A body of mass 2kg moving with a velocity of 5ms-1 collide with a statuary body of Mass 1/2kg. If the two bodies move together after the impact, calculate their common velocity
To calculate the common velocity of the two bodies after the impact, we can apply the principle of conservation of momentum.
The momentum of an object is defined as the product of its mass and velocity. It is expressed as:
Momentum = Mass × Velocity
According to the conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision.
Before the collision, the first body with a mass of 2 kg has a velocity of 5 m/s, and the second body with a mass of 1/2 kg is initially stationary. Therefore, the total momentum before the collision is:
Momentum_before = (Mass1 × Velocity1) + (Mass2 × Velocity2)
= (2 kg × 5 m/s) + (0.5 kg × 0 m/s)
= 10 kg·m/s
After the impact, the two bodies move together with a common velocity. Let's call this final common velocity V.
Now, we can use the principle of conservation of momentum to calculate the final common velocity:
Momentum_before = Momentum_after
10 kg·m/s = (Total_mass × Final_common_velocity)
Since the total mass is the sum of the individual masses of the two bodies (2 kg + 0.5 kg), we have:
10 kg·m/s = (2.5 kg × V)
Dividing both sides of the equation by 2.5 kg:
V = (10 kg·m/s) / (2.5 kg)
V = 4 m/s
Therefore, the common velocity of the two bodies after the impact is 4 m/s.