Can someone tell me if my answers are correct?
A .145 kg block of wood hangs from the ceiling by a string. A bullet with a mass of .004 kg and a speed of 540 m/s strikes the block. After the collision, the block with the bullet embedded rises 42 cm up. a) What is the velocity of the block and the bullet immediately after the collision? b) What percentage of the kinetic energy was lost when the bullet struck the block?
For part a) i have 14.5 m/s and b) 97.3%. I have a feeling this might be wrong though. Pls help!
(a) M = mass of block m = mass of bullet
(M+m)gH = (1/2)(M+m)V^2
V = sqrt(2gH), where H = 0.42 m
You answer is indeed wrong.
(b) Compare (1/2)*m*Vbullet^2 with
(1/2)(M+m)V^2
The difference divided by the bullet initial KE is the fraction of kinetic energy lost.
To check if your answers are correct, we can break down the problem and go through the steps to find the solutions.
First, let's look at part a) to find the velocity of the block and the bullet immediately after the collision.
Step 1: Conservation of momentum
In this scenario, we can assume that the collision is perfectly elastic, meaning that both momentum and kinetic energy are conserved.
Using the principle of conservation of momentum:
Initial momentum before the collision = Final momentum after the collision
The initial momentum is given by the bullet's momentum:
Initial momentum = mass of the bullet × initial velocity of the bullet
Final momentum is the sum of the momentum of the block with the embedded bullet:
Final momentum = (mass of the block + mass of the bullet) × final velocity of the block and the bullet
Step 2: Calculate the final velocity
We can now set up these equations:
mass of the bullet × initial velocity of the bullet = (mass of the block + mass of the bullet) × final velocity of the block and the bullet
Substituting the given values:
(0.004 kg) × (540 m/s) = (0.145 kg + 0.004 kg) × final velocity of the block and the bullet
Now solve for the final velocity of the block and the bullet.
Step 3: Solve the equation
Rearrange the equation to find the final velocity:
final velocity of the block and the bullet = (0.004 kg × 540 m/s) / (0.145 kg + 0.004 kg)
Calculate the value to get the final velocity.
So, if you do the calculation correctly, you should be able to find the final velocity of the block and the bullet after the collision.
Moving on to part b), we need to find the percentage of kinetic energy lost when the bullet struck the block.
Step 1: Calculate the initial and final kinetic energy
The initial kinetic energy is given by:
Initial kinetic energy = (1/2) × mass of the bullet × (initial velocity of the bullet)^2
The final kinetic energy is given by:
Final kinetic energy = (1/2) × (mass of the block + mass of the bullet) × (final velocity of the block and the bullet)^2
Step 2: Calculate the percentage of kinetic energy lost
The percentage of kinetic energy lost can be found using the following formula:
percentage of kinetic energy lost = 100% × (Initial kinetic energy - Final kinetic energy) / Initial kinetic energy
Substitute the given values and solve for the percentage of kinetic energy lost.
Now, if you perform the calculations accurately, you should be able to determine if your answers of 14.5 m/s for part a) and 97.3% for part b) are correct.