Vectors and moments (Vector diagram, horizontal/vertical components, weight)


by jspake
Tags: components, diagram, moments, vector, vectors, weight
jspake
jspake is offline
#1
Oct27-12, 02:20 PM
P: 1
Hello,
I was solving a vector & moments question as a part of my revision and got stuck somewhere. I really need your help.. some sub-questions are solved, please correct me if I'm wrong.
Here's the question (Its kinda long) :

The free-body diagram shows three forces that act on a stone hanging at rest from two strings.



(a) Calculate the horizontal component of the tension in each string. Why should these two components be equal in magnitude?

String 1: =F cosθ = 1 x cos60 =0.5 N
String 2: =F cosθ = 0.58 x cos30 = 0.5 N

The components are equal in magnitude because the stone is at rest and there is no horizontal movement.

(b) Calculate the vertical component of the tension in each string

String 1: F Sin θ = 1 x sin60 = 0.87N
String 2: F Sinθ = 0.58 x sin30 = 0.29N

(c) Use your answer to (b) to calculate the weight of the stone

= 0.87 + 0.29 N
= 1.16N
(Not sure about this answer)

(d) Draw a vector diagram of the forces on the stone. This should be a triangle of forces

I don’t know how to solve this one – please help!

(e) Use your diagram in (d) to calculate the weight of the stone

This one too.. help!!
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mfb
mfb is offline
#2
Oct27-12, 04:04 PM
Mentor
P: 10,853
Quote Quote by jspake View Post
The components are equal in magnitude because the stone is at rest and there is no horizontal movement.
No horizontal acceleration.

The approach for c is fine.

(d) Draw a vector diagram of the forces on the stone. This should be a triangle of forces

I don’t know how to solve this one – please help!
Hint: You already have all the forces in your diagram. Just shift the arrows around (and adjust their lengths) to get a triangle.
This will allow you to measure the length of the downwards force, too.


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