Question

A cardinal (Richmondena cardinalis) of mass 3.70×10−2 kg and a baseball of mass 0.144 kg have the same kinetic energy. What is the ratio of the cardinal's magnitude pc of momentum to the magnitude pb of the baseball's momentum?

Answer 1

Answer:

$\frac{p_{c}}{p_{b}}\approx 0.507$

Explanation:

Since the cardinal and ball have the same kinetic energy, it is possible to determine the ratio between speeds. (c for cardinal, b for baseball)

$K_{c} = K_{b}$

$\frac{1}{2}\cdot m_{c}\cdot v_{c}^{2}= \frac{1}{2}\cdot m_{b}\cdot v_{b}^{2}$

$\frac{v_{c}}{v_{b}}=\sqrt{\frac{m_{b}}{m_{c}} }$

The ratio is obtained by multiplying each side by $\frac{m_{c}}{m_{b}}$:

$\frac{p_{c}}{p_{b}}=\frac{m_{c}}{m_{b}}\cdot \sqrt{\frac{m_{b}}{m_{c}} }$

$\frac{p_{c}}{p_{b}}= \sqrt{\frac{m_{c}}{m_{b}} }$

The value of this ratio is:

$\frac{p_{c}}{p_{b}}\approx 0.507$

Answer 2

Explanation:

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