Power
Name: _______________________
I. WHAT IS POWER? Power is defined as the rate at which work is done. The average power, ̅ , equals the work divided by the time it takes to do it.
done
Date: ___________ Period: _____ The instantaneous power, P, is the work done at each instant.
̅ Since the work done in a process involves the transformation of energy from one type (or object) to another, power can also be defined as the rate at which energy is transformed. The work done in a process is equal to the energy transferred from one object to another object. For example, when you throw a baseball, your muscles do work to transfer energy from your body into the baseball. In this process energy is transformed from chemical energy in your body into mechanical energy of the baseball. The power of your throw is simply the rate, or how quickly, you transfer energy from your body to the baseball.
̅ In SI units, power is measured in joules per second, and this unit is given a special name, the watt (W): 1 W = 1 J/s. We are most familiar with the watt for electrical devices: the rate at which an electric lightbulb or heater changes electrical energy into light or thermal energy. But the watt is used for other types of energy transformation as well. For practical purposes a large unit is often used, the horsepower. One horsepower (hp) is defined as 550 ft lb/s, which equals 746 watts. An engine’s power is usually specified in hp or in kW (1 kW hp). II. ENERGY VS. POWER To see the distinction between energy and power, consider the following example. A person is limited in the work he or she can do, not only by the total energy required, but also by how fast this energy is transformed: that is, by power. For example, a person may be able to walk a long distance or climb many flights of stairs before having to stop because so much energy has been expended. On the other hand, a person who runs very quickly up stairs may feel exhausted after only a flight or two. He or she is limited in this case by power, the rate at which his or her body can transform chemical energy into mechanical energy. Karina Bonnie 1. Karina and Bonnie climb up two identical flights of stairs with height 2 meters. They both 2m have mass of 60-kg, but Karina walks up the stairs while Bonnie jogs up the stairs. (a) Who does more work? Explain.
AP Physics C – 2013
(b) Who had more power output? Explain.
Work and Energy – Page 5
12/5/13
III. POWER IN TERMS OF FORCE 2. Write an expression for power in terms of the net force applied to an object and its velocity. (a) Write the equation instantaneous power.
(b) Write the equation for the work done by a variable force.
(c) Now solve for equation.
(d) Rewrite using the definition of the dot product.
and plug into the power
IV. EXAMPLE PROBLEMS 3. How long will it take a 1750-W motor to lift a 335-kg piano to a window on the sixth story which is 16.0 m above the ground?
4. A 1400-kg sports car accelerates from rest to 26 m/s in 7.4 s. What is the average power delivered by the engine?
5. Calculate the power required of a 1400-kg car under the following circumstances. Assume that the average retarding force (from friction and drag) on the car is 700 N throughout. (a) The car climbs a 10° hill (a fairly steep hill) at a steady rate of 22 m/s.
(b) The car accelerates along a level road from 25 m/s to 30 m/s in 7.0 s to pass another car.
