Help with conical pendulum problem

In summary, a conical pendulum with a 500g ball and a 1.0m long string moving in a horizontal circle of radius 20cm has a tension of 5N. This can be solved using the equation Tcos(theta)=mg, with the hint that the vertical component of acceleration is zero. The tension force should be on the y-axis at 90 degrees on the free body diagram, while the weight force should be on the y-axis at 270 degrees.
  • #1
pammy345
1
0

Homework Statement



okay here is the problem: A conical pendulum is formed by attaching a 500g ball to a 1.0m long string, then allowing the mass to move in a horizontal circle of radius 20cm. What is the tension in the string?

Homework Equations



My professor gave a hint that said use the fact that the vertical component of acceleration is zero since there is no vertical motion.

If i use the equation Tcos(theta)=mg, i get the given answer 5N. if this is correct should my Tension force be on the y-axis at 90 degrees on my FBD and my weight force on the y-axis at 270 degrees?
 
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  • #2
pammy345 said:
If i use the equation Tcos(theta)=mg, i get the given answer 5N. if this is correct should my Tension force be on the y-axis at 90 degrees on my FBD and my weight force on the y-axis at 270 degrees?
Sounds good to me :approve:
 
  • #3


I would like to clarify a few points about the problem and provide some guidance on how to approach it.

Firstly, it is important to understand the concept of a conical pendulum. It is a type of pendulum in which the bob (in this case, the 500g ball) moves in a horizontal circle instead of a vertical one. This motion is caused by the tension in the string, which acts as the centripetal force, keeping the bob in its circular path.

Now, let's address the given hint from your professor. The fact that the vertical component of acceleration is zero is crucial in solving this problem. This means that the bob is not moving up or down, and therefore the net force in the vertical direction must be zero. This leads us to the equation Tcos(theta) = mg, where T is the tension in the string, theta is the angle between the string and the vertical direction, and mg is the weight of the bob.

Next, let's look at the given answer of 5N. This is the correct answer, but it is important to understand how it was derived. In this case, the angle theta is equal to 90 degrees, as the string is perpendicular to the vertical direction. This means that cos(theta) = 0, and the equation becomes 0 = mg. Solving for T, we get T = mg = (0.5kg)(9.8m/s^2) = 4.9N, which is approximately equal to 5N.

To address your question about the tension and weight forces on the y-axis, it is important to remember that forces act in all directions. In this case, the tension force is acting in the y-direction (perpendicular to the string), while the weight force is acting in the negative y-direction (opposite to the direction of the tension force). However, since the net force in the y-direction is zero, these two forces cancel each other out, and we are left with the tension force as the only force acting in the y-direction.

In conclusion, to solve this problem, you need to use the equation Tcos(theta) = mg, where T is the tension in the string and theta is the angle between the string and the vertical direction. The fact that the vertical component of acceleration is zero is crucial in solving this problem. Remember to consider all forces acting on the bob and use the
 

1. What is a conical pendulum?

A conical pendulum is a type of pendulum where the weight is attached to a string or rod that is suspended from a fixed pivot point. The weight moves in a circular path instead of a back and forth motion like a traditional pendulum.

2. How do you calculate the period of a conical pendulum?

The period of a conical pendulum can be calculated using the formula T = 2π√(L/g), where T is the period, L is the length of the string, and g is the acceleration due to gravity. This formula assumes that the mass of the weight is concentrated at a single point and that the amplitude of the pendulum's swing is small.

3. What factors affect the period of a conical pendulum?

The period of a conical pendulum is primarily affected by the length of the string, the mass of the weight, and the acceleration due to gravity. Other factors that may have a small impact include air resistance and the amplitude of the pendulum's swing.

4. How do you find the tension in the string of a conical pendulum?

The tension in the string of a conical pendulum can be calculated using the formula T = (m*v^2)/L, where T is the tension, m is the mass of the weight, v is the velocity of the weight, and L is the length of the string. This formula assumes that the weight is moving at a constant speed and that the string is massless.

5. How does the angle of the string affect the motion of a conical pendulum?

The angle of the string affects the motion of a conical pendulum by determining the shape and size of the path that the weight follows. A larger angle will result in a wider, more elliptical path, while a smaller angle will create a narrower, more circular path. The angle also affects the tension in the string and the period of the pendulum.

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