Momentum: A Deeper Look into Motion

Which of the following has the most Momentum? Question 1 A hockey puck at rest A bowling ball at rest Both have the same momentum

Which of the following has the most Momentum? Question 2 A VW beetle moving at a high velocity A big truck moving at the same speed Both have the same momentum

Which of the following has the most Momentum? Question 3 A VW beetle moving at a slow speed The same VW beetle moving at a fast speed Both have the same momentum

Which of the following has the most Momentum? Question 4 A tennis ball falling freely A bowling ball falling freely for the same amount of time Both have the same momentum

Which of the following has the most Momentum? Question 5 A bullet fired from a rifle (which was initially at rest) The rifle from which it was fired (immediately after firing) Both have the same momentum

Which of the following has the most Momentum? Question 6 A car moving at 50 mi/hr The passengers inside that car Both have the same momentum

Which of the following has the most Momentum? Question 7 A golf ball hit with 200 N of force for .01 seconds The same ball hit with 20 N of force for .1 seconds Both have the same momentum

Which of the following has the most Momentum? Question 8 A 900 kg VW beetle moving at 10 m/s A 9000 kg truck moving at 1 m/s Both have the same momentum

Which of the following has the most Momentum? Question 9 A VW beetle going uphill at a constant speed The same beetle going downhill at the same speed Both have the same momentum

Which of the following has the most Momentum? Question 10 A tennis ball sitting motionless on a shelf A bowling ball sitting on the same shelf Both have the same momentum

# Option A Option B A, B, or Same? Why? 1 Hockey Puck at rest Bowling Ball at rest C v = 0 for both, so p = 0 2 VW moving const. speed Truck w/ same speed B v is same, so larger m has larger p 3 VW moving slowly VW moving quickly m is same, so larger v has larger p 4 Tennis ball in free fall Bowling ball in free fall 5 Bullet fired from rifle Rifle that fired bullet Δp are equal and opposite 6 Car moving 50 mph Passengers inside A 7 Ball 200 N for 0.01 s Ball 20 N for 0.1 s I=Δp=FΔt 8 900 kg VW @ 10 m/s 9000 kg truck @ 1m/s p=mv 9 VW uphill VW downhill @ same speed v is same, m is same, so p is same 10 Tennis ball on shelf Bowling ball on shelf

What Is Momentum? What factors do you think determine an object’s momentum? Momentum can be conceptually defined as the “strength of motion” It is kind of like inertia, but relates to the tendency of a moving object to continue moving 𝒑 =𝑚∙ 𝒗

Does This Look Familiar?

Newton’s 2nd Law (The Original Version!)

What About Impulse? 𝑰 = 𝑭 ∙Δ𝑡 What does an applied force do to an object? Exactly! It causes an acceleration…which changes its velocity…which changes its momentum! The amount of change depends on the amount of time it is applied An impulse is defined as a force applied for a given length of time 𝑰 = 𝑭 ∙Δ𝑡

Impulse with 2 Objects 𝑰 = Δ 𝒑 =𝑚∙∆ 𝒗 For an interaction between 2 objects, where one object acts on another object… Impulse is a change in momentum Since 2nd Law tells us 𝑭 = ∆ 𝒑 ∆𝑡 : 𝑰 = Δ 𝒑 =𝑚∙∆ 𝒗

Units!! kg∙m 𝑠 or N·s 𝑭 ·Δ𝑡 = 𝑚 ·Δ 𝒗 N · sec⁡= kg · m s 𝑭 ·Δ𝑡 = 𝑚 ·Δ 𝒗 N · sec⁡= kg · m s kg∙m s 2 ·sec= kg · m s kg∙m 𝑠 =kg · m s So, impulse and momentum can be expressed in kg∙m 𝑠 or N·s

Nùmero Uno Paul deTrigga fires a rifle. The rifle recoils from firing the bullet. The acceleration of the rifle’s recoil is small because the: Force against the rifle is less than the force against the bullet Acceleration is mainly concentrated in the bullet since it is being fired. Rifle has more mass than the bullet. Momentum of the rifle has changed None of these C. Think back to Newton’s Laws! Forces are equal (Newton’s 3rd Law), but different masses mean different accelerations (according to Newton’s 2nd Law).

Nummer Zwei Pat, a karate expert, executes a swift blow and severs a cement block with her bare hand. Which of the following are true statements? The impulse on both the block and Pat’s hand have the same magnitude. The force on both the block and Pat’s hand have the same magnitude. The time of impact on both the block and Pat’s hand is the same. All of the above None of the above D. Forces are the same due to Newton’s 3rd Law. Times have to be the same! Thus impulse is the same, as we defined a few slides ago.

Think-Pair-Share: Impulse in Car Crashes In a car collision, the driver’s body must change speed from a high value to zero. This is true whether or not an airbag is used, so why use an airbag? How does it reduce injuries? Explain using momentum and impulse. The air bag increases the time over which the force is applied. Since the change in momentum is the same, this means that the impulse is the same. So increasing time decreases force! The air bag increases the time over which the force is applied. Since the change in momentum is the same, this means that the impulse is the same. So increasing time decreases force!

Think-Pair-Share: Impulsive Actions You want to close an open door by throwing either a 400 gram lump of clay or a 400 g rubber ball toward it. You can throw either object with the same speed, but they are different in that the rubber ball bounces off the door while the clay just sticks to the door. Which projectile will apply the larger impulse to the door and be more likely to close it? Explain. The ball! Since it bounces off the door, its change in momentum is greater because in addition to losing its initial momentum toward the door, it now has momentum in the opposite direction, hence a greater change. Since the change in momentum is greater, so is the impulse, and thus the force will be as well. The ball! Since it bounces off the door, its change in momentum is greater because in addition to losing its initial momentum toward the door, it now has momentum in the opposite direction, hence a greater change. Since the change in momentum is greater, so is the impulse, and thus the force will be as well.

A New Version of Newton’s 3rd Law All IMPULSES are equal and opposite! Thus, we can say all changes in momentum are equal and opposite! Another way to say this is that momentum is conserved in all interactions as long as there are no external forces involved Total momentum before = Total momentum after 𝒑 𝒃𝒆𝒇𝒐𝒓𝒆 = 𝒑 ′ 𝒂𝒇𝒕𝒆𝒓

Think – Pair – Share: Earth Moving? Okay, let’s assume that an average person has a mass of 65.0 kg. There are 7 billion people or so on the Earth. If all 7 billion people somehow managed to all start from rest and accelerate to a velocity of 4.00 m/s in the same direction at the same time… How much change in momentum would they have? By how much would the Earth’s momentum change? If the Earth has a mass of 5.98 x 1024 kg, then by how much would the Earth’s velocity change? If all the people took 1.50 seconds to change their velocity, how much force was exerted? mpeople = (7.00 x 109) (65.0 kg) = 4.55 x 1011 kg Δp people = p2-p1= mpeople v2 – 0 = (4.55 x 1011 kg) (4.00 m/s) = 1.82 x 1012 N∙s Δp people = Δp Earth= 1.82 x 1012 N∙s Δp Earth= mEarth ∙Δv Earth Δv Earth = Δp Earth / mEarth = (1.82 x 1012 N∙s) / (5.98 x 1024 kg) = 4.52 x 1010 m/s I = Δp people = F Δt F = I / Δt = (1.82 x 1012 N∙s) / (1.50 s) = 1.21 x 1012 N

Think – Pair – Share: Earth Moving? How much change in momentum would they have? 𝑚 𝑝𝑒𝑜𝑝𝑙𝑒 =(7.00×109)∙(65.0 kg)=4.55×1011 kg ∆𝑝 𝑝𝑒𝑜𝑝𝑙𝑒 = 𝑝 2 − 𝑝 1 = 𝑚 𝑝𝑒𝑜𝑝𝑙𝑒 ∙ 𝑣 2 −0 ∆𝑝 𝑝𝑒𝑜𝑝𝑙𝑒 = 4.55×1011 kg ∙ 4.00 m s −0 ∆𝒑 𝒑𝒆𝒐𝒑𝒍𝒆 =𝟏.𝟖𝟐× 𝟏𝟎 𝟏𝟐 𝐤𝐠∙𝐦 𝐬 By how much would the Earth’s momentum change? ∆𝒑 𝑬𝒂𝒓𝒕𝒉 =−𝟏.𝟖𝟐× 𝟏𝟎 𝟏𝟐 𝐤𝐠∙𝐦 𝐬 mpeople = (7.00 x 109) (65.0 kg) = 4.55 x 1011 kg Δp people = p2-p1= mpeople v2 – 0 = (4.55 x 1011 kg) (4.00 m/s) = 1.82 x 1012 N∙s Δp people = Δp Earth= 1.82 x 1012 N∙s Δp Earth= mEarth ∙Δv Earth Δv Earth = Δp Earth / mEarth = (1.82 x 1012 N∙s) / (5.98 x 1024 kg) = 3.04 x 10-13 m/s I = Δp people = F Δt F = I / Δt = (1.82 x 1012 N∙s) / (1.50 s) = 1.21 x 1012 N

Think – Pair – Share: Earth Moving? If the Earth has a mass of 5.98 x 1024 kg, then by how much would the Earth’s velocity change? ∆ 𝑝 𝐸𝑎𝑟𝑡ℎ = 𝑚 𝐸𝑎𝑟𝑡ℎ ∙ ∆𝑣 𝐸𝑎𝑟𝑡ℎ ∆ 𝑣 𝐸𝑎𝑟𝑡ℎ = ∆ 𝑝 𝐸𝑎𝑟𝑡ℎ 𝑚 𝐸𝑎𝑟𝑡ℎ = 1.82 × 10 12 kg∙m s 5.98× 10 24 kg ∆ 𝒗 𝑬𝒂𝒓𝒕𝒉 =𝟑.𝟎𝟒× 𝟏𝟎 −𝟏𝟑 𝒎 𝒔 If all the people took 1.50 seconds to change their velocity, how much force was exerted? 𝐼𝑚𝑝𝑢𝑙𝑠𝑒= ∆ 𝑝 𝐸𝑎𝑟𝑡ℎ =𝐹∙∆𝑡 𝐹= 𝐼𝑚𝑝𝑢𝑙𝑠𝑒 ∆𝑡 = 1.82 × 10 12 kg∙m s 1.50 s 𝑭=𝟏.𝟐𝟏× 𝟏𝟎 𝟏𝟐 𝐍 mpeople = (7.00 x 109) (65.0 kg) = 4.55 x 1011 kg Δp people = p2-p1= mpeople v2 – 0 = (4.55 x 1011 kg) (4.00 m/s) = 1.82 x 1012 N∙s Δp people = Δp Earth= 1.82 x 1012 N∙s Δp Earth= mEarth ∙Δv Earth Δv Earth = Δp Earth / mEarth = (1.82 x 1012 N∙s) / (5.98 x 1024 kg) = 3.04 x 10-13 m/s I = Δp people = F Δt F = I / Δt = (1.82 x 1012 N∙s) / (1.50 s) = 1.21 x 1012 N

Conservation of Momentum If the quantity of the amount after an interaction does not change, we say that it is conserved Because the momentum in a defined system is the same before a collision as it is afterwards, we say that momentum is conserved

Collisions! 𝑚1𝒗𝟏+𝑚2𝒗𝟐 = 𝑚1𝒗𝟏’+𝑚2𝒗𝟐’ 𝑚1𝒗𝟏+𝑚2𝒗𝟐 = (𝑚1+𝑚2 )𝒗’ Elastic Collisions (Bouncy): Objects involved bounce off each other 𝑚1𝒗𝟏+𝑚2𝒗𝟐 = 𝑚1𝒗𝟏’+𝑚2𝒗𝟐’ Inelastic Collisions (Sticky): Objects involved stick together 𝑚1𝒗𝟏+𝑚2𝒗𝟐 = (𝑚1+𝑚2 )𝒗’ Examples of elastic: pool Inelastic: car crash

Elastic (aka “bouncy”) 𝒑 𝒃𝒆𝒇𝒐𝒓𝒆 = 𝒑 ′ 𝒂𝒇𝒕𝒆𝒓 𝑚1𝒗𝟏+𝑚2𝒗𝟐 = 𝑚1𝒗𝟏’+𝑚2𝒗𝟐’ A B

Inelastic (aka “sticky”) 𝒑 𝒃𝒆𝒇𝒐𝒓𝒆 = 𝒑 ′ 𝒂𝒇𝒕𝒆𝒓 𝑚1𝒗𝟏+𝑚2𝒗𝟐 = (𝑚1+𝑚2 )𝒗’ A B

(you might also see impulse defined as 𝑱 ) Let’s Recap! Momentum: inertia in motion 𝒑 = 𝑚∙ 𝒗 Impulse: 𝑰 = 𝑭 ∙Δ𝑡 𝑰 = Δ 𝒑 =𝑚∙∆ 𝒗 (you might also see impulse defined as 𝑱 ) 𝒑 𝒃𝒆𝒇𝒐𝒓𝒆 = 𝒑 ′ 𝒂𝒇𝒕𝒆𝒓