In a closed system like a cannon and cannonball, the conservation of momentum plays a crucial role in understanding how changes in mass affect the kinetic energy of the cannonball when fired.
When the cannon fires the cannonball, the total momentum before firing (which is zero) must equal the total momentum after firing. The momentum can be expressed as:
\[ \text{momentum} = \text{mass} \times \text{velocity} \]
If we consider that the cannon's mass \(m_c\) and the cannonball's mass \(m_b\) change, we can analyze two specific scenarios from your response options that could lead to an increase in the kinetic energy of the cannonball:
-
Decrease the mass of the cannon or increase the mass of the cannonball: This scenario is beneficial because reducing the cannon's mass allows it to recoil less, meaning more energy can be transferred to the cannonball, increasing its velocity and therefore its kinetic energy.
-
Increase the mass of the cannon or decrease the mass of the cannonball: This could lead to the cannonball gaining a velocity increase since more of the firing energy would be transferred to the cannonball if the cannon is heavier in comparison to a lighter cannonball.
Thus, the answer that indicates a scenario where the cannonball's kinetic energy increases appropriately is:
Decrease the mass of the cannon or increase the mass of the cannonball.
This scenario allows for a more efficient energy transfer resulting in an increased kinetic energy of the cannonball.
1 answer