An 8kg ball traveling to the east at 10m/s collides, with a 2kg ball traveling to the west with a velocity of 5m/s. After the collision, they move together. Determine the final velocity of the balls.
total momentum is conserved
(8 kg * 10 m/s)E + (2 kg * 5 m/s)W = 70 kg⋅m/s E
(70 kg⋅m/s) / (8 kg + 2 kg) = ? m/s
1om/s
To determine the final velocity of the balls after the collision, we can use the principles of conservation of momentum.
Conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision, assuming no external forces act on the system.
The momentum (p) of an object can be calculated by multiplying its mass (m) by its velocity (v). Mathematically, momentum is represented as:
p = m * v
In this case, we have an 8kg ball (ball A) traveling to the east at 10m/s and a 2kg ball (ball B) traveling to the west at 5m/s.
Initially, the momentum of ball A is given by:
p(A) = m(A) * v(A)
= 8kg * 10m/s
= 80 kg·m/s
Similarly, the momentum of ball B is given by:
p(B) = m(B) * v(B)
= 2kg * (-5m/s) (Note: velocity is negative since it is traveling in the opposite direction)
= -10 kg·m/s
Since momentum is conserved, the total momentum before the collision is equal to the total momentum after the collision. Therefore, we can write the equation for conservation of momentum as:
p(A) + p(B) = p(final)
Substituting the known values, we have:
80 kg·m/s + (-10 kg·m/s) = p(final)
Simplifying, we have:
70 kg·m/s = p(final)
Since the balls move together after the collision, they have a common final velocity. The mass of the system is the sum of the masses of the two balls.
Total mass (m(total)) = m(A) + m(B)
= 8kg + 2kg
= 10kg
The final velocity (v(final)) of the balls can be calculated by dividing the total momentum by the total mass:
v(final) = p(final) / m(total)
= 70 kg·m/s / 10kg
= 7m/s
Therefore, the final velocity of the balls after the collision is 7m/s.