Problem solving, page 246pi = pf

pCi + pDi = pCf + pDf

mCvCi + mDvDi = mCvCf + mDvDf

vCf = vDf = vf

mCvCi + mDvDi = (mC + mD) vf

Recoil

The skaters’ momentums after the push are equal in magnitude but opposite in direction. The backward motion of skater C is an example of recoil.

Recoil: Practical Applications

The rocket and the chemicals form: closed systemForces that expel the gases are internal forces: Isolated systemThus, objects in space can accelerate using the law of conservation of momentum and Newton’s third law of motion.

Two-Dimensional Collisions

The momentum is conserved in a closed, isolated system, regardless of the velocities of the objects before a collision.

Problem solving, page 250

Conservation of Angular Momentum

law of conservation of angular momentum - if no net external torque acts on an object, then its angular momentum does not change.

Lf = Li

Li = Lf

thus, Iiωi = Ifωf

Conservation of Angular Momentum

law of conservation of angular momentum - if no net external torque acts on an object, then its angular momentum does not change.

Lf = Li

Li = Lf

thus, Iiωi = Ifωf