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January 20, 2022
Do systems really have a fixed amount of energy?
Rutgers, The State University of New Jersey
University of Michigan - Ann Arbor
(I) What force is needed to accelerate a sled (mass = 55 kg) at 1.4 m/s$^2$ on horizontal frictionless ice?
(II) According to a simplified model of a mammalian heart, at each pulse approximately 20 $g$ of blood is accelerated from 0.25 m/s to 0.35 m/s during a period of 0.10 s. What is the magnitude of the force exerted by the heart muscle?
(I) A constant friction force of 25 N acts on a 65-kg skier for 15 s on level snow.What is the skier's change in velocity?
(I) A 110-kg tackler moving at 2.5 ms meets head-on (and holds on to) an 82-kg halfback moving at 5.0 m/s. What will be their mutual speed immediately after the collision?
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welcome to six on mechanical energy. Mechanical energy turns out to be the sum of kinetic energy, plus another type of energy that we haven't discussed yet. But we've started to see where it comes from. If you recall in one of the previous sections we talked about forces called restoring forces and the specific example we gave was that of a spring where a box would come in. And if the box compresses the spring to some distance, then some time later, the spring will actually push the box back. And the box will now have velocity this way instead of this way. Remember that kinetic energy is equal to one half m v squared. It doesn't care about the direction. So what happens here is it has some kinetic energy going in kinetic energy initial, and then it's got zero kinetic energy once it stops moving, and then suddenly it has kinetic energy back again as it left. So somehow this system stores and then returns kinetic energy. And the way it does it is by conserving the total amount of mechanical energy. So we're gonna I'm just going to tell you the name and write down the symbol here, and we'll discuss more what it means in the future. So you is what we call potential energy. Okay, it's potential. Energy is energy that could cause motion here and is tied to kinetic energy in this way. And it turns out that we can relate potential energy toe work as well. So the next few sections are all going to be about not just potential energy, but the relationship between kinetic energy and potential energy and how they combined to make this thing called mechanical energy, which is what we call conserved, meaning that unless some sort of external or dissipated forces brought into the system, mechanical energy will never change. It will always be conservative, will always be some total. So if I were going to draw a plot to illustrate what that looks like, it would be something like this. I would say I had different energies is a function of time. I might say I have kinetic energy here, and then I have potential energy here, and then I have total mechanical energy here. It's a function of time. Well, if kinetic energy starts low, then goes high and comes back, potential energy mark start high and then zero out and then come back. And meanwhile, mechanical energy. It's just constant because it is the sum of kinetic energy and potential energy. Therefore, it's since it's always adding these up and all of the energy and the system is either kinetic or potential energy that's causing motion. At least then all of that energy is adding up to the same amount at all times. As long as I said, as there's no dissipated forces removing energy, turning into thermal energy or anything else, any external force on the system will have this conservation of mechanical energy, So let's see how this all works.
Equilibrium and Elasticity
Moment, Impulse, and Collisions
Rotation of Rigid Bodies
Dynamics of Rotational Motion