Question on force applied to an object hanging from a cord

  • #1
410
11

Homework Statement


A ball of mass m hangs vertically from a massless string experiencing a tension T. What force is required to pull the ball out to an angle theta from the vertical?

  1. 1) mgsin(theta)

  2. 2) mgcos(theta)

  3. 3) mgtan(theta)

  4. 4) 2mg tan (theta)

  5. 5) mg/cos (theta)

Homework Equations


no equations

The Attempt at a Solution


Well, I thought that if we break down the components of gravity acting on an object at an angle theta from the lowest point of it hanging, then we would have a component mg * sin(theta) acting in a direction perpendicular towards the cord [restoring force] and a component mg * cos(theta) acting in a direction antiparallel to the cords tension.

Thus, I would need to apply an equivalent force to mg*sin(theta) in the opposite to counter react the force of gravity's component.

The solutions say that the answer is mg*tan
Well, I thought that if we break down the components of gravity acting on an object at an angle theta from the lowest point of it hanging, then we would have a component mg * sin(theta) acting in a direction perpendicular towards the cord [restoring force] and a component mg * cos(theta) acting in a direction antiparallel to the cords tension.

Thus, I would need to apply [number 3]. Could anyone please explain why their answer is right and why my approach is possibly wrong?
 

Answers and Replies

  • #2
TSny
Homework Helper
Gold Member
13,074
3,395
Hi, Robonerd!

I like your answer! The problem does not make any restriction on the direction of your applied force.

I think maybe they are assuming the applied force is horizontal. If you make that assumption, what answer would you get?
 
  • #3
410
11
I have no idea. Could you please guide me?
 
  • #4
TSny
Homework Helper
Gold Member
13,074
3,395
I have no idea.
Yes you do!
Could you please guide me?
A free body diagram will guide you.
 
  • #5
410
11
2016-05-06.png
 
  • #6
410
11
here is my free body diagram. kinda messy, i know.
 
  • #7
TSny
Homework Helper
Gold Member
13,074
3,395
Where's your applied force (that you are going to assume is horizontal)?
 
  • #8
410
11
Going rightwards starting from the point where the T and Fg forces intersect?
 
  • #9
TSny
Homework Helper
Gold Member
13,074
3,395
Yes. I suggest a fresh drawing. Do not break any of the forces into components yet. Make sure you label the angle θ correctly.
 
  • #12
TSny
Homework Helper
Gold Member
13,074
3,395
Good. (Your angle θ is drawn correctly in both figures. For some reason I initially thought it was in the wrong place.)

Now, spend a little time trying to solve for Fapp using your drawing.
 

Related Threads on Question on force applied to an object hanging from a cord

  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
4
Views
4K
Replies
1
Views
6K
Replies
3
Views
551
Replies
1
Views
2K
Replies
5
Views
1K
  • Last Post
Replies
11
Views
7K
  • Last Post
Replies
1
Views
9K
Top