Part A:

A cardinal (Richmondena cardinalis) of mass 4.50×10^−2 kg and a baseball of mass 0.142 kg have the same kinetic energy. What is the ratio of the cardinal's magnitude p(c) of momentum to the magnitude p(b) of the baseball's momentum?

Part B:
A man weighing 650 N and a woman weighing 460 N have the same momentum. What is the ratio of the man's kinetic energy K(m) to that of the woman K(w)?

See Wed,11-28-12,7:45am post.

Part A:

To find the ratio of the cardinal's momentum to the baseball's momentum, we need to first calculate their respective momenta.

The momentum of an object is given by the equation:

p = m * v

Where p is the momentum, m is the mass, and v is the velocity. In this case, we are comparing the kinetic energy, which is given by:

KE = (1/2) * m * v^2

Since the objects have the same kinetic energy, we can set their kinetic energy equations equal to each other:

(1/2) * m(c) * v(c)^2 = (1/2) * m(b) * v(b)^2

Here, m(c) represents the mass of the cardinal, v(c) represents the velocity of the cardinal, m(b) represents the mass of the baseball, and v(b) represents the velocity of the baseball.

We can simplify this equation by dividing both sides by (1/2):

m(c) * v(c)^2 = m(b) * v(b)^2

To find the ratio p(c) / p(b), we can divide both sides of the equation by v(b):

m(c) * v(c) = m(b) * v(b)

Now, we have:

p(c) = m(b) * v(b) / v(c)

p(b) = m(b)

The ratio of the cardinal's momentum to the baseball's momentum can be calculated by:

p(c) / p(b) = (m(b) * v(b) / v(c)) / m(b)

We can plug in the given values to compute the ratio.

Part B:
To find the ratio of the man's kinetic energy to that of the woman, we need to calculate their respective kinetic energies.

The kinetic energy of an object is given by the equation:

KE = (1/2) * m * v^2

Where KE is the kinetic energy, m is the mass, and v is the velocity. In this case, we are given that the momentum of the man and woman is the same.

The momentum of an object is given by the equation:

p = m * v

Since the momentum of the man and woman is the same, we can set their momentum equations equal to each other:

m(m) * v(m) = m(w) * v(w)

Here, m(m) represents the mass of the man, v(m) represents the velocity of the man, m(w) represents the mass of the woman, and v(w) represents the velocity of the woman.

We can solve this equation for v(m):

v(m) = (m(w) * v(w)) / m(m)

Now, we need to substitute this expression for v(m) back into the kinetic energy formula:

KE(m) = (1/2) * m(m) * ((m(w) * v(w)) / m(m))^2

Simplifying this equation will allow us to find the ratio K(m) / K(w).

Part A:

First, we can calculate the kinetic energy of the cardinal and the baseball using the formula for kinetic energy:

Kinetic energy (K) = 1/2 * mass * velocity^2

Given:
Mass of the cardinal, m(c) = 4.50×10^−2 kg
Mass of the baseball, m(b) = 0.142 kg
Kinetic energy of both objects is equal

Since both objects have the same kinetic energy, we can set up the equation:

1/2 * m(c) * v(c)^2 = 1/2 * m(b) * v(b)^2

To simplify the equation, we can divide both sides by 1/2:

m(c) * v(c)^2 = m(b) * v(b)^2

Now, let's find the ratio of the magnitudes of momentum:

p(c) = m(c) * v(c)
p(b) = m(b) * v(b)

The ratio of p(c) to p(b) is given by:

p(c) / p(b) = (m(c) * v(c)) / (m(b) * v(b))

However, we need to simplify this further using the equation we derived earlier:

p(c) / p(b) = (m(c) * v(c)) / (m(b) * v(b))
= (m(c) * v(c)^2) / (m(b) * v(b)^2)
= 1 (since m(c) * v(c)^2 = m(b) * v(b)^2)

Therefore, the ratio of the magnitude of the cardinal's momentum (p(c)) to the magnitude of the baseball's momentum (p(b)) is 1.

Part B:

In this case, the momentum of the man (p(m)) is equal to the momentum of the woman (p(w)).

Given:
Weight of the man, W(m) = 650 N
Weight of the woman, W(w) = 460 N
Momentum of both objects is equal

We know that momentum is given by:

p = mass * velocity

Here, we're given the weights of the man and the woman. Weight is the force of gravity acting on an object (W = mass * g, where g is the acceleration due to gravity). So, we can calculate their masses:

Mass of the man, m(m) = W(m) / g
Mass of the woman, m(w) = W(w) / g

Next, we can find the ratio of kinetic energy:

K(m) = 1/2 * m(m) * v(m)^2
K(w) = 1/2 * m(w) * v(w)^2

Now, let's find the ratio of the man's kinetic energy (K(m)) to the woman's kinetic energy (K(w)):

K(m) / K(w) = (1/2 * m(m) * v(m)^2) / (1/2 * m(w) * v(w)^2)

Canceling out the common factors and simplifying the equation, we get:

K(m) / K(w) = (m(m) * v(m)^2) / (m(w) * v(w)^2)
= (W(m) / g * v(m)^2) / (W(w) / g * v(w)^2)
= (W(m) * v(m)^2) / (W(w) * v(w)^2)

Thus, the ratio of the man's kinetic energy (K(m)) to the woman's kinetic energy (K(w)) is:

K(m) / K(w) = (W(m) * v(m)^2) / (W(w) * v(w)^2)