A 10kg ball ‘A’ moving at a speed of 8m/s collides with a 20 kg ball B initially at rest. After
The collision, the balls A and B move along the direction of 30 & 45 respectively with the
initial direction of motion of A. Find the final speed of balls A and B?
To find the final speed of the two balls after the collision, we can apply the principles of conservation of momentum and conservation of kinetic energy.
1. Conservation of momentum:
The total momentum before the collision is equal to the total momentum after the collision. Mathematically, it can be expressed as:
(mA * vA) + (mB * vB) = (mA * vAf) + (mB * vBf)
where
mA = mass of ball A
vA = initial velocity of ball A
mB = mass of ball B
vB = initial velocity of ball B
vAf = final velocity of ball A
vBf = final velocity of ball B
In this case, ball B is initially at rest, so vB = 0. The equation simplifies to:
(mA * vA) = (mA * vAf) + (mB * vBf)
Plug in the given values:
(10kg * 8m/s) = (10kg * vAf) + (20kg * vBf)
2. Conservation of kinetic energy:
The kinetic energy before the collision is equal to the kinetic energy after the collision. Mathematically, it can be expressed as:
0.5 * (mA * vA^2) + 0 = 0.5 * (mA * vAf^2) + 0.5 * (mB * vBf^2)
Again, since ball B is initially at rest, the equation simplifies to:
0.5 * (mA * vA^2) = 0.5 * (mA * vAf^2) + 0.5 * (mB * vBf^2)
Plug in the given values:
0.5 * (10kg * (8m/s)^2) = 0.5 * (10kg * vAf^2) + 0.5 * (20kg * vBf^2)
We now have two equations with two unknowns (vAf and vBf) that can be solved simultaneously to find the final speeds of both balls.