The mass of the ball is m, and the length of the string is L

In summary, the conversation discusses a problem involving a Yo-Yo ball with a mass of m and a string length of L. The ball moves in a circular motion on a vertical plane and the goal is to find the difference in string tension at the lowest and highest points. The solution involves using the formula for centripetal force, which gives an answer of 2mg. However, it is noted that the correct answer is actually 6mg, indicating that the problem lies in the assumption that the ball has the same speed at both points. The suggested approach is to use conservation of energy to relate the top and bottom speeds.
  • #1
rbwang1225
118
0

Homework Statement



A man plays a Yo-Yo ball as shown in the figure. The mass of the ball is m, and the length of the string is L. The ball moves in a circle along a vertical plane. What is the difference of the string tension at the lowest point ([itex](T_{2})[/itex]) and the highest point ([itex](T_{1})[/itex])
yo yo.jpg


The Attempt at a Solution



([itex]\frac{mv^{2}}r=T_1+mg=T_2-mg[/itex])
[itex]\Rightarrow T_2-T_1=2mg[/itex]
But the answer is 6mg, I guess the problem is that v is not equal at the two different positions. In this case, I don't know how to solve it.
 
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  • #2


Your guess is correct.
Try to use conservation of energy to relate the top speed with the bottom speed.
 

FAQ: The mass of the ball is m, and the length of the string is L

1. What is the relationship between the mass of the ball and the length of the string?

The mass of the ball and the length of the string are directly proportional. This means that as the mass of the ball increases, the length of the string will also increase.

2. How does the mass of the ball affect the motion of the string?

The mass of the ball affects the motion of the string by determining the tension and speed at which the string will move. A heavier ball will require more force to move, resulting in a slower motion compared to a lighter ball.

3. Is there a limit to the mass of the ball that can be attached to the string?

Yes, there is a limit to the mass of the ball that can be attached to the string. This is because as the mass of the ball increases, the tension in the string also increases, which can eventually exceed the breaking point of the string.

4. Does the length of the string affect the period of the ball's motion?

Yes, the length of the string does affect the period of the ball's motion. The longer the string, the longer it will take for the ball to complete one full swing. This is because a longer string will have a larger amplitude, resulting in a longer period of motion.

5. How does the length of the string affect the gravitational force acting on the ball?

The length of the string does not directly affect the gravitational force acting on the ball. However, the longer the string, the greater the distance between the ball and the point of suspension, which can result in a longer period of motion due to the increased distance traveled by the ball.

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