Momentum
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Momentum. Introduction to Momentum. What is Momentum?. The quantity of motion of a moving body Depends on mass and velocity Measured by multiplying mass to the velocity Vector Measured in kg*m/s or N*s. How is momentum measured?. Momentum = mass x velocity p=mV p=momentum m =mass (kg)

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Momentum

Momentum

Introduction to Momentum


What is momentum

What is Momentum?

  • The quantity of motion of a moving body

  • Depends on mass and velocity

  • Measured by multiplying mass to the velocity

  • Vector

  • Measured in kg*m/s or N*s


How is momentum measured

How is momentum measured?

  • Momentum = mass x velocity

  • p=mV

    • p=momentum

    • m=mass (kg)

    • V=velocity (m/s)


Example

Example

  • Calculate the momentum of a 6.2 kg pumpkin traveling at a velocity of 5.0 m/s west.


Clicker question

Clicker Question

  • A baseball of mass 0.14 kg is moving at 35.0 m/s. Find the momentum of the baseball.

  • A)4.9

  • B)1.4

  • C)35

  • D)250


Clicker question1

Clicker question

  • Find the velocity of a bowling ball with a mass of 7.6 kg and a momentum of 4.9 kg m/s.

  • A)283

  • B)37.2

  • C)0.64

  • D).20


Impulse change in momentum

Impulse-Change in Momentum

  • When an object stops or changes its velocity the momentum changes

  • Δp=mΔV

  • Or Δp=m(Vf-Vi)


Example1

Example

  • A 0.50 kg water balloon is thrown against a wall at 32 m/s coming to a stop. What was its change in momentum?


Clicker question2

Clicker Question

  • A 0.50 kg bouncy ball is thrown at 32 m/s, bouncing back with the same speed. How does its change in momentum compare to that of the water balloon?

  • A) -32 kg m/s so twice as large

  • B) There is no difference

  • C) There is 0 change in momentum


Momentum1

Momentum

Momentum-Impulse Theory


What is impulse

What is impulse?

  • It is the change in momentum (Δp)

  • Δp=mΔV or m(Vf-Vi)

  • The impulse-momentum theorem states that when a net force is applied to an object over a certain time interval, the force will cause a change in the object’s momentum.

  • So Impulse can be defined as the product of the force and the time in which the force is acting on an object

  • Δp=FΔt

  • So… FΔt=mΔV


Example2

Example

  • Luigi is sick of taking orders. He swings a 9.0 kg hammer at 16 m/s when Mario’s mustache brings it to a stop in 0.25 s. What is the net force exerted on Mario’s mustache?


Clicker question3

Clicker Question

  • A soccer player kicks a 0.450 kg ball at 25.0 m/s east. If the goalie stops the ball by exert 215 N of force, how long does it take the ball to stop?

  • A)2418 s

  • B)0.052 s

  • C)3 s

  • D)1 s


Clicker question4

Clicker Question

  • If the goalie stops the 6.5 kg bowling ball traveling at the same velocity in the same amount of time, how much force is required?

  • A)6000

  • B)3250

  • C)2000

  • D)1000


Discuss

Discuss

  • Coaches for many sports such as baseball, tennis and golf can often be heard telling their athletes to “follow through” with their swing. How does this help a weaker player hit a ball farther than a stronger player?

  • Use the momentum-impulse theory


Discuss1

Discuss

  • Using the principle of impulse, explain why an airbag can help people sustain less damage during a collision.


Momentum2

Momentum

Law of Conservation of Momentum


Recall

Recall

  • Newton’s 3rd Law

  • Every action force has an equal and opposite reaction force

  • Two colliding objects experience equal and opposite forces for the same amount of time, then their impulses must be equal and opposite


Example3

Example

  • A cue ball is traveling with a momentum of 5 kg m/s east and strikes the 8 ball. If the cue ball comes to a stop what is the change in momentum on the cue ball? How about on the 8 ball?


Example4

Example

  • A clown is stuck on a sheet of frictionless ice. He hurls one of his clown shoes with momentum of 80 kg m/s east. What is his momentum before and after he throws his shoe?


Momentum

  • A fullback is traveling to the right with a momentum of 120 kgm/s while a linebacker is traveling to the left with a momentum of 110 kgm/s. If they stick together, what is their total momentum before and after they collide


Law of conservation of momentum

Law of Conservation of Momentum

  • In an isolated system, momentum is not created or destroyed during any interaction (collision)

  • An isolated system means no external forces act on the system

  • Total initial momentum = Total final momentum

  • pi=pf

  • m1V1i + m2V2i = m1v1f + m2V2f


Elastic collision

Elastic Collision

  • A collision in which the total momentum and the total kinetic energy are conserved is called an elastic collision

  • The objects will separate from each other after the collision

  • m1V1i + m2V2i = m1v1f + m2V2f


Example5

Example

  • A 7.1 kg bowling ball is rolling to the right at 3.8 m/s when it collides with a stationary 0.40 kg bowling pin. After the collision, the bowling ball is traveling at 2.9 m/s to the right. How fast is the pin moving after the

    collision?


Momentum

  • A 0.25 kg cue ball is traveling east at 4.5

    m/s when it collides head on with a 0.25 kg eight ball traveling west at 5.0 m/s. After the collision the cue ball Is traveling west at 2.0 m/s. What is the final velocity of the eight ball

    A) 4.5 m/s

    B) 1.5 m/s

    C) 9.5 m/s

    D) 2.0 m/s


Inelastic collisions

Inelastic Collisions

  • A collision in which two objects stick together after colliding and move together as one mass is called a perfectly inelastic collision.

  • m1V1i + m2V2i = (m1+ m2)Vf


Example6

Example

  • A 0.105-kg hockey puck moving at 48 m/s is caughtbya 75-kg goalieatrest. Iftheiceisfrictionless, atwhatvelocity will thegoalieslide on theiceafter catchingthepuck?


Clicker question5

Clicker Question

  • A 35.0-g bullet strikes a 5.0-kg stationary wooden block and embeds itself in the block. The block and bullet move together at 8.6 m/s. What was the original velocity of the bullet?

  • A) 12 m/s

  • B) 9.9 m/s

  • C) 1200 m/s

  • D) 40 m/s


Explosions

Explosions

  • In a situation in which you have one object separate into pieces

  • The initial momentum is zero

  • The law of conservation will still apply here

  • 0= m1v1f + m2V2f


Example7

Example

  • A 0.050 kg bullet is fired from a 5.0 kg gun.

    If the velocity of the bullet is 275 m/s, what is the recoil velocity of the gun?


Clicker question6

Clicker Question

  • A firecracker sits in a 7.0 kg pumpkin. After

    It explodes, the pumpkin splits into two chunks. A 5.0 kg piece travels west at 10.0 m/s. What is the mass and velocity of the other piece? (Ignore the mass of the

    firecracker)

  • 25 m/s B) 40 m/s

    C) 10 m/s D) 50 m/s


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