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Page 213: Practice Problems

Exercise 47

Step 1

1 of 2

In this problem, Engine 1 does twice the work of Engine 2. We are asked if the given information is enough to conclude that engine 1 produces twice as much power as engine 2.

Step 2

2 of 2

The answer is **no**. The definition of power states that power is the rate in which work is done. We are not given the time in which the work is done, so we cannot compare the power the engines produce.

Exercise 48

Step 1

1 of 6

In this problem, a runner of mass $m = 70.0~mathrm{kg}$runs up a flight of stairs. There was a total of $1576$ steps, with each step having an altitude of $0.20~mathrm{m}$ and the total time is 9 min 33 s. We calculate the average power in watts and in horsepower. We use $g = 9.81~mathrm{m/s^{2}}$.

Step 2

2 of 6

First, we convert the time into seconds.

$$
t = 9~mathrm{min}~30~mathrm{} = 570~mathrm{s}
$$

Step 3

3 of 6

The total change in elevation is the product of the number of steps and the altitude of each step.

$$
begin{aligned}
h &= left( 1576 right) left( 0.20~mathrm{m} right) \
h &= 315.2~mathrm{m}
end{aligned}
$$

Step 4

4 of 6

The total work done must be equal to the increase in potential energy. Hence

$$
W = mgh
$$

Step 5

5 of 6

One hp is equal to $746~mathrm{W}$. Hence, the power is also

$$
begin{aligned}
P &= 379.73305~mathrm{W} times frac{1~mathrm{hp}}{746~mathrm{W}} \
&= 0.50903~mathrm{hp} \
P &= boxed{ 0.509~mathrm{hp} }
end{aligned}
$$

Result

6 of 6

$$
P = 380.~mathrm{W} = 0.509~mathrm{hp}
$$

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Page 213: Practice Problems

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