Two balls are involved in a completely inelastic collision. The first ball has a mass of 0.25 kg and an initial velocity of 9.27 m/s in the x-direction The second ball has a mass of 0.50 kg with an initial velocity of 2.61 m/s in the -x-direction. What is the speed of the two balls after the collision in m/s?
m1•v1- m2•v2 =(m1+m2) •u,
u= (m1•v1- m2•v2)/(m1+m2)
To find the final velocity of the two balls after the collision, we can use the principles of conservation of momentum and conservation of kinetic energy.
1. Conservation of momentum:
In an inelastic collision, the total momentum before and after the collision remains the same.
The total initial momentum before the collision is given by:
p_initial = m1 * v1_initial + m2 * v2_initial
Here, m1 and v1_initial are the mass and initial velocity of the first ball, and m2 and v2_initial are the mass and initial velocity of the second ball.
Substituting the given values:
p_initial = (0.25 kg) * (9.27 m/s) + (0.50 kg) * (-2.61 m/s)
2. Conservation of kinetic energy:
In an inelastic collision, the total kinetic energy before the collision is not necessarily conserved. However, we can use it to find the final velocities.
The total initial kinetic energy before the collision is given by:
KE_initial = (1/2) * m1 * v1_initial^2 + (1/2) * m2 * v2_initial^2
Substituting the given values:
KE_initial = (1/2) * (0.25 kg) * (9.27 m/s)^2 + (1/2) * (0.50 kg) * (-2.61 m/s)^2
3. Finding the final velocities:
Let v1_final and v2_final be the final velocities of the first and second balls, respectively.
Since the collision is completely inelastic, the two balls stick together after the collision. Therefore, their final velocities will be the same.
The total final momentum after the collision is given by:
p_final = (m1 + m2) * v_final
Using the conservation of momentum:
p_initial = p_final
m1 * v1_initial + m2 * v2_initial = (m1 + m2) * v_final
Substituting the given values and solving for v_final:
(0.25 kg) * (9.27 m/s) + (0.50 kg) * (-2.61 m/s) = (0.25 kg + 0.50 kg) * v_final
Simplifying the equation gives us:
2.3175 kg·m/s - 1.305 kg·m/s = 0.75 kg * v_final
Combining the terms gives:
1.01 kg·m/s = 0.75 kg * v_final
Solving for v_final gives:
v_final = 1.01 kg·m/s / 0.75 kg
v_final = 1.34 m/s
Therefore, the speed of the two balls after the collision is 1.34 m/s.
To find the speed of the two balls after the collision, we need to apply the concept of conservation of momentum.
Conservation of momentum states that the total momentum of a system remains constant before and after a collision, as long as no external forces are acting on it.
The formula for momentum is given by:
Momentum = mass × velocity
Let's calculate the initial momentum of the system before the collision:
Initial momentum = (mass of the first ball × velocity of the first ball) + (mass of the second ball × velocity of the second ball)
Initial momentum = (0.25 kg × 9.27 m/s) + (0.50 kg × (-2.61 m/s))
Now, since the collision is completely inelastic, the two balls will stick together after the collision. This means they will move as a single object with a common velocity.
Let's assume the final velocity of the combined mass is V.
To find V, we can equate the initial momentum to the final momentum:
Initial momentum = Final momentum
(0.25 kg × 9.27 m/s) + (0.50 kg × (-2.61 m/s)) = (combined mass) × V
Simplifying, we get:
(2.3175 kg·m/s) - (1.305 kg·m/s) = (0.75 kg) × V
0.8125 kg·m/s = (0.75 kg) × V
Dividing both sides by 0.75 kg, we find:
V = 0.8125 kg·m/s ÷ 0.75 kg
V ≈ 1.0833 m/s
Therefore, the speed of the two balls after the collision is approximately 1.0833 m/s.