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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
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…
- 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!
- Recall, Newton’s first law…The Law of Inertia
- The study of inertia for moving objects is the study of “momentum”
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
- 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?
- 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
- 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…
- 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:
- 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
- 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…
- 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
- 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
- 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:
- Rain vs. hail
- Lester Pelton
- Broken Bat Home runs?
- Can you think of any more?
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
- 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
- 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
- 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
- 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?
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
- 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
- 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
- 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
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
- Find the Center of Mass of the Earth-Moon system. Can you find it’s speed?
