A lead bullet of mass 50g is fixed with a velocity of 200ms into a lead block of mass 950g given that the lead can move freely
To solve this problem, we need to use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of an isolated system remains constant before and after a collision. In this case, the isolated system consists of the lead bullet and the lead block.
The momentum of an object is defined as the product of its mass and velocity:
Momentum = Mass × Velocity
Before the collision, the bullet has a mass of 50g and a velocity of 200m/s, while the block has a mass of 950g and is initially at rest.
The total initial momentum of the system is the sum of the individual momenta:
Initial momentum = (mass of bullet × velocity of bullet) + (mass of block × velocity of block)
Plugging in the values we have:
Initial momentum = (0.05 kg × 200 m/s) + (0.95 kg × 0 m/s)
Initial momentum = 10 kg·m/s
After the collision, the bullet is fixed into the lead block, and they move together with a common final velocity.
To find this final velocity, we can use the conservation of momentum principle:
Initial momentum = Final momentum
10 kg·m/s = (total mass of bullet and block) × (final velocity)
The total mass of the bullet and block is the sum of their individual masses:
Total mass = mass of bullet + mass of block
Total mass = 0.05 kg + 0.95 kg
Total mass = 1 kg
Now we can calculate the final velocity:
Final velocity = 10 kg·m/s ÷ 1 kg
Final velocity = 10 m/s
So, after the collision, the lead bullet fixed in the lead block will move with a velocity of 10 m/s.