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(II) A driver notices that her $1080-\mathrm{kg}$ car slows down from95 $\mathrm{km} / \mathrm{h}$ to 65 $\mathrm{km} / \mathrm{h}$ in about 7.0 $\mathrm{s}$ on the level when it is inneutral. Approximately what power (watts and hp) isneeded to keep the car traveling at a constant 80 $\mathrm{km} / \mathrm{h} ?$

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$2.9 \times 10^{4} W$$38 \mathrm{hp}$

03:42

Michael Mackenzie

Physics 101 Mechanics

Chapter 8

Conservation of Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Cornell University

University of Washington

Simon Fraser University

McMaster University

Lectures

04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

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Alright this question here is all about power and how it relates to the conservation of energy. So power's definition is changing energy over time and it's measured in watts. So we have that equation right here changing energy final minus initial energy divided by the time in seconds. Now the energy has to be in the standard units as well and that's in jewels. So for that to occur I need my velocities and meters per second. So up here, Very first step when I start listening out, what do I know in the problem? I've got my mask 1080 kg, that's in the standard unit necessary. But the velocities are not there in kilometers per hour. So I need to correct this by taking 1000 divided by 3600 and multiply that by 95 that will change two m/s. So that's an conversion that you should be familiar with at this point converting from kilometers per hour to meters per second. There's 1000 divided by 3600. So I do that to both velocities so that I'm in energy. So I can calculate the amount of energy and jewels here. The time is in seven seconds. So that's in standard units. So we're good there so I can start plugging in what I have. So I've got the power due to friction and we often think of power as things that are being generated that are generating energy or giving us energy but we can also look at it in terms of how fast is it taking away the energy. And so we can look at the power that the friction has, How much energy is it taking away per second. So if I take the final uh kinetic energy minus the initial kinetic energy one half mv squared minus one half mv O squared. And then divide that by the time that that energy last occurs, I can get the power of friction, which is a negative number, which makes sense since it's taking away energy every second when I calculated that. And then I get this negative 28,522 watts. That's telling me in every second a little over 28,500 jewels of energy is being lost due to friction and at each sector at the time. So that's quite a bit. So we need to have an engine that's actually maintaining that. And this is where the conservation of energy comes into play. Well, if I want to maintain the same amount of energy as I did, if it was a frictionless environment And friction is taking away over 28,500 per second and I need a car that will do the opposite of that and add that back in. So the friction friction and the car's powers need to be equal to each other. And so that we can say that the car's power needs to be around 2.9 times 10 to the fourth watts. And I used to significant figures because we had two significant figures on the time, as well as on the speeds.

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