Conical Pendulum Homework: Determine Force, Find Radial Acceleration

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SUMMARY

The discussion centers on solving a conical pendulum problem involving an 81.0 kg bob suspended by a 10.0 m wire at a 2.00° angle. The horizontal force exerted by the wire is calculated as 27.7484 N, while the vertical force is 794.61 N, derived from the equations Fcos(theta) = mg and Fsin(theta). To find the radial acceleration, the radius is determined using r = 10sin(2°), and the relationship a = v²/r is established. The horizontal force allows for the calculation of horizontal acceleration, which is essential for determining the velocity needed for radial acceleration.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with trigonometric functions in physics
  • Knowledge of conical pendulum dynamics
  • Ability to resolve forces into components
NEXT STEPS
  • Calculate the velocity of the bob using the horizontal force and mass with F = ma
  • Explore the concept of centripetal acceleration in circular motion
  • Study the effects of varying the angle on the forces in a conical pendulum
  • Learn about the implications of tension in pendulum systems
USEFUL FOR

Physics students, educators, and anyone studying dynamics and forces in pendulum systems will benefit from this discussion.

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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?

Homework Equations


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?
 
Physics news on Phys.org
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.
 

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