Two balls collide head-on on a table. The first ball has a mass of 0.50 kg and an initial velocity of 12.0 m/s. The second ball has a mass of 0.75 kg and an initial velocity of -16.0 m/s. After the collision, the first ball travels at a velocity of -21.6 m/s. What is the velocity of the second ball after the collision? Assume a perfectly elastic collision and no friction between the balls and the table.
-6.4 m/s
When the balls are moving in opposite directions
v₁= {-2m₂v₂₀ +(m₁-m₂)v₁₀}/(m₁+m₂)
v₂={ 2m₁v₁₀ - (m₂-m₁)v₂₀}/(m₁+m₂)
To find the velocity of the second ball after the collision, 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 of an object is given by the product of its mass and velocity. Mathematically, momentum (p) is calculated using the formula:
p = m * v
Where:
p is the momentum,
m is the mass of the object, and
v is the velocity of the object.
Let's calculate the initial momentum of the system (two balls) before the collision.
Momentum of the first ball (p1) = mass of the first ball (m1) * initial velocity of the first ball (v1)
p1 = 0.50 kg * 12.0 m/s
p1 = 6.0 kg⋅m/s
Similarly, let's calculate the initial momentum of the second ball (p2).
Momentum of the second ball (p2) = mass of the second ball (m2) * initial velocity of the second ball (v2)
p2 = 0.75 kg * -16.0 m/s
p2 = -12.0 kg⋅m/s (Note: Here, the negative sign indicates the direction of motion.)
Now, let's find the total initial momentum (p_initial) of the system (p_initial = p1 + p2).
p_initial = 6.0 kg⋅m/s + (-12.0 kg⋅m/s)
p_initial = -6.0 kg⋅m/s
Since the collision is perfectly elastic, the total momentum after the collision will also be -6.0 kg⋅m/s.
Now we can find the velocity of the second ball (v2_final) using the equation p = m * v.
Final momentum of the second ball (p2_final) = mass of the second ball (m2) * final velocity of the second ball (v2_final)
-6.0 kg⋅m/s = 0.75 kg * v2_final
Now, rearranging the equation to solve for v2_final:
v2_final = (-6.0 kg⋅m/s) / 0.75 kg
v2_final = -8.0 m/s
Therefore, after the collision, the second ball travels at a velocity of -8.0 m/s.