A 0.13 kg bullet traveling at 614 m/s hits a 5.7 kg block of wood and stays in the wood. What is the velocity (speed)of the wood block immediately after the bullet hits it
Use the law of conswervation of mometnum.
0.13 * 614 = (0.13 + 5.7)*Vfinal
Solve for Vfinal
To find the velocity of the wood block immediately after the bullet hits it, we can use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum before an event is equal to the total momentum after the event, provided that no external forces act on the system. Mathematically, this can be expressed as:
Total momentum before = Total momentum after
The momentum of an object is defined as the product of its mass and velocity:
Momentum = mass × velocity
Let's denote the velocity of the wood block as V1 (initial velocity) and the velocity after the bullet hits it as V2 (final velocity).
The bullet is initially moving, while the wood block is at rest before the bullet hits it. Therefore, the initial momentum of the bullet is given by:
Momentum of bullet before = mass of bullet × velocity of bullet
= 0.13 kg × 614 m/s
Since the wood block is initially at rest, its initial momentum is zero:
Momentum of wood block before = mass of wood block × velocity of wood block
= 5.7 kg × 0 m/s
= 0 kg m/s
After the bullet hits the wood block, they become a single system. So, the final momentum of the system, which includes both the bullet and the wood block, can be calculated using the principle of conservation of momentum:
Momentum of bullet + momentum of wood block = momentum of wood block + bullet after collision
Therefore,
(mass of bullet × velocity of bullet) + (mass of wood block × velocity of wood block) = (mass of wood block + mass of bullet) × velocity of wood block + bullet after collision
Now we can plug in the given values and solve for V2 (velocity of the wood block after the collision):
(0.13 kg × 614 m/s) + (5.7 kg × 0 m/s) = (5.7 kg + 0.13 kg) × V2
So, (0.13 kg × 614 m/s) = (5.83 kg) × V2
Simplifying:
V2 = (0.13 kg × 614 m/s) / (5.83 kg)
Now we can calculate V2 to find the velocity (speed) of the wood block immediately after the bullet hits it.