Rock hanging from ceiling swinging uniform circular motion

Click For Summary

Homework Help Overview

The problem involves a rock of mass 5.5 kg hanging from the ceiling and moving in uniform circular motion with a radius of 0.8 m and a rope angle of 15 degrees from vertical. The original poster seeks to determine the magnitude of the force of the cord, the acceleration of the rock, the angular speed, and the revolutions per second.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the need to account for various forces, including centripetal force and tension in the rope. There are attempts to use free body diagrams and equations related to circular motion, but confusion remains regarding the calculations of velocity and acceleration.

Discussion Status

The discussion is ongoing, with participants exploring different aspects of the problem. Some have offered guidance on resolving forces and using equations, while others express uncertainty about how to proceed with the calculations.

Contextual Notes

There are indications of confusion regarding the correct application of angles in force calculations and the need for additional equations to find the required values. The original poster has noted difficulty in finding relevant equations in their textbook.

iamtheone
Messages
7
Reaction score
0

Homework Statement



A rock of mass 5.5kg is hanging from the ceiling moving in uniform circular motion. The radius of the orbit is .8m. The angle of the rope in comparison to if it were hanging straight down is 15 degrees outward.

What is the magnitude of the force of the cord on the mass? I already found out this is about 55.801 N

What is the magnitude of the acceleration of the rock?

What is the angular speed of the rock?

How many revolutions per second does the rock make?

Homework Equations



angular speed = v/r

f = ma

centripetal accel = (v^2)/r

..others probably as well...

The Attempt at a Solution



*To get the magnitude of the acceleration of the rock:

Ftotal = Frope + Fweight = 109.701

plug into F = ma, a=19.9457 (incorrect)

I'm guessing I need to include another force...or take the magnitude of both those force vectors added together? I don't know how to get the Frope force vector though.

Any help with thi swould be apreciated.
 
Physics news on Phys.org
iamtheone said:
I'm guessing I need to include another force...

You mentioned centripetal acceleration, so there is a centripetal force, too.
 
i don't know how to calculate it. And I mentioned it merely because I THINK it applies.
 
iamtheone said:
i don't know how to calculate it. And I mentioned it merely because I THINK it applies.

Did you draw a free body diagram? What equations can you work out from the diagram?
 
I did, but I'm still pretty much clueless.
 
Well, regarding the second question, what kind of an acceleration does the rock possess?
 
centripetal, but i don't know the velocity, so I can't calculate that either...
 
iamtheone said:
centripetal, but i don't know the velocity, so I can't calculate that either...

Well, which equation did you use to obtain the force in the rope? Which equation can you use to obtain the magnitude of the centripetal force (and the velocity)?
 
I used Fcos(20) = mg -> which is just a version of f = ma

I can't find equations for the magnitude of the centripetal force or the velocity...which is very annoying. I've been looking in my book for a while now.
 
  • #10
iamtheone said:
I used Fcos(20) = mg -> which is just a version of f = ma

I can't find equations for the magnitude of the centripetal force or the velocity...which is very annoying. I've been looking in my book for a while now.

I'll quote your first post:

iamtheone said:
f = ma

centripetal accel = (v^2)/r

Can you find the magnitude of the centripetal force now?
 
  • #11
that gives the acceleration...not force.
 
  • #12
And force equals..?what?..*acceleration?
 
  • #13
mass, but i can't calculate v - I've already tried this many times...i guess the question comes down to being able to calculate v.
 
  • #14
The tension is given by T=mg/(cos(15)), not by mg/(cos(20)!

Now, what is the planar radial component of this tension?
 
  • #15
well if v^2/r=a and R is known, then we need another eqn to solve for the a. You have Tension which you have calculated, what if you were to resolve that into x and Y components? edit: whoops didn't mean to butt in.
 

Similar threads

Acceleration in uniform circular motion is uniform or non-uniform?
  • · Replies 55 ·
2
Replies
55
Views
3K
Relation between the velocity vector and the acceleration vector of an object
  • · Replies 1 ·
Replies
1
Views
856
Is Centripetal Acceleration Constant in Uniform Circular Motion?
  • · Replies 38 ·
2
Replies
38
Views
4K
How to Add Acceleration Vector in Uniform Circular Motion
  • · Replies 14 ·
Replies
14
Views
4K
Uniform Circular Motion Inside a Sphere of Charge
  • · Replies 7 ·
Replies
7
Views
3K
Circular Motion Questions (energies, forces, angular velocities, etc.)
  • · Replies 2 ·
Replies
2
Views
2K
Circular Motion - Hanging object swinging around
  • · Replies 7 ·
Replies
7
Views
5K
Projectile and Uniform Circular Motion
  • · Replies 3 ·
Replies
3
Views
3K
Circular Motion of a Cyclist and a Car going around a bend in the road
  • · Replies 6 ·
Replies
6
Views
4K
Magnitudes and Directions In Uniform Circular Motion
  • · Replies 1 ·
Replies
1
Views
2K