Impulse and Momentum

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Impulse and Momentum •

Momentum

– There are two kinds of momentum, linear and angular. A spinning object has angular momentum; an object traveling with a velocity has linear momentum. For now, and throughout chapter 7, we'll deal with linear momentum, and just refer to it as momentum, without the “linear”. – Things to know about momentum. • how momentum is defined, as the product of mass times velocity: –

momentum :

p

mv

– momentum is a vector, momentum has the same direction as the velocity.

– Linear momentum p of an object is the product of the object’s mass m and its velocity v (p=mv)….P and v are vector quantities, so linear momentum is a vector that points in the same direction as the objects velocity. – Newton’s 2nd Law was originally written in terms of

F

m

v t

mv f

mv0 t

ma

– logical extension of this is as the impulse-momentum theorem described by: automotive airbags reduce the force on your body during a collision by way of increasing in the impulse-momentum relationship (unfortunately mass cannot be changed! at least quickly) UCVTS AIT Physics

Impulse and Momentum

• Impulse – relationship between momentum and force • there is a strong connection between force and momentum. In fact, Newton's second law was first written in terms of momentum, rather than acceleration. A force acting for a certain time (this is known as an impulse) produces a change in momentum.

F

m

(

F) t

J

F t

v t

mv f

mv f

mv0

mv0 t J

ma p

– Again, this is a vector equation, so the change in momentum is in the same direction as the force. UCVTS AIT Physics

Impulse and Momentum

• Impulse – Momentum Theorem – When a net force acts on an object, the impulse of the net force is equal to the change in momentum of the object – Automobile airbags are examples of the impulse momentum theorem at work in real life, why? Which variable/s in the impulse-momentum equation below does an airbag change?

J

F t

mv f

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mv0

Momentum

• Increasing Momentum Examples – Apply the greatest force for as long as possible • Large Impulse – Impulse=Force X Time » Sling shot, bow and arrow, driving a golf ball, » Other examples??

• Decreasing Momentum Examples – Decrease force over as long of time as possible • Low Impulse – Impulse = Force X Time » Hitting a concrete wall or a wall of tires? » Dashboard or airbag?

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Momentum-Impulse • "It's not the fall that hurts you, it's the sudden stop at the end.“ •

Seatbelts and airbags works because they increase the time it takes for our bodies to slow down in a car accident, thus reducing the maximum force exerted on the body. –

As far as safety equipment goes, the idea is to maximize time to minimize the force experienced by the body. Air bags and seatbelts take longer to slow you down then say a windshield or a dashboard, so the injuries tend to be bruises rather than broken bones.

•

This is the same reason why some of the most lethal accidents are sudden and relatively mild looking. If a car going 200 mph flips over and rolls three times before finally coming to a stop, the maximum force on it isn't nearly as large as a car that slams into a wall at 200 mph and suddenly stops.

•

Skydivers are taught to tumble as they land. This is because tumbling spreads out the force of impact over time.

•

Water is great at slowing people down slowly. That's why we can dive into a deep pool from as high as 15 ft without any fear.

•

Much of the martial arts depends on the idea of minimizing the time used to deliver maximum force.

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Impulse and Momentum •

Conservation of Linear Momentum

– Important point about momentum is that momentum is conserved

• the total momentum of an isolated system is constant. Note that "isolated" means that no external force acts on the system, which is a set of interacting objects. • If a system does have a net force acting, then the momentum changes according to the impulse equation.

– Momentum conservation applies to a single object, but it's a lot more interesting to look at a situation with at least two interacting objects. If two objects (a car and a truck, for example) collide, momentum will always be conserved.

Hard steel ball rebounds to its original height

Partially deflated basketball has very little bounce

• Types of collisions: (momentum is conserved in each case) – – –

elastic - kinetic energy is conserved inelastic - kinetic energy is not conserved completely inelastic - kinetic energy is not conserved, and the colliding objects stick together after the collision.

– The total energy is always conserved, but the kinetic energy does not have to be; kinetic energy is often transformed to heat or sound during a collision.

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Deflated basketball has no bounce at all

Momentum • Conservation of Momentum – Conservation? What does that mean?

• Momentum= m X v

pf

p0

– M1 X V1 = M2 X V2

• Elastic and Inelastic Collisions (momentum conservation in both cases) – Elastic collisions • Objects collide without being permanently deformed and without generating heat – The objects bounce perfectly (totally elastic collision)

– Inelastic collisions • Objects collide and become distorted and generate heat during a collision – The objects collide and become entangled and attached after the collision (totally inelastic collision)

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Impulse and Momentum •

Conservation of Linear Momentum – Example 7

M1=0.25kg V01=5.00m/s

M1=0.80kg V02=0

M1=0.25kg Vf1=?

M1=0.80kg Vf2=?

m1v f 1 m2v f 2

m1v01 m2v02

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