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Chapter 9: Q. 41 (page 229)

A $70$ kg human sprinter can accelerate from rest to $10$ m/s in $3.0$ s. During the same time interval, a $30$ kg greyhound can go from rest to $20$ m/s. What is the average power output of each? Average power over a time interval $鈭� t$ is $\frac{鈭� E}{鈭� t}$

Short Answer

Expert verified

Average power output of sprinter is $1166.67 W$ and of greyhound is $2000 W$ .

Step by step solution

01

Concept

Concept:
The K.E. of an object moving with velocity is

v

K = \frac{1}{2} m v^{2}

Here

m

is that the mass ofthe thing.
The average output is calculated by dividing the ultimate mechanical energy by the quantity of your time it tookto induce that energy:

P = \frac{K}{喂}

Here

t

is that the time.
Substitute the expression for K.E. within the above equation.

$P = \frac{\frac{1}{2} m v^{2}}{t}$

02

Typical Power

In the case of the sprinter,the typical power output is:
$P = \frac{\frac{1}{2} m v^{2}}{t}$
Substitute $70 k g$ for mass, $20 m / s$ for speed and $3 s$ for time.

$\begin{aligned} P = \frac{\frac{1}{2} (70 kg) (10 m / s)^{2}}{3 s} \end{aligned}$

$= 1166.67 W$

03

Step 3. Average power output

The greyhound's average power output is:
$P = \frac{\frac{1}{2} m v^{2}}{t}$

Substitute $30 k g$ for mass, $10 m / s$ for speed, and $3 s$ for time.

\begin{aligned} P = \frac{\frac{1}{2} (30 kg) (20 m / s)^{2}}{3 s} \end{aligned}

$= 2000 W$

So, the greyhound is truly outputting more average power than the sprinter in this period of timel

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Most popular questions from this chapter

Evaluate the dot product $\overset{鈫�}{A} 路 \overset{鈫�}{B}$ if

a). role="math" localid="1647759176820" $\overset{鈫�}{A} = 3 \hat{i} + 4 \hat{j}$ and $\overset{鈫�}{B} = 2 \hat{i} - 6 \hat{j}$

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a. What is the cyclist鈥檚 power output while riding at a steady $7.3 m / s (16 m p h)$ ?

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c. The food calorie is equivalent to $4190 J .$ How many calories does the cyclist burn if he rides over level ground at $7.3 m / s f o r 1 h r$ ?

A $10$ -cm-long spring is attached to the ceiling. When a $2.0$ kg mass is hung from it, the spring stretches to a length of $15$ cm.

a. What is the spring constant?

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