# W16 Mechanics Week 6

Day 1: Gravitational Energy and Escape Speed
Integrate force to find potential energy for gravitational potential energy (graphs).
Use Conservation of energy in order to find velocity at different distances from a planet.

Before Class:

In Class

• Hand in PS#4
• Questions on PS#4

After Class

Day 2: Centripetal Acceleration and the Satellite Problem

Before Class

• Read Chapter 6 in your text. You don’t have to read it exhaustively, but please understand where the information is. Chapter 6.2 explains centripetal acceleration. 6.3 discussion forces that produce circular motion, using the word “centripetal force”, which I find to be a damaging term. Please come prepared to ask and answer the question, “why is there no such thing as ‘centripetal force’?” 6.4 deals with other fictitious forces like “centrifugal force” and “Coriolis Force”. It is important to know what these forces are… or claim to be so that you will know not to use them.
• Watch derivation of Centripetal Acceleration and how to use it. Make sure you can do this for Big Exam.
• PS#5 posted
• I posted MT#1 solutions – they may not be the best solutions, but they’re the way I’d do it.
• Solutions in the process of being posted for PS#4. I am embarrassed to realize that there was no diagram for Problem #7, so I’ll be interested to see how you did it. In any case, I posted the solution and encourage you to examine the work as it’s a pretty important part of mechanics education. – I apologize for the gaff.

In Class

After Class

Day 3: Circular Dynamics

sum of the forces = m*a, for centripetal acceleration
Take away Concept: When dealing with circular motion, dynamics is just the same as always: the vector sum of the forces = m*a. The only difference is that “a” is centripetal acceleration.

Before Class:

• A video on the conical pendulum
• I posted MT#1 solutions – they may not be the best solutions, but they’re the way I’d do it.
• Yesterday in class, we did an experiment together. I would like you to repeat the experimental calculations without a calculator or trigonometry. Here is what happened: I raised the angle of the turntable’s metal surface until the mass slid. The angle made a roughly 3-4-5 right triangle (Dynamics… follow the protocol). Then I wanted to find out how far a mass would go as it fell about a meter in height after it slipped from the turntable’s surface from a 20 cm radius as I sped it up. In the process please identify all the lenses… I used all of them except momentum as far as I can remember. Please make good use of the dynamics protocol. Here is what I got: coefficient of friction ~ 0.75 (explain why you know it’s the dynamics protocol), the speed at which it leaves the turntable ~ 1.2 m/s, the vertical speed it attains when I drop it from the ~ 1m height, ~ 4.5 m/s (explain why you know it’s energy conservation). The time it takes to fall ~ 0.4 s (explain how you use kinematics). The horizontal distance it should travel as it falls with parabolic trajectory from the turntable as it falls downward, ~ 1/2 meter (kinematics). See if you can get these answers.

Where do you weigh more on a perfectly spherical world: On the equator or at the pole?

For Big Exam #4 – make sure you can derive the expression for centripetal acceleration

Day 4: Trigonometry! Projectile Motion; Full Kinematics in one- and two-dimensions

In Class:

• Use Algebra to solve one-dimensional problems – solve the “catching the bus”, or “catching the speeder” problem.
• Use trigonometry to solve projectile motion problems

Before Class

• Solutions to BE#4 posted on main webpage. Please see them. I forgot to include that the speed of the car going over the hill was 20 m/s, I’m dreadfully sorry! Please see the solutions before class and understand how to work this problem.
• From Textbook: Read chapter 2 – most of it is review, and you should skim over it. However, check out the stuff that’s new, and know where some of the other information.
• See and then you’re allowed to use those two unhelpful (in my opinion) equations, although hopefully, you’ve realized by now that you can get along without them just fine.
• Read section 3.4 on projectile motion. See how they do it and compare it to the video on projectile motion.

In Class

• Shooting the Monkey
• problem solving! PS#5

After Class