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Hello everyone.
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So for this video, we'll be going over work, energy, and power, and specific power.
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So for this problem, we are asked to find specific power, and we are given that we have this quarterback that weighs 95 kilograms, and he accelerates a 0 .42 kilogram ball from rest to 24 meters per second.
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And that change in energy happens in .083 seconds.
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So let's go over the concepts that we know.
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So the concepts that we know regarding energy, so we know that energy is equal to the kinetic energy plus potential energy.
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And in this problem, we will be looking at the change in energy.
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So the change in energy is equal to the change in kinetic energy plus the change in potential energy.
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And just to review this delta, so we will have the change in connect energy plus the change in potential energy.
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And this delta, this triangle symbol you see, is equal to initial minus final.
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So if i write this out, we'll have that the, oh, so this delta, i mean, this delta symbol is equal to, is similar to saying final minus initial.
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So this delta, and let me just point at it with this green arrow, this delta, this triangle symbol, delta means the change of, so the change of energy and the change of potential and the change of kinetic energy.
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So the change in energy is equal to the final energy minus the initial energy.
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And if i want to write this out fully, it will be that the final kinetic energy minus the initial kinetic energy plus the final potential energy, minus the initial potential energy.
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And that's how we can describe the energy of the system, or the change in energy of the system.
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Now, we also know that kinetic energy, so kinetic energy is equal to one -half mv squared, and that potential energy is equal to m -g -h.
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Now, we are also asked to solve for power.
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And what i'm going to do is i'm actually write potential energy so that we don't confuse it with power.
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I'm going to write it pe for potential energy.
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And i'm going to use capital p.
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So let me include the potential.
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Let me include the e's over here.
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So we have potential energy, potential energy.
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And i'm going to say that.
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Capital p would stand for power.
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So power would be equal to the change in energy over the change in time.
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So this change in energy over the change in time will give us units of joules per second, which is in watts.
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So joules per second can also be, is another way of saying watts.
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So watts is joules per second and is the unit of power.
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But we are asked to find specific power.
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So specific power, we can label this as p.
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So sp will stand for specific power.
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Specific power is equal to the power.
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So the power of the transformation, which we will write as p.
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So it will be the power of the transformation divided by, the time or divided by the mass of the agent that caused that transformation.
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So specific power is equal to the power of the transformation divided by the mass of the agent that caused that transformation.
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So the units will be in watts per kilogram.
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And that covers all the concepts that we need to know for this problem.
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So we have to know this relationship with change of energy.
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We have to keep in mind that kinetic energy is equal to 1 .5 mv squared and that power is equal to the change in energy over time and the specific power is equal to power of the transformation divided by the mass of the agent to cause the transformation.
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Now in green, i'll write out our givens.
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So we were given the mass of the quarterback.
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So the quarterback weighs 95 kilograms, and i will label that as capital m.
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So capital m is equal to 95.
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So our quarterback here is equal to 95 kilograms.
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And he is our agent.
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He is the one that caused this transformation.
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He threw the ball, which then, cause the ball to accelerate from zero meters per second to 24 meters per second.
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And that is another thing that we have.
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So we have that our initial velocity is that, so the ball starts at rest.
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So our initial velocity is zero.
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So we have an initial velocity of zero.
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And we have a final velocity.
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So it will be final.
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We have a final velocity of 24 meters per second.
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Now we are also given that the mass of the ball, so the mass of the ball is, was given to be, and i'll label this m sub b, so little m sub b, is equal to 0 .42 kilograms.
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So we're given that our ball is 0 .42, weighs 0 .42 kilograms.
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And we're also given the time at which the ball went from rest to 24 meters per second.
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So this is the time of the transformation.
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So the time of the change of energy is 0 .083 seconds.
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So that is everything that was given to us for this problem.
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So to start off this problem, we want to find specific power.
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So specific power, so let's see, step one would be to, so we have this equation for specific power, which tells us that the specific power is equal to the power of the transformation divided by the mass of the agent.
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So we're given the mass of the agent, which is the quarterback, that's 95 kilograms, but we're not given the power, but we know this description of power.
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And so that's the first thing we want to do is we need to find what power is.
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So find the power.
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We need to find the power of this transformation.
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So to find power, we have this description of power to be the change of energy divided by the change in time.
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So this change in energy over the change in time, we know the change in time.
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We're given that as well to be 0 .083 seconds.
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So that's the time at which the ball went from rest to 24 meters per second.
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Now this change of energy is the energy that the system started with and ended with.
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So, or rather the reverse.
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So it's the, it is the, so the change in energy is equal to the final energy minus the initial energy.
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And we could specifically look at it like this.
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So we have that the change in energy is equal to, is equal to the change in kinetic energy plus the change in potential energy...