Momentum: three balls move in the same straight line. Balls A and B move in the same direction at velocities of 2m/s and 8m/s respectively. Ball AC moves in the opposite direction at 6m/s and collides with ball B, whereafter ball B collides with ball A. the masses of balls A, B and C are 4kg, 12kg and 10kg respectively calculate: the velocity of and direction of ball C after the collision between balls B and C

Question

Momentum: three balls move in the same straight line. Balls A and B move in the same direction at velocities of 2m/s and 8m/s respectively. Ball AC moves in the opposite direction at 6m/s and collides with ball B, whereafter ball B collides with ball A. the masses of balls A, B and C are 4kg, 12kg and 10kg respectively calculate: the velocity of and direction of ball C after the collision between balls B and C

Answer 1

To calculate the velocity and direction of Ball C after the collision between Balls B and C, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

The momentum (p) of an object is given by the product of its mass (m) and velocity (v), so p = m * v.

Before the collision:
The momentum of Ball A is given by: pA = mA * vA = 4 kg * 2 m/s = 8 kg·m/s.
The momentum of Ball B is given by: pB = mB * vB = 12 kg * 8 m/s = 96 kg·m/s.
The momentum of Ball C is given by: pC = mC * vC = 10 kg * (-6 m/s) = -60 kg·m/s (negative because it is moving in the opposite direction).

We know that the total momentum before the collision is equal to the total momentum after the collision. So, pTotalBefore = pTotalAfter.

pTotalBefore = pA + pB + pC = 8 kg·m/s + 96 kg·m/s + (-60 kg·m/s) = 44 kg·m/s.

Now, let's consider the collision between Balls B and C. After the collision, the momentum of Ball C is given by: pC' = mC * vC'.

We can rewrite the total momentum after the collision as: pTotalAfter = pA + pB' + pC' = 44 kg·m/s, where pB' is the momentum of Ball B after the collision.

Since we have the mass of Ball B (12 kg) and velocity of Ball B before the collision (8 m/s), we can find the momentum of Ball B before the collision: pB = mB * vB = 12 kg * 8 m/s = 96 kg·m/s.

Now, we can rewrite the equation as: 44 kg·m/s = 8 kg·m/s + 96 kg·m/s + pC'.

Simplifying, we get: 44 kg·m/s = 104 kg·m/s + pC'.

Subtracting 104 kg·m/s from both sides, we find: pC' = -60 kg·m/s.

To find the velocity of Ball C after the collision, we divide pC' by the mass of Ball C: vC' = pC' / mC = (-60 kg·m/s) / 10 kg = -6 m/s.

Therefore, the velocity of Ball C after the collision with Ball B is -6 m/s (moving in the opposite direction to its original velocity).