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Unit 4

4.2 Impulse and Momentum ๐Ÿฅš

2 min readโ€ขnovember 5, 2020

dandelion

Daniella Garcia-Loos


AP Physics C: Mechanicsย โš™๏ธ

Bookmarkedย 1kย โ€ขย 54ย resources
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4.2: Impulse and Momentum ๐Ÿฅš

In this unit, we'll only be talking about linear momentum, but look forward to angular momentum in the next unit! Conceptually, its quite hard to describe without using quantities, but essentially, it is a measurement of mass in motion. The most basic equation for linear momentum is:
p = mv
Momentum Fast (haha) Facts:
  • It's a vector
  • Units are kg*m/s
  • It is NOT the same as kinetic energy
    • Kinetic energy is a scalar and describes a different relationship
Let's try to derive Newton's Second Law using momentum!
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-KoJ3X10dJj2g.png?alt=media&token=d13e5518-2be2-45c4-8f3b-f55ffdb1bdb1
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-aC98bdkI6m6h.png?alt=media&token=91e246ce-edd3-450d-a0f3-b6e8cb1657c2
Now that looks pretty familiar, doesn't it?
Let's take a closer look at one part of this derivation.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-GviNROQ4YhZf.png?alt=media&token=db4d4e68-e88f-42e9-8b27-84eb01f18d6f
This change in momentum actually has a special name, Impulse! (Or as some like to call, Jimpulse)
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-p8MrMmtUJ1i1.png?alt=media&token=d5f5ee61-8c81-45a0-9110-6fb27a4c86a1
Or the calculus version:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-DmiuBloC3Tim.png?alt=media&token=1ffdb574-45f2-4d2e-8ec6-2282ee688782
We tend to use calculus when the force or the mass is variable, like with a rocket!
Impulse is a vector because force has a direction, and the units are the same as momentum(N*s). Additionally, AP loves to ask questions about impulse in relation to graphs!
Impulse is the area under the curve (check out the integral!) of a Force vs. Time graph.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-A951jAPxoAt6.png?alt=media&token=ac869d46-ea74-4c03-a115-5a6e2164d488

Taken from Physics Forums

The curves won't always look this pretty like they did in AP Physics 1 because we have the power of calculus now!
โš ๏ธ So..what does impulse really mean?
Have you ever tried an egg drop experiment? One where you tried to shield a poor egg from cracking as soon as it hit the ground?
Think back to which experiments worked best...theoretically the ones that work best should be the ones that increase the amount of time of impact!

Practice Questions

During the 2007 French Open, Venus Williams hit the fastest recorded serve in a premier womenโ€™s match, reaching a speed of 58 m/s (209 km/h). What is the average force exerted on the 0.057-kg tennis ball by Venus Williamsโ€™ racquet, assuming that the ballโ€™s speed just after impact is 58 m/s, that the initial horizontal component of the velocity before impact is negligible, and that the ball remained in contact with the racquet for 5.0 ms (milliseconds)?(Taken from Lumen Learning)

Answer: To determine the change in momentum, substitute the values for the initial and final velocities into the equation above.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FAnswer2-tHG3D82gdxwf.png?alt=media&token=a6d552b9-c189-4081-842c-f5a18e8b4b3a
Now the magnitude of the net external force can determined by usingย 
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-tgJt9Ft7v7Pn.png?alt=media&token=ba7b180b-cb96-4f00-904b-424777aadf9a

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-dWRvYsPRl4aR.png?alt=media&token=a34f057e-9b8b-4de1-9b4a-8cd5544c2df6
Answer:
Use the Impulse formula on your formula chart, and don't forget to include your bounds/limits of integration!
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-LjDJYCPRRZ4P.png?alt=media&token=de0504bf-8f63-4a2f-8701-32ed15bbddb3

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-Qzy0FAFqR3En.png?alt=media&token=c4f5e63e-e89f-4971-a024-390be9e082e8

Taken from College Board

Answer:
Again, use the formula on your chart and integrate with bounds. Take note that there is an alternate form of resolving this with another impulse formula
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-UhszufbpPtVA.png?alt=media&token=cb2e5c02-18a9-4317-aa7e-c7c6dd5f5d5d

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