Question
Changes in Energy Quick Check
1 of 51 of 5 Items
Question
Use the computational model of a cannon and cannonball shown to answer the question below.
If the mass of the cannonball increases, and all other initial conditions stay the same, what would happen to the velocity and kinetic energy of the cannonball?
(1 point)
Responses
The velocity increases, and the kinetic energy decreases.
The velocity increases, and the kinetic energy decreases.
The velocity decreases, and the kinetic energy decreases.
The velocity decreases, and the kinetic energy decreases.
The velocity increases, and the kinetic energy increases.
The velocity increases, and the kinetic energy increases.
The velocity decreases, and the kinetic energy increases.
1 of 51 of 5 Items
Question
Use the computational model of a cannon and cannonball shown to answer the question below.
If the mass of the cannonball increases, and all other initial conditions stay the same, what would happen to the velocity and kinetic energy of the cannonball?
(1 point)
Responses
The velocity increases, and the kinetic energy decreases.
The velocity increases, and the kinetic energy decreases.
The velocity decreases, and the kinetic energy decreases.
The velocity decreases, and the kinetic energy decreases.
The velocity increases, and the kinetic energy increases.
The velocity increases, and the kinetic energy increases.
The velocity decreases, and the kinetic energy increases.
Answers
Answered by
GPT-4o mini
To answer the question, we need to consider the physics of a cannon and cannonball.
1. When the **mass of the cannonball increases**, while all other initial conditions remain the same, the initial velocity imparted to the cannonball from the cannon (due to the explosion) does not depend on the mass of the ball. The same force will launch a heavier cannonball, but the acceleration it receives will be less, due to Newton's second law (\( F = ma \)). Therefore, the cannonball’s initial velocity **decreases**.
2. The kinetic energy (KE) of an object is given by the formula:
\[
KE = \frac{1}{2} mv^2
\]
Here, \( m \) is the mass and \( v \) is the velocity of the cannonball. Since the mass has increased but the velocity has decreased, we need to analyze how these two factors affect kinetic energy.
Since the velocity decreases, the kinetic energy can also be expected to decrease, even though the mass is larger, since velocity contributes to the kinetic energy squared.
As a result, we find:
- The **velocity decreases** due to increased mass.
- The **kinetic energy decreases** because although mass increases, the reduction in velocity (which is squared in the kinetic energy formula) will likely lead to a net decrease in kinetic energy.
Based on this analysis, the correct response is:
**The velocity decreases, and the kinetic energy decreases.**
1. When the **mass of the cannonball increases**, while all other initial conditions remain the same, the initial velocity imparted to the cannonball from the cannon (due to the explosion) does not depend on the mass of the ball. The same force will launch a heavier cannonball, but the acceleration it receives will be less, due to Newton's second law (\( F = ma \)). Therefore, the cannonball’s initial velocity **decreases**.
2. The kinetic energy (KE) of an object is given by the formula:
\[
KE = \frac{1}{2} mv^2
\]
Here, \( m \) is the mass and \( v \) is the velocity of the cannonball. Since the mass has increased but the velocity has decreased, we need to analyze how these two factors affect kinetic energy.
Since the velocity decreases, the kinetic energy can also be expected to decrease, even though the mass is larger, since velocity contributes to the kinetic energy squared.
As a result, we find:
- The **velocity decreases** due to increased mass.
- The **kinetic energy decreases** because although mass increases, the reduction in velocity (which is squared in the kinetic energy formula) will likely lead to a net decrease in kinetic energy.
Based on this analysis, the correct response is:
**The velocity decreases, and the kinetic energy decreases.**
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