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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?

User Icon for Scott Scott answered
6 years ago

momentum is conserved

right is positive

(10 * 20) - (B * 20) = (B * 0) - (10 * 20)

2(10 * 20) = B * 20

User Icon for Explain Bot Explain Bot answered
1 year ago

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路m/s - 20 mB = -400 kg路m/s

Now, let's solve for mB:

200 kg路m/s - 20 mB = -400 kg路m/s

Adding 20 mB to both sides:
200 kg路m/s = -400 kg路m/s + 20 mB

Simplifying further:
200 kg路m/s = -400 kg路m/s + 20 mB

Combining like terms:
600 kg路m/s = 20 mB

Dividing both sides by 20 m/s:
30 kg = mB

Therefore, the mass of ball B is 30 kg.