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?
momentum before = momentum after
50 * 10 + 100 * 0 = 150 * v
To find the final velocity after the collision, we can use the principle of conservation of momentum.
The momentum of an object is given by the product of its mass and velocity. According to the conservation of momentum, the total momentum before the collision will be equal to the total momentum after the collision.
Before the collision, the body has a mass of 50 kg and a velocity of 10 m/s. The momentum of the body before the collision is then:
Momentum of the body before = mass of the body * velocity of the body = 50 kg * 10 m/s = 500 kg m/s.
The box is stationary before the collision, so its velocity is 0 m/s. The momentum of the box before the collision is therefore:
Momentum of the box before = mass of the box * velocity of the box = 100 kg * 0 m/s = 0 kg m/s.
The total momentum before the collision is the sum of the individual momenta:
Total momentum before = Momentum of the body before + Momentum of the box before = 500 kg m/s + 0 kg m/s = 500 kg m/s.
After the collision, the body and the box move together with a common final velocity. Let's call this final velocity "Vf". The mass of the combined system (body + box) is the sum of their individual masses:
Mass of the combined system = mass of the body + mass of the box = 50 kg + 100 kg = 150 kg.
The momentum of the combined system after the collision is given by:
Momentum of the combined system after = mass of the combined system * final velocity = 150 kg * Vf.
According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:
Total momentum before = Total momentum after.
This can be expressed as an equation:
500 kg m/s = 150 kg * Vf.
To find the final velocity, we can rearrange the equation and solve for Vf:
Vf = (500 kg m/s) / (150 kg) = 3.33 m/s.
Therefore, the final velocity after the collision is 3.33 m/s.