4 Review of Conservation of Energy

Instructor’s Note


This unit, in fact this entire course, will spend a lot of time talking about energy: a topic covered extensively in Physics 131 as well as in your Biology and Chemistry courses. This chapter is therefore a bit different: we provide links to the relevant sections on energy from the Physics 131 textbook Forces, Energy, Entropy for your reference, with the key takeaways from each section. Just review what you need.

There are also a few homework problems at the end, just to make sure everyone is on the same page.

Relevant parts from Physics 131: Forces, Energy, Entropy:

A Video Reviewing Problem Solving with Conservation of Energy

This example can be either watched or read

With what minimum speed must you toss a  140 \, \mathrm{g} ball straight up to hit the  14 \, \mathrm{m} meter high roof of a gymnasium if you release the ball  1.3 \, \mathrm{m}  above the ground? With what speed does the ball hit the ground?

You can use conservation of energy to solve this problem.

What is the initial energy state of the ball? We have some kinetic energy and some potential energy, so we have both. How do we know we have kinetic energy? Because we throw the ball, if the ball has no initial Kinetic energy which means it’s not moving that means it doesn’t go up, it had to have had some kinetic energy for it to actually go up and had to have some initial velocity when we threw it. Does it have any initial potential energy? The ball starts  1.3 \, \mathrm{m} above the ground initially, this tells me it started out with some potential energy, it’s already above the ground.

What is its final energy state in the perfect world in physics land? Does it have Kinetic energy at the roof? No, we’re assuming it just touches the roof and has zero velocity at the roof for that moment in time, so its kinetic final energy is actually zero. All we have left is potential final energy.

 E_i = E_f

K_i + U_i = K_f + U_f

 \frac{1}{2} m v^2 + mgh_i = 0 + mgh_f

 \frac{1}{2}v^2 + gh_i = gh_f

What speed does it hit the ground? Energy initial equals energy final, what’s the initial energy state? My initial is the ball at the top of the ceiling. My final is just before it hits the ground. How fast does it hit the ground? It started from the roof, falls down. What is the energy state at the roof? It’s all potential. What’s the energy state the moment before it hits the ground? It’s lost all its potential energy, and its converted into kinetic energy.

 E_i  = E_f

 U_i  = K_f

 mgh_i  = \frac{1}{2} mv^2_f

 gh_i  = \frac{1}{2} v^2_f

 v_f = \sqrt{2 g h_i}

 v_f = \sqrt{2 \cdot (9.8 \, \mathrm{m/s^2}) \cdot (14 \, \mathrm{m}) } = 16.6 \, \mathrm{m/s}

Your friends Frisbee has become stuck 26 meters above the ground in a tree. You want to dislodge the Frisbee by throwing a rock at it. The Frisbee is stuck pretty tight, so you figure the rock needs to be traveling at least 5.4m/s when it hits the Frisbee. If you release the rock 1.6 meters above the ground, with what minimum speed must you throw it?

Energy initial has to equal energy final, what is my initial state of affairs? When I’m throwing the rock, that’s my initial state of affairs. Do I have kinetic energy in the beginning? I must have it. How do I know I must have kinetic energy? Because I’m throwing the rock, so the rock has to have some initial velocity. Do I have any initial potential energy? Yes, because I started 1.6 meters above the ground. What’s my final state of affairs? Do I have any kinetic energy at the end? When the rocks up there at the frisbee, does it have any kinetic energy? I know that it had to have a velocity, 5.4m/s, I know that the moment before I hit the frisbee I had to have this velocity. Therefore, I know I had some kinetic energy up there. Do I have any final potential energy? Yes, because it is up in the tree.

 E_i  = E_f

 K_i  + U_i  = K_f  + U_f

 \frac{1}{2} mv^2_i  + mgh_i  = \frac{1}{2} mv^2_f  + mgh_f

 \frac{1}{2} v^2_i  + gh_i  = \frac{1}{2} v^2_f  + gh_f

 v_i = \sqrt{2 \left( \frac{1}{2} v_f^2 + gh_f - gh_i \right) }


Homework Problems

Problem 5: Assuming negligible air resistance, what is the final speed of a rock thrown from a bridge?

Problem 6: How many DNA molecules can a single electron from an old-fashioned TV break?




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Physics 132: What is an Electron? What is Light? by Roger Hinrichs, Paul Peter Urone, Paul Flowers, Edward J. Neth, William R. Robinson, Klaus Theopold, Richard Langley, Julianne Zedalis, John Eggebrecht, and E.F. Redish is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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