4.2.3 Power

Question 1

Power

Answer 1

• Average power is the amount of work done per unit time: .
• Instantaneous power is the rate at which work is done at an instant in time: , or equivalently, .
• The mks unit of power is the watt (W): 1W

Question 2

A variable force described by the equation
F (t) = at ^2 + 5bt, where a and b are positive constants, moves an object 4 m in 3 s. The force is directed in the direction of motion of the object. Which of the following is the average power used to move the object?

Answer 2

24a + 20b

Question 3

A 50 kg girl runs up a staircase in 20 s, and a 60 kg boy runs up the same staircase in 15 s. Which of the following is the ratio of the power generated by the girl to the power generated by the boy?

Answer 3

5 : 8

Question 4

A 4-N force is used to move an object 2 m in 10 s. Which of the following is the power generated while moving the object?

Answer 4

0.8 W

Question 5

A 150-horsepower engine is moving a vehicle at a constant speed of 20 m / s. Which of the following is the average force in newtons the engine is applying to the vehicle?

Answer 5

5,595 N

Question 6

Evaluate the following statement as true or false. When you lift something that weighs twice as much as another object, and it takes 50% more time to lift the heavier object the same height as the lighter object, you are generating the same amount of power in both instances.

Answer 6

false

Question 7

An Olympic athlete with a mass of 65 kg runs up a large hill that is 0.6 km high. The total distance the athlete runs to get to the top of the hill is 3.0 km. If it takes the runner 30 minutes to do this, which of the following is the average power generated in both watts and horsepower?

Answer 7

210 W, 0.28 hp

Question 8

A roller coaster car with a mass of 1,000 kg starts at rest on a hill that is 30 m high. As it travels, computerized brakes reduce the speed by 5 m / s in 2.0 s as the car goes around a sharp turn. This turn is at a height of 10 m. How much power must the brakes generate in order to slow the roller coaster car? Assume all friction is negligible.

Answer 8

43,750 W

Question 9

True or false?
If a power company charges eight cents per kilowatt-hour (kWh), and a customer keeps a 100-watt outdoor light bulb on for 10 hours every night for a 30-day charging period, the customer’s bill for that single light bulb is over $5.00 for that period of time.

Answer 9

false

Question 10

The power generated by an unknown force is given by the expression P = 6at − b, where a and b are positive constants. How much work would be done by the unknown force in 10 s?

Answer 10

300a − 10b