A 8.05- g bullet from a 9-mm pistol has a velocity of 346.0 m/s. It strikes the 0.785- kg block of a ballistic pendulum and passes completely through the block. If the block rises through a distance h = 16.04 cm, what was the velocity of the bullet as it emerged from the block?
initial momentum = .00805 * 346
final momentum just after collision
= M V + m v
so
.00805 = MV + m v
we can do MV from how far up it goes
(1/2) M V^2 = M g h =M (9.81)(.1504)
cancel M and find V
now we have it
initial momentum = final momentum
.00805 * 346 = .785 V + .00805 v
we know V
solve for v
To find the velocity of the bullet as it emerged from the block, we can use the principle of conservation of momentum.
The conservation of momentum states that the total momentum before an event is equal to the total momentum after the event, assuming there are no external forces acting on the system.
In this case, we consider the bullet and the block of the ballistic pendulum as the system.
Before the collision:
- The bullet has a mass of 8.05 g (or 0.00805 kg) and a velocity of 346.0 m/s.
- The block of the ballistic pendulum has a mass of 0.785 kg and is at rest.
After the collision:
- Since the bullet passes completely through the block, the bullet and the block move together.
- The block and the bullet have a common final velocity, denoted as V.
According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
Initial momentum = Final momentum
(mass of bullet) * (initial velocity of bullet) + (mass of block) * (initial velocity of block) = (mass of bullet + mass of block) * (final velocity of the system)
(0.00805 kg) * (346.0 m/s) + (0.785 kg) * (0 m/s) = (0.00805 kg + 0.785 kg) * (V)
We can now solve for V:
(0.00805 kg * 346.0 m/s) = (0.00805 kg + 0.785 kg) * (V)
2.7773 kg·m/s = 0.79305 kg * V
V = (2.7773 kg·m/s) / (0.79305 kg)
V ≈ 3.5026 m/s
Therefore, the velocity of the bullet as it emerged from the block is approximately 3.5026 m/s.