Question

A cardinal (Richmondena cardinalis) of mass 4.20×10−2 kg and a baseball of mass 0.146 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

Step-by-step explanation:

It is given that,

Mass of cardinal,
`m_c=4.2* 10^(-2)\ kg`

Mass of baseball,
`m_b=0.146\ kg`

Both cardinal and baseball have same kinetic energy. We need to find the ratio of the cardinal's magnitude
`p_c` of momentum to the magnitude
`p_c` of the baseball's momentum.

`E_c=E_b`

Kinetic energy is given by,
`E=(p^2)/(2m)`

`(p_c^2)/(2m_c)=(p_b^2)/(2m_b)`

`((p_c)/(p_b))^2=(m_c)/(m_b)`

`(p_c)/(p_b)=\sqrt{(m_c)/(m_b)}`

`(p_c)/(p_b)=\sqrt{(4.2* 10^(-2))/(0.146)}`

So,
`(p_c)/(p_b)=(53)/(100)`

So, the ratio of cardinal's magnitude of momentum to the magnitude of the baseball's momentum is 53 : 100