Newton’s Third Law:Impulse & Momentum

“How many horses had to die for this

stupid, itchy wig?”

a momentous topic

“For every action, there exists an equal and opposite reaction.”

- Isaac Newton, Principia Mathematica

maF

tvv

tva if

tvmFso

vmtFand

“For every action, there exists an equal and opposite reaction.”

- Isaac Newton, Principia Mathematica

Is known as the

“Impulse-Momentum”

theorem, where

Change in momentum

Impulse

vmtF

“For every action, there exists an equal and opposite reaction.”

- Isaac Newton, Principia Mathematica

Inertia in motion**

Product of mass

& velocity

Momentum? Huh?

**For subatomic-sized particles moving really, really fast (~90% of light speed), momentum is defined differently. It’s impossible to determine BOTH position and momentum at the same instant in time because of some freaky mathematics; hence, we have Heisenberg’s Uncertainty Principle.

“For every action, there exists an equal and opposite reaction.”

- Isaac Newton, Principia Mathematica

Heisenberg may have slept here

. . . but, for relatively large objects (like molecules) that are moving fairly slowly (<0.9c), the classical definition of momentum works just fine, and is much less complicated.

p = mv + mv Or BOTH may change!

“For every action, there exists an equal and opposite reaction.”

- Isaac Newton, Principia Mathematica

For momentumto change,

the mass can change,

the velocity can change,

pp = mv

m*v m*v

These two canoeists (each of

mass 60 kg) propel their canoe (30 kg)

at 5 m/s towards an unseen rock on

this pond. After the 0.5-s collision,

the canoe moves back at 1 m/s. This canoe can

withstand a force of 1500 N without

puncturing.

Big rock just under here

Will the canoe break?

What is the change in momentum of the canoe/passengers?

“For every action, there exists an equal and opposite reaction.”

- Isaac Newton, Principia Mathematica

kgmasses 150

sm

smv 51

p = mv

p = (150 kg)(6 m/s)

p = 900 kg m/s

-5 m/s

1 m/s

if vvvelocityinchange

“For every action, there exists an equal and opposite reaction.”

- Isaac Newton, Principia Mathematica

vmtF

tvmF

ssmkg

F5.0

900

F = 1800 N

“For every action, there exists an equal and opposite reaction.”

- Isaac Newton, Principia Mathematica

A 75-kg driver is traveling at 100 m/s when his car comes to a sudden stop. The driver is not wearing a seatbelt. He collides with the steering column for 0.005 s. The human body can withstand about 9 times the weight of the body as impact force. Has this driver committed suicide-sans-seatbelt?

                                       

“For every action, there exists an equal and opposite reaction.”

- Isaac Newton, Principia MathematicaA 75-kg driver is traveling at 100 m/s when his car comes to a sudden stop. The driver is wearing a seatbelt. He collides with the steering column for 1.2 s. The human body can withstand about 9 times the weight of the body as impact force. Has this driver committed suicide-sans-seatbelt?

This crash occurred in Oahu; yes, the driver was wearing a seat belt

AND WALKED AWAY!

Many mooses’ mass may be more than your Maserati’s mass. This moose’s mass is 680 kg, and it is initially moving at 9 m/s. If the collision lasts for 0.5 s, how much force is sustained by the car?

Water leaves a fire hose at a rate of 125 kg/s with a speed of 200 m/s and strikes a wall, which stops it. (We’re ignoring

any splashing back.) What is the force exerted by the water on the wall?

FYI: Fire hoses were used in the 1960’s to break up peaceful civil rights demonstrations.

Calculate the force exerted on a rocket, given that the propelling gases are expelled at a rate of 1000 kg/s, with a speed of 60,000 m/s (at takeoff).

Your assignment for next time:

pp. 83+: RQ 1-8; T&E 1,3-12,15