A 25 g bullet traveling at 280 m/s passes completely through a wooden block, initially at rest on a smooth table. The block has a mass of 1000 g. The bullet emerges traveling in the same direction, but at 50 m/s. What percentage of total kinetic energy is lost in the process?
Find kinetic energy before, aka 1/2(mass of bullet)(velocity)^2. Then find the kinetic energy afterwards, which is 1/2(mass of bullet)(velocity afterwards)^2 + 1/2(mass of block)(whatever you got for part a)^2. Then divide whatever you got for the second part, divide it by the first part, and subtract the resulting decimal from 1 to find the percentage that was lost.
To find the percentage of total kinetic energy lost in the process, we need to calculate the initial and final kinetic energies and then compare them.
1. Calculate the initial kinetic energy of the bullet before it passes through the block:
The initial kinetic energy (KE) can be calculated using the formula: KE = 0.5 * mass * velocity^2.
Since the mass of the bullet is given as 25 g, which is equivalent to 0.025 kg, and the velocity is given as 280 m/s, we can calculate the initial kinetic energy as follows: KE_initial = 0.5 * 0.025 kg * (280 m/s)^2.
2. Calculate the final kinetic energy of the bullet after it passes through the block:
The final kinetic energy can be calculated using the same formula as before: KE_final = 0.5 * mass * velocity^2.
Since the mass of the bullet is still 25 g, or 0.025 kg, and the velocity is given as 50 m/s, we can calculate the final kinetic energy as follows: KE_final = 0.5 * 0.025 kg * (50 m/s)^2.
3. Calculate the percentage of kinetic energy lost:
To find the percentage of kinetic energy lost, we need to compare the difference between the initial and final kinetic energies with respect to the initial kinetic energy and then multiply by 100.
The percentage of kinetic energy lost can be calculated using the formula: (KE_initial - KE_final) / KE_initial * 100.
Substituting the calculated values, we can now find the percentage of kinetic energy lost in the process.