In a closed system consisting of a cannon and a cannonball, the kinetic energy of a cannon is 72,000 J. If the cannonball is 18 kg and has a velocity of 23 m/s when fired from the cannon, what is the total kinetic energy of the system?
A) 71,793 J
B) 72,207 J
C) 76,761 J
D) 67,239 J
I think 76,761 is correct. Can you check?
To find the total kinetic energy of the system, we need to consider the kinetic energy of both the cannon and the cannonball.
The kinetic energy of the cannon can be calculated using the formula:
Kinetic energy = 1/2 * mass * velocity^2
Given that the kinetic energy of the cannon is 72,000 J, we can rearrange the formula to solve for the mass:
72,000 J = 1/2 * mass * velocity^2
Mass = (2 * 72,000 J) / velocity^2
Mass = 144,000 J / (23 m/s)^2
Mass = 144,000 J / 529 m^2/s^2
Mass = 272.36 kg (approx.)
Now we can calculate the total kinetic energy of the system using the formula:
Total kinetic energy = kinetic energy of the cannon + kinetic energy of the cannonball
The kinetic energy of the cannonball is given by:
Kinetic energy = 1/2 * mass * velocity^2
Kinetic energy = 1/2 * 18 kg * (23 m/s)^2
Kinetic energy = 1/2 * 18 kg * 529 m^2/s^2
Kinetic energy = 4,771 J
Total kinetic energy = 72,000 J + 4,771 J
Total kinetic energy = 76,771 J
Therefore, the total kinetic energy of the system is 76,771 J.
The correct answer is C) 76,761 J
To find the total kinetic energy of the system, we need to calculate the kinetic energy of both the cannon and the cannonball separately, and then add them together.
The kinetic energy of an object is given by the equation: KE = 0.5 * mass * velocity^2
For the cannonball:
Mass of the cannonball = 18 kg
Velocity of the cannonball = 23 m/s
Substituting these values into the equation, we find the kinetic energy of the cannonball:
KE_cannonball = 0.5 * 18 kg * (23 m/s)^2
Now let's calculate the kinetic energy of the cannon:
Kinetic energy of the cannon = 72,000 J (given in the question)
Finally, we can calculate the total kinetic energy of the system by adding the kinetic energy of the cannonball and the kinetic energy of the cannon:
Total kinetic energy = KE_cannonball + Kinetic energy of the cannon
Now, if we substitute the calculated values into the equation, we can find the total kinetic energy of the system:
Total kinetic energy = 0.5 * 18 kg * (23 m/s)^2 + 72,000 J
Calculating this expression will give us the total kinetic energy of the system, which we can then compare to the answer choices provided to find the correct option.