The mass of ball A is 10 kilograms and the mass of ball B is 5 kilograms. If the initial velocity is set to 3 meters per second for each ball, what is the final velocity of ball B if the final velocity of ball A is 2 meters per second?Use the elastic collision equation to find the final velocity of ball B. Assume ball A initially moves from right to left and ball B moves in the opposite direction. Identify each mass, velocity, and unknown. Show your work, including units, and indicate the direction of ball B in your answer.
To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision, as long as no external forces are acting on the system. In this case, we have an elastic collision between ball A and ball B.
The formula for the conservation of momentum is:
m1 * v1_initial + m2 * v2_initial = m1 * v1_final + m2 * v2_final
where:
m1 and m2 are the masses of ball A and ball B, respectively.
v1_initial and v2_initial are the initial velocities of ball A and ball B, respectively.
v1_final and v2_final are the final velocities of ball A and ball B, respectively.
Given:
m1 = 10 kg (mass of ball A)
m2 = 5 kg (mass of ball B)
v1_initial = 3 m/s (initial velocity of ball A)
v1_final = 2 m/s (final velocity of ball A)
We need to find v2_final (final velocity of ball B).
Now, let's substitute these values into the conservation of momentum equation:
10 kg * 3 m/s + 5 kg * 3 m/s = 10 kg * 2 m/s + 5 kg * v2_final
Simplifying the equation, we have:
30 kg * m/s + 15 kg * m/s = 20 kg * m/s + 5 kg * v2_final
45 kg * m/s = 20 kg * m/s + 5 kg * v2_final
Next, let's isolate the final velocity of ball B (v2_final) by rearranging the equation:
5 kg * v2_final = 45 kg * m/s - 20 kg * m/s
5 kg * v2_final = 25 kg * m/s
v2_final = (25 kg * m/s) / 5 kg
v2_final = 5 m/s
Therefore, the final velocity of ball B is 5 m/s in the opposite direction of its initial velocity (right to left).
Mb*V1 + Ma*V2 = Mb*V3 + Ma*V4.
5*3 - 10*3 = 5*V3 + 10*2,
-15 = 5V3 + 20,
V3 = -7 m/s = 7 m/s to the left.