A bullet of mass 40g strikes a stationary wooden block of mass 6kg horizontally at 500m/s the bullet goes through the block,and emerges from from the other side at 200m/s.calculate the velocity of the block once the bullet emerges from it
original momentum = .04*500
= 20 kg m/s
that will be the final momentum so
6 v + .04*200 = .04*500
6 v = .04*300
v = .04*50
v = 2 m/s
To calculate the velocity of the block once the bullet emerges from it, we can use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of a system remains constant if no external forces are acting on it. In this case, we can consider the bullet and the block as a closed system.
The initial momentum of the system can be calculated as the sum of the momenta of the bullet and the block before the collision. The final momentum can be calculated as the sum of the momenta of the bullet and the block after the collision.
Let's calculate the initial momentum of the system first:
Initial momentum (before collision) = mass of bullet × velocity of bullet + mass of block × velocity of block (since the block is stationary, its initial velocity is zero)
= (40g) × (500 m/s) + (6kg) × (0 m/s)
= 0.04 kg × 500 m/s + 6 kg × 0 m/s
= 20 kg·m/s
Next, let's calculate the final momentum of the system:
Final momentum (after collision) = mass of bullet × velocity of bullet + mass of block × velocity of block
= (40g) × (200 m/s) + (6kg) × (velocity of block)
Now, since momentum is conserved, the initial momentum and the final momentum should be equal. Therefore, we can set up an equation:
Initial momentum = Final momentum
20 kg·m/s = 0.04 kg × 200 m/s + 6 kg × (velocity of block)
Simplifying the equation:
20 kg·m/s = 8 kg·m/s + 6 kg × (velocity of block)
12 kg·m/s = 6 kg × (velocity of block)
Dividing both sides of the equation by 6 kg:
2 m/s = velocity of block
Therefore, the velocity of the block once the bullet emerges from it is 2 m/s in the same direction as that of the bullet.