A body of mass 5kg moving with a speed of 3m/s collides head on with a body of mass 3kg moving in the opposite direction at speed of 2m/s The first body stops after the collision The final velocity of the second body is
Ans:3m/s
system momentum is conserved
(5 * 3) - (3 * 2) = 3 * v
To find the final velocity of the second body, we can use the principle of conservation of momentum.
The momentum before the collision is given by:
Initial momentum = (mass of first body × velocity of first body) + (mass of second body × velocity of second body)
= (5kg × 3m/s) + (3kg × (-2m/s))
= 15kg*m/s - 6kg*m/s
= 9kg*m/s
The momentum after the collision is given by:
Final momentum = (mass of first body × velocity of first body) + (mass of second body × velocity of second body)
Since the first body comes to a stop after the collision, its final velocity is 0m/s.
Therefore, we can write the equation as:
0 = (5kg × 0m/s) + (3kg × final velocity of second body)
Simplifying the equation, we get:
0 = 3 * final velocity of second body
To solve for the final velocity of the second body, we divide both sides of the equation by 3:
final velocity of second body = 0m/s / 3
= 0m/s
Therefore, the final velocity of the second body is 0m/s.
To find the final velocity of the second body 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 total momentum before the collision can be calculated by multiplying the mass of the first body (5kg) by its initial velocity (-3m/s) and the mass of the second body (3kg) by its initial velocity (2m/s):
Total momentum before collision = (5kg x -3m/s) + (3kg x 2m/s)
= -15kgm/s + 6kgm/s
= -9kgm/s
After the collision, the first body comes to rest, so its final velocity is 0m/s. The momentum of the second body is calculated by multiplying its mass (3kg) by its final velocity (vf):
Momentum of second body = 3kg x vf
According to the principle of conservation of momentum, the total momentum before the collision (-9kgm/s) is equal to the total momentum after the collision (0kgm/s + momentum of second body). Therefore:
-9kgm/s = 0kgm/s + 3kg x vf
We can rearrange this equation to solve for the final velocity of the second body (vf):
-9kgm/s = 3kg x vf
vf = (-9kgm/s) / 3kg
vf = -3m/s
The negative sign indicates that the final velocity of the second body is in the opposite direction to its initial velocity. Taking only the magnitude, the final velocity of the second body is 3m/s.