Momentum Ratio: Why is it Wrong?

[David112234]

Homework Statement

Homework Equations

KE = 1/2 M V²
P = M V

The Attempt at a Solution

p = mv
p_cardinal = .0450v_cardinal
p_baseball= .144v_baseball

0450v_cardinal/144v_baseball
Why is this not the correct answer?

I know KE are equal so
KE_cardinal= ½ .0450 v²
KE_baseball= ½ .144 v²

so .0450 v² = .144 v²
how is knowing the KE are equal any helpful, and why is my original answer not right?

 

[haruspex]

Yes, the ratio of the momenta is m_cardv_card/(m_basev_base), but you do not know what those velocities are. In your attempted answer you seem to have assumed they are the same.
In your KE equations you even used v for both velocities, ending up with a statement that is clearly not true.
Write the KE equations again, being careful to use different variables for the two velocities, and use them to find the velocity ratio.

 

[David112234]

Yes, the ratio of the momenta is m_cardv_card/(m_basev_base), but you do not know what those velocities are. In your attempted answer you seem to have assumed they are the same.
In your KE equations you even used v for both velocities, ending up with a statement that is clearly not true.
Write the KE equations again, being careful to use different variables for the two velocities, and use them to find the velocity ratio.

I know KE are equal so
KEcardinal= ½ .0450 v_cardinal2
KEbaseball= ½ .144 v_baseball2

.0450 = v_baseball²
______ _________
.144 = v_cardinal²

 

[David112234]

and now I take the square root to find v_c/v_bb and plug that into
mv_c/mv_bb ?

 

[haruspex]

and now I take the square root to find v_c/v_bb and plug that into
mv_c/mv_bb ?

Yes. (But it is better technique to keep everything algebraic, only plugging in numbers at the final step. This has many advantages.)

 

[David112234]

Yes. (But it is better technique to keep everything algebraic, only plugging in numbers at the final step. This has many advantages.)

m_c*√m_bb
-------------------------------------
m_bb*√m_c

.0450√.144 / .144√.0450

Is this correct?

 

[haruspex]

m_c*√m_bb
-------------------------------------
m_bb*√m_c

.0450√.144 / .144√.0450

Is this correct?

Yes, but you can simplify that a little. I would move everything inside the square root function.

 

[David112234]

Yes, but you can simplify that a little. I would move everything inside the square root function.

√.002025*.144/ √.020736*.0450 = .5590169944
I put it in and it is correct. thank you

 

[haruspex]

√.002025*.144/ √.020736*.0450 = .5590169944
I put it in and it is correct. thank you

ok!
But I meant, simplify it while still in algebraic form. Never plug numbers in until the final step. Many advantages to be had.