Question

a cannon fires a cannonball as shown below. which of the following statements is false?

• the total momentum of the system after the cannonball is fired equals the total momentum before being fired.
• the cannon and the cannonball have the same magnitude momentum after being fired.
• the net force on the system is zero.
• the momenta of the cannon and cannonball remain the same before and after being fired.

Explanation:

Step 1: Analyze the initial state

Before firing, both the cannon and the cannonball are at rest, so their individual momenta are zero.

$$p_{\text{cannon, initial}} = 0, \quad p_{\text{ball, initial}} = 0$$

Step 2: Analyze the final state

After firing, the cannonball moves forward with momentum \(p_{\text{ball}}\) and the cannon recoils backward with momentum \(p_{\text{cannon}}\).

$$p_{\text{ball, final}} eq 0, \quad p_{\text{cannon, final}} eq 0$$

Step 3: Evaluate the statements

Since individual momenta change from zero to non-zero values, the statement claiming they remain the same is false.

$$p_{\text{initial}} eq p_{\text{final}} \quad \text{for individual components}$$

Answer:

D. The momenta of the cannon and cannonball remain the same before and after being fired.