Fall 2016 Mechanics Week 7

This week, we look at systems of masses, like two masses tied together and a single mass that is both moving and rotating – with both linear and rotational kinetic energy. We can solve these problems with a dynamics lens as individual masses (resulting in linear equations), or as a system of masses where forces act on the system. However, I find the easiest way to look at them is through an energy lens. How does the system’s energy change? You decide what’s best for you.
For Tuesday,

first hour we look at a linear system.

Before Class

• Midterm #2 is next Tuesday, Nov. 8, from about 2:30 – 3:30.
• PS#6 is posted on the class main page. It’s due on Thursday! Please look at it as soon as possible.
• Read 6.0 Systems of masses that I wrote up for you
• Watch an introduction to simple systems This is an important video to understand systems.
• Please check out the standard process for solving the system with simultaneous dynamics equations, one equation for each mass: Atwood Machine by individual masses I won’t spend any more time on this method, but you are welcome to use it if you like.
• Then see the video about how to solve the A System of Masses Using EnergyWOW, I watched the video myself and … really it’s fast. It’s hard for me to follow it (and I made it). I remind you that I condense these discussions as much as possible. They are meant to be stopped every few seconds so you can take notes on the video or just think about what was said.

During Class

• Collect PS#5
• Looking at some physics systems

Second Hour we look at a rotational system

During Class

• A day at the races, racing rolling downhill!

Hi everyone!! – I was thinking about our discussion today about comparing how fast different objects roll down the hill…. and how there was lots of discussion about friction. We spoke about the different moments of inertia resulting in different amounts of rotational kinetic energy, but we didn’t talk about why friction and surface area doesn’t matter. However, we should be able to understand that friction shouldn’t matter:

• Using an energy lens, we understand that the potential energy turns to linear and rotational kinetic energy. There’s no heat energy produced because the surfaces don’t slide.
• We are dealing with static friction, so the different coefficients of friction don’t matter. Friction will be as large as it needs to be in order to roll without slipping. So yes, we can talk about friction because the friction does slow the rolling ball down (but not the cart), but not because the surface area or coefficient of friction are great. It’s because the object with the larger moment of inertia needs more frictional force to provide more torque get rotating. So, again it’s about the moment of inertia, not about the surface interaction.
• Lastly, the force of friction doesn’t depend on surface area. It depends on normal force and coefficient of friction, right? If you lower the surface area – like you stand on the ball of one foot instead of both feet flat on the ground, it isn’t easier to slide. When the surface area goes down with the same normal force, the same normal force is distributed over a smaller surface area, but results in the same frictional force.

I think it’s important to check in with ourselves that we are fixated on something and keep coming back to it. It’s kind of confusing to me too, but I look forward to returning to it some time.
Thanks for your efforts in class everyone – Pete

First Hour
We look at the parallel axis theorem and consider how it can make a problem easier to solve.

Before Class

Second Hour,

• BIG EXAM! and preparing for MT#2 next Tuesday