Ball A, with a mass of 10kg, is moving to the right at 20 m/s. Ball B is moving to the left at 20 m/s. Upon collision, Ball B comes to a standstill, and Ball A moves to the left at twice its original speed. What is the mass of ball B?
How do I do this?
momentum is conserved
right is positive
(10 * 20) - (B * 20) = (B * 0) - (10 * 20)
2(10 * 20) = B * 20
To solve this problem, we can use the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity. Therefore, the momentum of an object with mass m1 and velocity v1 is given by p1 = m1 * v1.
Let's denote the velocity of ball A after the collision as vA' and the mass of ball B as mB. We know the following information:
Ball A (before collision):
- Mass: mA = 10 kg
- Velocity: vA = 20 m/s to the right
Ball B (before collision):
- Velocity: vB = 20 m/s to the left
After collision:
- Ball B comes to a standstill (velocity is 0 m/s).
- Ball A moves to the left at twice its original speed: vA' = -40 m/s
Now, we can apply the law of conservation of momentum:
Total momentum before collision = Total momentum after collision
(mA * vA) + (mB * vB) = (mA * vA') + (mB * vB')
Substituting the given values:
(10 kg * 20 m/s) + (mB * (-20 m/s)) = (10 kg * (-40 m/s)) + (mB * 0 m/s)
Simplifying the equation:
200 kg·m/s - 20 mB = -400 kg·m/s
Now, let's solve for mB:
200 kg·m/s - 20 mB = -400 kg·m/s
Adding 20 mB to both sides:
200 kg·m/s = -400 kg·m/s + 20 mB
Simplifying further:
200 kg·m/s = -400 kg·m/s + 20 mB
Combining like terms:
600 kg·m/s = 20 mB
Dividing both sides by 20 m/s:
30 kg = mB
Therefore, the mass of ball B is 30 kg.