Chapter Review
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Chapter 7: Work and Kinetic Energy Chapter Review |
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7-4 Power
From a practical standpoint, the mere fact that a certain amount of work is done is not always good enough. The question of how long it takes to do this work often determines the practical values of certain devices. For example, everyone wants a car that can go from 0 to 60 mi/h, but no one wants it if it takes 5 min. The quantity we use to measure how rapidly work is done is called power.
Power is the rate at which work is done. For the applications of interest to us, we will mainly use the average power, which is determined as the amount of work done W divided by the amount of time t required to do it
The unit of power must be the unit of work divided by the unit of time, or joules per second (J/s). In the SI unit J/s is given the name watt (W). You are probably familiar with this unit, as it is common to give the power rating of light bulbs in watts. For cases when work is being done by a constant force on an object moving at constant speed, the power delivered by that force is given by
P = Fv
Verify, that the product Fv has SI units of watts. Also be aware that the above equation can be useful even if the force or the speed is not constant. In these cases the average power can be calculated by substituting the average force or the average speed: P = Favv = Fvav. If both F and v vary, use P = Favvav.
Example 7.5 An Industrial Pulley: The motor of a chain-linked industrial pulley, designed to lift heavy weights, is rated to deliver 3000 watts of power on average. If the mechanism is only 80% efficient, how long would it take to raise a 55 kg crate a height of 12 m at a constant speed?
Picture the Problem The picture shows part of the pulley system lifting the crate with a constant upward velocity v.
Strategy The amount of time it takes is related to how much work is done and the rate at which it is done (the power). Therefore, we will determine the work done and the actual power output.
Solution
| 1. Get the expression for the time t: |  |
| 2. Since the pulley applies a force in the same direction as the displacement: | Wpulley = Fpulleyd |
| 3. Since its velocity is constant the force of the pulley must exactly balance the weight: |  |
| 4. Using the fact that the motor is 80% efficient, find the time t: |  |
Insight This problem could also have been solved by finding the velocity and calculating the time for the crate to move the 12 m distance. Try it.
Physlet Illustration: The Hill Climb | |
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| The engine of the yellow Lamborghini shown above delivers 50 hp to the drive wheels. The car moves up a slope at its maximum speed. The distance grid is in meters and the time is shown in seconds. Neglecting the effects of air resistance, what is the value of the maximum speed? Why? Start | |
Hints
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Exercise 7.6 Test Driving: The manufacturer of a 1500 kg automobile advertises that the engine delivers 175 hp. If all of this power is transferred to the motion of the car with 100% efficiency, what 0 to 60 mi/h time would you expect the car to achieve?
Solution: The following information is given in the problem:
Given: m = 1500 kg, P = 175 hp, vi = 0.0 m/s, vf = 60 mi/h; Find: t
We have a mix of units here, so let's convert everything to SI.
, and
The time for the car to reach 60 mi/h depends on the amount of work done: t = W/P. The work done by the car can be determined from the work-energy theorem
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So, the expected 0 to 60 time would be
Look up some typical 0 to 60 times. What does this say about the efficiency at which the car converts the engine's power into the motion of the car?
Practice Quiz
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