# Conical Pendulum Homework: Determine Force, Find Radial Acceleration

• sailsinthesun
In summary, the conversation discusses a conical pendulum with a 81.0 kg bob on a 10.0 m wire at an angle of 2.00° with the vertical. The horizontal and vertical components of the force exerted by the wire on the pendulum are calculated using the equations F=ma and a=v^2/r. The horizontal force is found to be Fsin(theta) and the vertical force is Fcos(theta). To find the radial acceleration of the bob, the radius is calculated using r=10sin(2deg) and then a=v^2/r is used to solve for the acceleration. The horizontal force can also be used to calculate the horizontal acceleration.
sailsinthesun

## Homework Statement

Consider a conical pendulum with a 81.0 kg bob on a 10.0 m wire making an angle of theta= 2.00° with the vertical.

(a) Determine the horizontal and vertical components of the force exerted by the wire on the pendulum.
(b) What is the radial acceleration of the bob?

F=ma
a=v^2/r

## The Attempt at a Solution

(a)After drawing the FBD for the wire and resolving the vectors, I get the horizontal force to be Fsin(theta) and the vertical to be Fcos(theta). Fcos(th)=mg so F=mg/cos(th). Then Fsin(th)=27.7484N and Fcos(th)=794.61N.

I'm pretty sure I did these correctly, but I'm not sure how to get the second part.
(b)I calculated the radius using r=10sin(2deg). Here is where I'm lost. I know a=v^2/r, and I have r, but need to find v. Any help or hints?

If you have the horizontal force, then you know the horizontal acceleration from F=ma. That 'a' is the same 'a' as in a=v^2/r.

Great job on calculating the horizontal and vertical components of the force exerted by the wire on the pendulum. Your approach seems correct and your calculations are consistent with the given information. For the second part, you are on the right track. As you mentioned, the equation for radial acceleration is a=v^2/r. In this case, v represents the tangential velocity of the bob, which can be found using the equation v=ωr, where ω is the angular velocity. To find ω, you can use the equation ω=√(g/L), where L is the length of the wire (10 m in this case). Once you have calculated ω, you can plug it into the equation for v and then use that value to calculate the radial acceleration. I hope this helps. Keep up the good work!

## 1. What is a conical pendulum?

A conical pendulum is a type of pendulum where the bob (weight) moves in a circular motion rather than a straight line, due to the pendulum string or rod being attached to a fixed point that is not directly above the bob's suspension point.

## 2. How do you calculate the force in a conical pendulum?

The force in a conical pendulum can be calculated using the formula F = m(v^2/r), where m is the mass of the bob, v is the tangential velocity of the bob, and r is the radius of the circular motion. This formula is derived from Newton's second law, which states that force is equal to mass times acceleration.

## 3. How do you find the radial acceleration in a conical pendulum?

The radial acceleration in a conical pendulum can be found using the formula a = v^2/r, where v is the tangential velocity of the bob and r is the radius of the circular motion. This formula is derived from the centripetal acceleration formula, which states that the acceleration towards the center of a circular motion is equal to the square of the tangential velocity divided by the radius.

## 4. What factors affect the force and radial acceleration in a conical pendulum?

The force and radial acceleration in a conical pendulum are affected by the length of the pendulum string or rod, the mass of the bob, and the speed at which the bob is moving. Additionally, the force and acceleration can also be affected by external factors such as air resistance or friction.

## 5. How can conical pendulum homework help in understanding physics concepts?

Conical pendulum homework can help in understanding physics concepts such as circular motion, centripetal force, and acceleration. By applying these concepts to real-world situations, students can deepen their understanding and develop problem-solving skills. Additionally, working on conical pendulum homework can also help in improving critical thinking and analytical skills.

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