A body moving with a velocity at 10 ms collides with a stationery box of mass 100 kg.I f the body has a mass of 50 kg and the two move together after collision.Find their final velocity?
conserve momentum:
50*10 = (50+100)v
3v-24=0
To find the final velocity of the body and the box after the collision, we can use the principles of conservation of momentum and kinetic energy.
1. Conservation of Momentum:
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Mathematically, this can be represented as:
(mass of body * initial velocity of body) + (mass of box * initial velocity of box) = (mass of body + mass of box) * final velocity
2. Conservation of Kinetic Energy:
In an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. However, in this case, the collision is not specified as elastic or inelastic. Therefore, we cannot assume conservation of kinetic energy. Instead, we need to use the conservation of momentum principle to solve for the final velocity.
Given information:
Mass of body (m1) = 50 kg
Velocity of body (v1) = 10 m/s
Mass of box (m2) = 100 kg
Velocity of box (v2) = 0 m/s (stationary)
Using the conservation of momentum, we can set up the equation as follows:
(m1 * v1) + (m2 * v2) = (m1 + m2) * final velocity
Substituting the given values:
(50 kg * 10 m/s) + (100 kg * 0 m/s) = (50 kg + 100 kg) * final velocity
(500 kg*m/s) = (150 kg) * final velocity
Now, let's solve for the final velocity:
final velocity = (500 kg*m/s) / (150 kg)
final velocity = 3.33 m/s (rounded to two decimal places)
Therefore, the final velocity of the body and the box after the collision is approximately 3.33 m/s.