a black ball of mass 2kg moving at velocity 10m/s collide with a stationary white ball of mass 3kg.find their common velocity if they stick together after collision?
Answer
To find the common velocity of the balls after the collision, we need to apply the principles of conservation of momentum.
1. Firstly, calculate the initial momentum of each ball. Momentum (p) is calculated by multiplying the mass (m) of an object by its velocity (v).
Momentum of the black ball: p1 = m1 * v1 = 2 kg * 10 m/s = 20 kg*m/s
Since the white ball is stationary, the momentum of the white ball is 0.
2. The total momentum before the collision is the sum of the individual momenta of the balls.
Total initial momentum: p_initial = p1 + p2 = 20 kg*m/s + 0 kg*m/s = 20 kg*m/s
3. During the collision, the total momentum should be conserved. Therefore, the total momentum after the collision should also be 20 kg*m/s.
4. Let the common velocity of both balls after the collision be 'v'.
Momentum after the collision: p_final = (m1 + m2) * v
5. Since the balls stick together after the collision, their masses combine (m1 + m2).
p_final = (2 kg + 3 kg) * v = 5 kg * v
6. Equating the momentum before and after the collision:
p_initial = p_final
20 kg*m/s = 5 kg * v
7. Solving the equation, we find:
v = 20 kg*m/s / 5 kg = 4 m/s
Therefore, their common velocity after the collision is 4 m/s.
the black ball's initial momentum is now shared by both balls
find the initial momentum (it is conserved)
use the combined mass to find the new velocity
Given:
M1 = 2 kg, V1 = 10 m/s.
M2 = 3 kg, V2 = 0.
V3 = Velocity of M1 and M2 after collision.
p before = p after.
M1*V1 + M2*V2 = M1*V3 + M2*V3.
2 * 10 + 3 * 0 = 2*V3 + 3*V3,
V3 = m/s.