## Homework Helpers: Physics

**3 Work, Energy, Power, and Momentum**

**Lesson 3–4: Power**

Imagine two men employed to restock the shelves of a supermarket with cans of soup. Each time one of the men lifts a can, he exerts a force on it and lifts it up. By exerting a force on the can over a distance, he does work on it. If each man lifts the same number of cans from a box and places them on the same shelf, they have done the same amount of total work. If one man works faster than the other, he will have a higher power rating. **Power** is the rate at which work is done, and it is measured in the units called **watts** (W), which you may be familiar with from your experience changing lightbulbs. One watt is equal to one joule/second. A 60-watt bulb converts 60 joules of electrical energy to heat and light per second.

Let’s go over some examples.

**Example 1**

A man restocking a shelf lifts 24 cans of soup, each with a mass of 450 g, to a height of 55 cm in a period of 45 seconds. Find his average power output during this period of time.

The first thing that you will need to do is convert all of the given units into appropriate units. Remember: The unit of power (watt) is based on the newton, which is derived from meters and kilograms. We must convert our given quantities, as shown here:

**Convert:**

Now let’s calculate the total mass of cans that the man lifted.

**Given:** *m* = 11 kg g = 9.81 m/s^{2} *h* = 0.55 m Δ*t* = 45 s

**Find:** P

Let’s try the same situation but with a different unknown.

**Example 2**

Another man working on restocking the soup from __Example 1__ had an average power output of 1.6 W lifting 24 cans of soup to the same shelf, which has a height of 0.55 m. How long did it take him to finish the task?

**Given:** P = 1.6 W *m* = 11 kg g = 9.81 m/s^{2} *h* = 0.55 m

**Find:** Δ*t*

Another unit of power that you will sometimes encounter is horsepower, or hp for short. One horsepower is equal to 746 watts. If you encounter a problem involving horsepower, convert to watts before trying to solve.

**Example 3**

A motor has a power rating of 5.5 hp. How much work can it do, operating at full power, in 3.0 minutes?

**Example 4**

A worker pushes a box with a force of 35 N over a period of 6.0 s, moving the box 2.5 m. How much power does the worker supply?

**Given:** F = 35 N Δ*t* = 6.0 s d = 2.5 m

**Find:** P

Lesson 3–4 Review

__1.__ _______________ is the rate of doing work, measured in watts.

__2.__ A crane lifts a packing crate with a mass of 355 kg to a height of 15.5 m with a motor operating at a constant rate of 2.50 × 10^{3} watts. How long does it take to lift the crate?

__3.__ What power would be required to lift a 340 N weight to a height of 3.50 m in 5.0 seconds?