Question

. (a) Show that the kinetic energy K and the momentum magnitude p of a particle with mass m are related by (b) A 0.040-kg cardinal (Richmondena cardinalis) and a 0.145-kg baseball have the same kinetic energy. Which has the greater magnitude of momentum? What is the ratio of the cardinal’s magnitude of momentum to the baseball’s? (c) A 700-N man and a 450-N woman have the same momentum. Who has the greater kinetic energy? What is the ratio of the man’s kinetic energy to that of the woman?

Answer 1

Answer with Explanation:

a.We know that kinetic energy of particle=$K.E=\frac{1}{2}mv^2$

Momentum  of particle=P=mv

$v=\frac{P}{m}$

Using the formula

$K.E=\frac{1}{2}m(\frac{P}{m})^2=\frac{P^2}{2m}$

$P=\sqrt{{2mK.E}$

b.Mass of cardina,m=0.04 kg

Mass of baseball,m'=0.145 lg

Kinetic energy of both both  are same.

Momentum is directly proportional to mass

When mass is greater than then object will have greater magnitude of momentum.

The object of small mass will have small magnitude of momentum.

The mass of baseball is greater then, it will have greater magnitude of momentum.

$\frac{P}{P'}=\sqrt{\frac{0.040}{0.145}}=0.53$

c.Weight of man=W=700 N

Weight of woman=W'=450 N

Mass ,m=$\frac{W}{g}$

Using the formula

Mass of man,m=$\frac{700}{g}= kg$

Mass of woman,m'=$\frac{450}{g}$

$K=\frac{P^2}{2\times\frac{700}{g}}$

$K'=\frac{P^2}{2\times\frac{450}{g}}$

$\frac{K}{K'}=\frac{450}{700}=0.64$

Kinetic energy is inversely proportional to mass .

When object of greater mass will have small kinetic energy and object of small mass will have greater kinetic energy.

Hence, the mass of woman is small therefore, the woman have greater kinetic energy when the momentum of man and woman are same.

Answer 2

Answer:

Explanation:

a)

kinetic energy of a particle is given as:

$KE=\frac{1}{2}m.v^2$ ........................(1)

Momentum is given as:

$P=m.v$ ......................(2)

where:

m = mass of the particle

v = velocity of the particle

Now from eq. (1) & (2)

• $KE=\frac{1}{2} P.v$

b)

mass of cardinal, $m_c=0.04\ kg$

mass of baseball, $m_b=0.145\ kg$

According to question the their kinetic energies are equal:

$KE_c=KE_b$

$\frac{1}{2} m_c.v_c^2=\frac{1}{2} m_b.v_b^2$

where:

$v_c=$ velocity of cardinal

$v_b=$ velocity of baseball

$\frac{1}{2} \times 0.04\times v_c^2=\frac{1}{2}\times0.145\times v_b^2$

$v_c=1.9039\times v_b$

Now the momentum of the respective bodies:

For cardinal

$P_c=m_c.v_c$

$P_c=0.04\times 1.9039\times v_b$

$P_c=0.0762\times v_b$ ...................(3)

&

For baseball

$P_b=0.145\times v_b$ .........................(4)

From equations 3 & 4:

$P_b>P_c$

c)

weight of man,

weight of woman, $w_w=750\ N$