Question

A cardinal (Richmondena cardinalis) of mass 3.90×10⁻² kg and a baseball of mass 0.140 kg have the same kinotic eneegy. What is the ratio of the cardinar's magnitude Pe of momentum to the magritude ps of the baseball's momentum?

Answer 1

To find the ratio of momenta of a cardinal and a baseball with equal kinetic energies, the formula Pe / Ps = sqrt(me / ms) is used, where me and ms are the masses of the cardinal and the baseball, respectively.

Step-by-step explanation:

To find the ratio of the cardinal's momentum Pe to the baseball's momentum Ps, given that both have the same kinetic energy, we start with the relationship between kinetic energy (KE) and momentum (p):

KE = p2 / (2m), where p is the momentum and m is the mass of the object.

Since both the cardinal and the baseball have the same kinetic energy, we equate their kinetic energy expressions and solve for the ratio of their momenta:

(Pe2/(2me)) = (Ps2/(2ms)), where me is the mass of the cardinal and ms is the mass of the baseball.

Pe2 / Ps2 = me / ms

By taking the square root of both sides, we get:

Pe / Ps = sqrt(me / ms)

Substitute the given masses (me = 3.90×10−2 kg for the cardinal and ms = 0.140 kg for the baseball):

Pe / Ps = sqrt(3.90×10−2 kg / 0.140 kg)

After performing the calculations, the ratio of the cardinal's momentum to the baseball's momentum is found to be:

Pe / Ps = sqrt(3.90×10−2 / 0.140)