All Solutions

Page 199: Practice Problems

Exercise 16

Step 1

1 of 3

In this problem, a goldfish of mass $m = 13 times 10^{-3}~mathrm{kg}$ has a speed of $v = 8.5~mathrm{m/s}$. We calculate its kinetic energy.

Step 2

2 of 3

From the definition, the kinetic energy is

$$
begin{align*}
KE &= frac{1}{2}mv^{2} \
&= frac{1}{2} left( 13 times 10^{-3}~mathrm{kg} right) left( 8.5~mathrm{m/s} right)^{2} \
&= 0.46962~mathrm{J} \
KE &= boxed{ 0.47~mathrm{J} }
end{align*}
$$

Result

3 of 3

$$
KE = 0.47~mathrm{J}
$$

Exercise 17

Step 1

1 of 3

In this problem, the kinetic energy of a small boat is $KE = 15000~mathrm{J}$. The boat’s speed is $v = 5.0~mathrm{m/s}$. We calculate its mass.

Step 2

2 of 3

From the definition, we have

$$
begin{align*}
KE &= frac{1}{2}mv^{2} \
implies m &= frac{2KE}{v^{2}} \
&= frac{2 left( 15000~mathrm{J} right)}{left( 5.0~mathrm{m/s} right)^{2}} \
m &= boxed{1200~mathrm{kg}}
end{align*}
$$

Result

3 of 3

$$
m = 1200~mathrm{kg}
$$

Exercise 18

Step 1

1 of 3

In this problem, a baseball has mass $m = 0.15~mathrm{kg}$ and has kinetic energy $KE = 77~mathrm{J}$. We calculate its speed.

Step 2

2 of 3

From the definition of kinetic energy, we have

$$
begin{align*}
KE &= frac{1}{2}mv^{2} \
implies v^{2} &= frac{2KE}{m} \
v &= sqrt{frac{2KE}{m}} \
&= sqrt{frac{2 left( 77~mathrm{J} right)}{0.15~mathrm{kg}}} \
&= 32.04164~mathrm{m/s} \
v &= boxed{ 32~mathrm{m/s} }
end{align*}
$$

Result

3 of 3

$$
v = 32~mathrm{m/s}
$$

unlock

All Solutions

Page 199: Practice Problems

Haven't found what you were looking for?

Search for samples, answers to your questions and flashcards