Asked by loser
A ball of mass on a string is rotating about the center axis with a velocity . If the tension force in the string is , what is the radius of the circular path of the ball?
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the radius of the circular path of the ball, we need to analyze the forces acting on it. When an object is rotating in a circular path, it experiences centripetal force, which is provided by the tension in the string.
The centripetal force \( F_c \) required to keep the ball moving in a circular path is given by the equation:
\[
F_c = \frac{m v^2}{r}
\]
Where:
- \( m \) is the mass of the ball,
- \( v \) is the tangential velocity of the ball,
- \( r \) is the radius of the circular path.
In this case, the tension in the string \( T \) provides the centripetal force. Thus, we can set the tension equal to the centripetal force:
\[
T = \frac{m v^2}{r}
\]
To find \( r \), we can rearrange this equation:
\[
r = \frac{m v^2}{T}
\]
This equation gives the radius of the circular path of the ball in terms of its mass \( m \), its velocity \( v \), and the tension \( T \) in the string.
The centripetal force \( F_c \) required to keep the ball moving in a circular path is given by the equation:
\[
F_c = \frac{m v^2}{r}
\]
Where:
- \( m \) is the mass of the ball,
- \( v \) is the tangential velocity of the ball,
- \( r \) is the radius of the circular path.
In this case, the tension in the string \( T \) provides the centripetal force. Thus, we can set the tension equal to the centripetal force:
\[
T = \frac{m v^2}{r}
\]
To find \( r \), we can rearrange this equation:
\[
r = \frac{m v^2}{T}
\]
This equation gives the radius of the circular path of the ball in terms of its mass \( m \), its velocity \( v \), and the tension \( T \) in the string.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.