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โš™๏ธย ap physics c: mech

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๐ŸŽขย Unit 3

ย ย โ€ขย ย โฑ๏ธ3 min read

3.1 Overview of Unit 3: Work, Energy, and Power and 3.1 Work-Energy Theorem ๐Ÿ’ช

โฑ๏ธ November 5, 2020

๐Ÿ“…โŒจ๏ธ

Unit 3: Work, Energy, and Power

Overview

Energy is one of the biggest concepts in physics, and you can see it in every unit we've covered in the past and will cover in the future. A tip given to me by a wise physics teacher was that almost every FRQ can be at least partially tackled with energy!

Big Ideas

Force Interactions

  • Why is no work done when you push against a wall, but work is done when you coast down a hill

Conservation:

  • Why does a stretched rubber band return to its original length?

  • Why is it easier to walk up a flight of steps, rather than run, when the gravitational potential energy of the system is the same?

Force Interactions:

Why is no work done when you push against a wall, but work is done when you coast down a hill?

Exam Impact

Unit 3 will cover approximately 14%-17% of the exam and should take around 10 to 20, 45-minute class periods to cover. The AP Classroom personal progress check has 20 multiple choice questions and 1 free response question for you to practice on.

3.1: Work-Energy Theorem ๐Ÿ’ช

The net work done on an (point-like) object is equal to the objectโ€™s change in the kinetic energy.

In equation form, the Work-Energy Theorem looks like this:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-QMErFKKeCOcD.PNG?alt=media&token=87ae6c2f-3dad-4a49-b4ff-f043f1a4aa4d

In which W is work and K is kinetic energy.

Kinetic energy is typically defined as:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-or1clCuOytPw.PNG?alt=media&token=236efa90-691b-4af4-a383-3cb634e9837a

where m๏ปฟ is mass and v๏ปฟ is velocity.

Here is the derivation of the Work-Energy Theorem:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-wQs7VafKFn7p.PNG?alt=media&token=1df91e9a-d3d4-4e39-b948-773c3e9845c6

F=dv/dt โ€‹๏ปฟ then use the chain rule

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-mRtjNbAzqL9F.PNG?alt=media&token=5b670cc3-20a0-4082-b682-8ac1cca4bd7f

And we know that the equation for work is W = Fxd so:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-Qu1KU3DdsMoM.PNG?alt=media&token=c82399ea-e1b4-4899-91cd-d6ae9893ec34

W=m[1/2(v^2)] evaluated from Vo to Vf

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-TfwuCdIUHmtk.PNG?alt=media&token=2bd3afb9-7496-4f3c-a1c3-106e091207de

Work done by a variable force is the area under a force vs radius plot! This can be seen in your formula chart as:

โš ๏ธWait...what is work?

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-7kyKTac47sl8.png?alt=media&token=02b7ea4d-7bf9-4175-86da-993e43d6f74c

Image from Wikimedia Commons

Work is when there is a force exerted on an object that causes the object to be displaced. Work is a scalar that can be negative or positive, depending on if there's energy put in or taken out of the system.

If you know about vectors, you should be aware that work is the scalar product between force and displacement. Only the force perpendicular to the direction of motion is included.

Here's the most popular formula for work that is not calculus based:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-U2GVhVl8U8uW.PNG?alt=media&token=f39dee8f-3b44-4989-836f-6205c2b4c020

Practice Questions:

1. (a) Calculate the work done on a 1500-kg elevator car by its cable to lift it 40.0 m at constant speed, assuming friction averages 100 N.

(b) What is the work done on the lift by the gravitational force in this process?

(c) What is the total work done on the lift? (Taken from Lumen Learning)

Answers:

(a) Start by drawing a free body diagram, with the force of tension and the gravitational force.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-V0mMEBoAFOpD.PNG?alt=media&token=0057a03c-4309-40db-b273-04fab1831aa6

(b)

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-dU62ajUZ9qN3.PNG?alt=media&token=e0de505f-ec91-48f4-b20d-a57bac9f5ba1

(c) The only two forces that are doing work on the lift are gravity and tension, not friction. Therefore the net amount of work is zero.

2. (a) Using energy considerations, calculate the average force a 60.0-kg sprinter exerts backward on the track to accelerate from 2.00 to 8.00 m/s in a distance of 25.0 m, if he encounters a headwind that exerts an average force of 30.0 N against him. (Taken from Lumen Learning)

Answer:

Always start by drawing your free body diagram!

Let's start off with a tried and true classic: Newton's Second Law

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-z98W2NL2ApKS.PNG?alt=media&token=5c26d898-7540-4ca6-8514-a5548d5048ad

We're looking for the force that the sprinter is exerting but we don't know his acceleration!

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-Olz5wR23PA2L.PNG?alt=media&token=d3f9b0ac-6891-4738-ab0c-6870f1e0125b

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