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?(1 point)

Question

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?(1 point)

Responses

71,793 J
71,793 J

72,207 J
72,207 J

76,761 J
76,761 J

67,239 J

Answer 1

To find the total kinetic energy of the system, we need to add the kinetic energy of the cannon and the kinetic energy of the cannonball.

The kinetic energy of the cannonball can be calculated using the formula: KE = 0.5 * mass * velocity^2
KE = 0.5 * 18 kg * (23 m/s)^2
KE = 0.5 * 18 kg * 529 m^2/s^2
KE = 0.5 * 9522 kg.m^2/s^2
KE = 4761 J

Adding the kinetic energy of the cannon and the cannonball, we get:
Total kinetic energy = 72,000 J + 4,761 J = 76,761 J

Therefore, the correct answer is 76,761 J.

Answer 2

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 can be calculated using the formula:

KE = (1/2) * mass * velocity^2

First, let's calculate the kinetic energy of the cannon. We are given that the kinetic energy of the cannon is 72,000 J. Let's assume the mass of the cannon is M kg and its velocity is V m/s. So we have:

72,000 = (1/2) * M * V^2

Now, let's calculate the kinetic energy of the cannonball. We are given that the mass of the cannonball is 18 kg and its velocity is 23 m/s. Using the same formula, we have:

KE_cannonball = (1/2) * 18 * 23^2

Now let's calculate the values:

KE_cannonball = (1/2) * 18 * 529
= 4,731 J

Now we can calculate the velocity of the cannon:

72,000 = (1/2) * M * V^2

V^2 = (72,000 * 2) / M
V^2 = 144,000 / M

Similarly, we can calculate the velocity of the cannonball:

4,731 = (1/2) * 18 * V^2

V^2 = (4,731 * 2) / 18
V^2 = 526.1667

Now we have two equations:

V^2 = 144,000 / M
V^2 = 526.1667

Since the velocity of the cannonball is given as 23 m/s, we can solve for M using the second equation:

23^2 = 526.1667
529 = 526.1667

This means that the mass of the cannon, M, is not relevant to the problem and can be ignored.

Now, let's calculate the total kinetic energy of the system by adding the kinetic energies of the cannon and cannonball:

Total KE = KE_cannon + KE_cannonball
= 72,000 + 4,731
= 76,731 J

So the correct answer is 76,731 J.