Kinetic Energy of Cardinal & Baseball: Momentum Ratio

[philo51]

A cardinal (Richmondena cardinalis) of mass 4.50×10−2 and a baseball of mass 0.140 have the same kinetic energy. What is the ratio of the cardinal's magnitude of momentum to the magnitude of the baseball's momentum?

i derived an equation of 1*p^2/2m and I am not sure where to go from there.

 

[ZapperZ]

A cardinal (Richmondena cardinalis) of mass 4.50×10−2 and a baseball of mass 0.140 have the same kinetic energy. What is the ratio of the cardinal's magnitude of momentum to the magnitude of the baseball's momentum?

i derived an equation of 1*p^2/2m and I am not sure where to go from there.

First of all, you should ALWAYS be in the habit of making sure all numerical values have the appropriate units. You left this out in your question.

Now you are told that KE1 = KE2, where 1=the bird, 2=ball.

So let p1 and m2 be for the bird, and p2,m2 be the ball. You then have

$$\frac{p_1^2}{2m_1} = \frac{p_2^2}{2m_2}$$

Solve for p1/p2. You have everything you need already there.

Zz.

 

[mezarashi]

Kinetic energy is defined as: E = 1/2 mv^2
Equate this kinetic energy for the cardinal and the baseball. You will now have the velocity of the cardinal in terms of the velocity of the baseball.

Now momentum is defined as: p = mv
The ratio of momentum is defined as Pcardinal/Pbaseball.

Knowing the relationship between the cardinal's velocity and the baseball will allow you to cancel out the v's and solve ultimately for a constant.

[oh, i was beat lol]

 

[philo51]

hah wow i completely missed doing that thanks!

 

[philo51]

the 2nd question i got wrong too A man weighing 730 N and a woman weighing 500 N have the same momentum. What is the ratio of the man's kinetic energy to that of the woman ?

so if p= sqrt(2Km) and P1= P2

sqrt(2K(man)m)=sqrt(2K(woman)m) and if i solve for Km/Kw why doesn't that work out?

 

[mezarashi]

This should be your opportunity to test your understanding of the problem-solving technique.

You are essentially trying to solve for the velocity of the man in terms of the woman's velocity by equating their momenta. Kinetic energy is expressed in terms of mass and velocity. But you know one in terms of the other. In ratio form, they will surely cancel out. It's no different than the original question. Step by step. Good luck.