Join Our Discord

Learn Moreย ย ๐Ÿ‘‡

caret down
caret up
discord-logo

Join our Discord

1,000s of Fiveable Community students are already finding study help, meeting new friends, and sharing tons of opportunities among other students around the world! Don't miss out!ย  ๐ŸŽ‰

group of students
group of students

โš™๏ธย ap physics c: mech

ย ย >ย ย 

๐ŸŽณย Unit 4

ย ย โ€ขย ย โฑ๏ธ2 min read

4.2 Impulse and Momentum ๐Ÿฅš

Daniella Garcia-Loos

daniella garcia-loos

โฑ๏ธ November 5, 2020

๐Ÿ“…

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

ap physics c: mech study guides

continue learning

Slide 1 of 5
Fiveable

Join Our Discord

discord-logo

Fiveable Community students are already meeting new friends, starting study groups, and sharing tons of opportunities for other high schoolers. Soon the Fiveable Community will be on a totally new platform where you can share, save, and organize your learning links and lead study groups among other students!๐ŸŽ‰

*apยฎ and advanced placementยฎ are registered trademarks of the college board, which was not involved in the production of, and does not endorse, this product.

ยฉ fiveable 2021 | all rights reserved.

2550 north lake drive
suite 2
milwaukee, wi 53211