Question

7. A ball of mass m makes a head-on elastic collision with a second ball (at rest) and rebounds with a speed equal to 0.450 its original speed. What is the mass of the second ball

Answer 1

Answer:

mass of the second ball is 0.379m

Explanation:

Given;

mass of first ball = m

let initial velocity of first ball = u₁

let final velocity of first ball  = v₁ = 0.45u₁

let the mass of the second ball = m₂

initial velocity of the second ball, u₂ = 0

let the final velocity of the second ball = v₂

Apply the principle of conservation of linear momentum;

mu₁ + m₂u₂ = mv₁ + m₂v₂

mu₁  +  0  = 0.45u₁m + m₂v₂

mu₁  = 0.45u₁m + m₂v₂ -------- equation (i)

Velocity for elastic collision in one dimension;

u₁ + v₁ = u₂ + v₂

u₁ + 0.45u₁ = 0 + v₂

1.45u₁ = v₂ (final velocity of the second ball)

Substitute in v₂ into equation (i)

mu₁  = 0.45u₁m + m₂(1.45u₁)

mu₁ = 0.45u₁m + 1.45m₂u₁

mu₁ - 0.45u₁m = 1.45m₂u₁

0.55mu₁ = 1.45m₂u₁

divide both sides by u₁

0.55m = 1.45m₂

m₂ = 0.55m / 1.45

m₂ = 0.379m

Therefore, mass of the second ball is 0.379m (where m is mass of the first ball)

Answer 2

The mass of the second ball is 0.379m and this can be determined by conserving the momentum.

Given :

A ball of mass 'm' makes a head-on elastic collision with a second ball (at rest) and rebounds with a speed equal to 0.450 its original speed.

In order to determine the mass of the second ball, apply conservation of linear momentum.

$\rm m_1u_1+m_2u_2=m_1v_1+m_2v_2$

where $m_1$ is the mass of the first ball, $m_2$ is the mass of the second ball, $u_1$ is the initial velocity of the first ball, $u_2$ is the initial velocity of the second ball, $\rm v_1$ is the final velocity of the first ball, and $\rm v_2$ is the final velocity of the second ball.

Now, substitute the known terms in the above formula.

$\rm mu_1+0=0.45u_1m+m_2v_2$

$\rm mu_1=0.45u_1m+m_2v_2$   ----  (1)

For elastic collision, the velocity is given by:

$\rm v_1+u_1=v_2+u_2$

$\rm 0.45u_1+u_1=0+v_2$

$\rm v_2 = 1.45u_1$

Now, substitute the value of $\rm v_2$ in the equation (1).

$\rm mu_1=0.45u_1m+1.45u_1m_2$

$\rm 0.55mu_1=1.45m_2u_1$

$\rm m_2=0.379m$

So, the mass of the second ball is 0.379m.

For more information, refer to the link given below:

https://brainly.com/question/19689434