The mass of ball A is 10kg and the mass of ball B is 5kg. If the initial velocity is set to 3 meters per sec 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 the right to left and ball B moves the opposite direction . Identify each mass, velocity, and unknown. Show your work inckuding units, and indicate the direction of ball B in your answer
Given:
M1 = 10km, V1 = -3 m/s.
M2 = 5kg, V2 = 3 m/s.
V3 = 2 m/s = Velocity of M1(ball A) after collision.
V4 = ? = Velocity of M2 (ball B) after collision.
Momentum before = Momentum after.
M1*V1 + M2*V2 = M1*V3 + M2*V4.
10*(-3) + 5*3 = 10*2 + 5*V4,
V4 = -7 m/s,Left = Velocity M2 after collision.
To find the final velocity of ball B using the elastic collision equation, we first need to understand the variables involved and their values:
Mass of ball A (m1) = 10 kg
Mass of ball B (m2) = 5 kg
Initial velocity of ball A (u1) = 3 m/s (moving from right to left)
Initial velocity of ball B (u2) = 3 m/s (moving from left to right)
Final velocity of ball A (v1) = 2 m/s (moving from right to left) [Given]
Final velocity of ball B (v2) = ? (This is the unknown we need to find)
Now, we can use the equation for elastic collision:
m1*u1 + m2*u2 = m1*v1 + m2*v2
Plugging in the known values:
10 kg * 3 m/s + 5 kg * 3 m/s = 10 kg * 2 m/s + 5 kg * v2
Simplifying:
30 kg*m/s + 15 kg*m/s = 20 kg*m/s + 5 kg * v2
45 kg*m/s = 20 kg*m/s + 5 kg * v2
Next, we can rearrange the equation to isolate v2:
5 kg * v2 = 45 kg*m/s - 20 kg*m/s
5 kg * v2 = 25 kg*m/s
Finally, we can find the final velocity of ball B (v2) by dividing both sides of the equation by 5 kg:
v2 = 25 kg*m/s ÷ 5 kg
v2 = 5 m/s
Therefore, the final velocity of ball B is 5 m/s. Additionally, since ball B initially moves from left to right, the direction of ball B remains the same in the final velocity: moving from left to right.