A 25 gm bullet is fired into a 2.25kg ballistic pendulum and becomes embedded in it. If the pendulum moves a vertical distance of 10cm, calculate:
A. The speed of the system after collision
B. The initial speed of the bullet
C. The percentage of the energy lost in the process.
you know conservation of momentum applies.
what PE is in the bullet/block at 10 cm? That must equal KE of the block/bullet after impact, so you can solve for the velocity.
Now momentum applies, so the initial momentum of the bullet must equal the momnetum of the block/bullet. That will solve it.
To solve this problem, we need to use the principle of conservation of momentum and energy.
A. The speed of the system after collision:
We can use the conservation of momentum to find the speed of the system after the collision. The momentum before the collision equals the momentum after the collision since no external forces act on the system.
Initially:
Momentum of bullet = mass of bullet * initial speed of bullet
Momentum of pendulum = mass of pendulum * 0 (assuming it starts from rest)
After collision:
Total momentum of the system = (mass of bullet + mass of pendulum) * final speed of the system
Since momentum is conserved, we can equate the initial and final momenta:
(mass of bullet) * (initial speed of bullet) = (mass of bullet + mass of pendulum) * (final speed of the system)
We know that:
mass of bullet = 25 gm = 0.025 kg
mass of pendulum = 2.25 kg
Let's solve for the final speed of the system:
(0.025 kg) * (initial speed of bullet) = (0.025 kg + 2.25 kg) * (final speed of the system)
Divide both sides by 0.025 kg:
initial speed of bullet = 2.25 * final speed of the system
Therefore, the speed of the system after the collision is 2.25 times the initial speed of the bullet.
B. The initial speed of the bullet:
We can use the equation from part A and solve for the initial speed of the bullet.
initial speed of bullet = (final speed of the system) / 2.25
C. The percentage of the energy lost in the process:
To calculate the percentage of energy lost, we need to compare the initial energy of the bullet to the final energy of the system.
Initial energy = 0.5 * mass of bullet * (initial speed of bullet)^2
Final energy = 0.5 * (mass of bullet + mass of pendulum) * (final speed of the system)^2
Percentage of energy lost = [(Initial energy - Final energy) / Initial energy] * 100
Now, you can substitute the values and calculate the final results.