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Impulse and Momentum. Saline High School Physics. Have you ever wondered…. Why golfers and bowlers “follow through”? Why skydivers bend their knees upon impact? Why Falling on a wood floor hurts less than falling on a cement one?. Have you ever wondered….

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Impulse and Momentum


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impulse and momentum

Impulse and Momentum

Saline High School Physics

have you ever wondered
Have you ever wondered…
  • Why golfers and bowlers “follow through”?
  • Why skydivers bend their knees upon impact?
  • Why Falling on a wood floor hurts less than falling on a cement one?
have you ever wondered3
Have you ever wondered…
  • What’s the best strategy to win the “water balloon toss” or the “egg toss”?
  • Why we make auto air bags and padded dash boards?
  • How the police can figure out how fast you were going BEFORE an accident by measuring your skid marks?
to answer all of these questions and more you need to understand impulse and momentum
To answer all of these questions--and more--you need to understand: Impulse and Momentum!
  • Recall, Newton’s first law…The Law of Inertia
  • The study of inertia for moving objects is the study of “momentum”
consider the following
Consider the following:
  • When a baseball bat hits a baseball, a force is applied OVER A SHORT PERIOD OF TIME.
  • How would a graph of Force vs. Time look?
impulse
Impulse
  • Defn: A force applied over a period of time is called an IMPULSE.
  • What are the SI units of Impulse?

I = F · ∆t

back to baseball which will have the greater speed afterward
Back to baseball...Which will have the greater speed afterward?
  • A large or a small ball?
  • A fast or a slow ball?
  • A large or a small bat?
  • A fast or a slow swing?
momentum
Momentum
  • Defn: The MOMENTUM of a body is equal to the product of its mass and its velocity.
  • Is momentum a vector or a scalar?
  • What are the SI units of momentum?

p = m · v

determine the following momentums
Determine the following momentums…
  • Ex #1 - A 1200lb car moving at 60mph
  • Ex #2 - A 5.0g bullet moving at 900m/s
  • Ex #3 - A 3 ton elephant sitting down
  • Ex #4 - A 150g hummingbird flying at 40mph
  • Could the momentum of the hummingbird ever be equal to that of the elephant?
making the connection
Making the Connection:
  • Look at the units of Impulse and Momentum…Do you notice anything?
  • Recall, F = m·a…can you rearrange the equation to say something about Impulse or Momentum?
the impulse momentum theorem
The Impulse-Momentum Theorem
  • When a net force acts upon a body for a period of time, the Impulse applied by the force is equal to the body’s change in Momentum!
  • This is similar to the Work-Energy Theorem…

F∆t = m∆v

applying the impulse momentum theorem 1 follow through etc
Applying the Impulse-Momentum Theorem #1: Follow Through etc…
  • If your Force is limited, how can you MAXIMIZE the impulse you apply?
  • By increasing the time of contact!
  • Golfing…Baseball…
applying the impulse momentum theorem 2 maximize time
Applying the Impulse-Momentum Theorem #2: Maximize ∆time
  • If your change in momentum is constant, how can you MINIMIZE the force applied to you?
  • By increasing the time of contact!
  • Bending knees upon impact, rolling with the punches, crumple zones, running shoes, air bags…
momentum changes and bouncing
Momentum Changes and Bouncing
  • Is it more dangerous when a flower pot falls on your head and breaks or stays in one piece and bounces back up?
  • When an object bounces, what happens to it’s velocity? How does that effect it’s change of momentum?
  • Since ∆p is greater in bouncing situations, the Impulse applied will be greater!
bouncing examples
Bouncing Examples:
  • Rain vs. hail
  • Lester Pelton
  • Broken Bat Home runs?
  • Can you think of any more?
the law of conservation of momentum
The Law of Conservation of Momentum
  • Internal forces are forces that act within a system, external forces are forces that act on a system from outside…
  • If a system is not affected by any net external force, it is said to be “ISOLATED”.
  • In an isolated system, the total linear momentum is always conserved!
example recoil
Example - Recoil
  • A hunter shoots a 0.22 rifle and the 3.0 kg gun recoils with a speed of 0.042 m/s. If the bullet has a mass of 0.5 g, find the muzzle speed of the gun.
example push off from rest
Example - Push off from rest
  • Two skaters push off each other from rest on a smooth, level ice rink. The man weighs 160lb and the woman weighs 120lb. If the woman leaves with a speed of 2.5 m/s, what is the speed of the man?
elastic and inelastic collisions
Elastic and Inelastic Collisions
  • Collisions in which the bodies crash and stick together are called “INELASTIC” Collisions
  • Collisions in which the bodies crash and bounce are called “ELASTIC” Collisions
example inelastic collision
Example - Inelastic Collision
  • In an accident, two cars travelling in opposite directions collide and stick together. The first car has a mass of 1000 kg and a speed of 20 m/s, the second has a mass of 1750 kg and a speed of -15 m/s. What is the speed of the two cars immediately after the crash?
example elastic collisions

V01 = 15 m/s

V02 = 0 m/s

Example - Elastic Collisions
  • In a pool game, two identical balls of mass 0.75 kg collide as shown below. Find their speeds right after the collision.
  • How far will the one on the right go if µ=0.65?
  • How would your answer change if the ball on the right had a speed of 12 m/s to the left?
example 2 elastic collisions
Example 2 - Elastic Collisions
  • Two identical blocks of mass 1.0 kg collide elastically, as shown below. Find their speeds right after the collision.
  • How far will the one on the right go if µ=0.65?
  • How would your answer change if the ball on the right had a speed of 12 m/s to the left?

V01 = 15 m/s

V02 = 12 m/s

the ballistic pendulum
The Ballistic Pendulum
  • A “ballistic pendulum” is made from a block of wood of known mass. It is used to find the speed of a bullet. If the bullet has a mass of 7.5 g and the pendulum has a mass of 2.5 kg and rises to a height of 65 cm, find the speed of the bullet (Hint: use conservation of momentum and energy).
collisions in two dimensions
Collisions in Two Dimensions
  • A 1000kg car travels east at 35 mph and another with mass 2000 kg, travels north at 40mph. If they collide inelastically, what velocity will they have after they crash?

N

center of mass

m1 x1 + m2 x2

Xcm =

m1 + m2

Center of Mass
  • The cneter of mass of a body is the point at which you could consider ALL the mass being if it were a point mass
  • It can be found geometrically…
  • or mathematically…we can also find it’s speed...

m1 v1 + m2v2

vcm =

m1 + m2

example
Example
  • Find the Center of Mass of the Earth-Moon system. Can you find it’s speed?