Question

1. Ball A, with a mass of 20 kilograms, is moving to the right at 20 meters per second. At what velocity should ball B, with a mass of 40 kilograms, move so they both come to a standstill upon collision? Identify each mass, velocity, and unknown. Show your work, including units, and indicate the direction of ball B in your answer.

2. Ball C, with a mass of 30 kilograms, is moving to the left at 10 meters per second. At what velocity should ball D, with a mass of 10 kilograms, move to the right and collide with ball C so that ball D rebounds to the left with a velocity of 30 meters per second and ball C rebounds to the right with a velocity of 10 meters per second? Assume the collision to be perfectly elastic. Identify each mass, velocity, and unknown. Show your work, including units, and indicate the direction of ball D in your answer.

3. Ball E, with a mass of 10 kilograms, is moving to the right at 20 meters per second. Ball F is moving to the left at 20 meters per second. Upon collision, ball F comes to a standstill and ball E moves to the left at twice its original speed. What is the mass of ball F? Identify each mass, velocity, and unknown. Show your work, including units.
(Show your work on all of them, please)

Answer 1

For each question, we will use the equation:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Where m₁ is the mass of the first ball, u₁ is the initial speed of the first ball, m₂ is the mass of the second ball and u₂ is the initial speed of the second ball, all before collision.
The right hand side contains final masses and final velocities after collision.
Movement to the right will be considered positive and movement to the left will be considered negative.
1. 20 x 20 + 40u₂ = 0
u₂ = -10 m/s
Ball B needs to be moving towards the left at 10 m/s

2. 30 x -10 + 10u₂ = 10 x -30 + 30 x 10
u₂ = 30 m/s to the right

3. 10 x 20 + m₂ x -20 = 10 x 20 x -2 + m₂ x 0
m₂ = 30 kg

Answer 2

For 1: The velocity of Ball B is 10m/s and is moving in left direction.

For 2: The velocity of Ball D is 30m/s and is moving in right direction.

For 3: The mass of Ball F is 30 kg.

Step-by-step explanation:

Let us assume that ball moving in left direction has a negative sign and the ball moving in right direction has a positive sign.

In collision reaction, the momentum remains conserved. The equation for this follows:

`m_1u_1+m_2u_2=m_1v_1+m_2v_2`

• For 1:

`m_1,u_1\text{ and }v_1` = mass, initial velocity and final velocity of ball A

`m_2,u_2\text{ and }v_2` = mass, initial velocity and final velocity of ball B.

We are given:

`m_1=20kg\\u_1=20m/s\\v_1=0m/s\\m_2=40kg\\u_2=?m/s\\v_1=0m/s`

Putting values in above equation, we get:

`20(20)+40(u_2)=20(0)+40(0)\\u_2=-10m/s`

The velocity of Ball B is 10m/s and is moving is left direction.

• For 2:

`m_1,u_1\text{ and }v_1` = mass, initial velocity and final velocity of ball C

`m_2,u_2\text{ and }v_2` = mass, initial velocity and final velocity of ball D.

We are given:

`m_1=30kg\\u_1=-10m/s\\v_1=10m/s\\m_2=10kg\\u_2=?m/s\\v_1=-30m/s`

Putting values in above equation, we get:

`30(-10)+10(u_2)=30(10)+10(-30)\\u_2=30m/s`

The velocity of Ball D is 10m/s and is moving is right direction.

• For 3:

`m_1,u_1\text{ and }v_1` = mass, initial velocity and final velocity of ball E

`m_2,u_2\text{ and }v_2` = mass, initial velocity and final velocity of ball F.

We are given:

`m_1=10kg\\u_1=20m/s\\v_1=-40m/s\\m_2=?kg\\u_2=20m/s\\v_1=0m/s`

Putting values in above equation, we get:

`10(20)+m_2(-20)=10(-40)+m_2(0)\\m_2=30kg`

The mass of Ball E is 30kg.