Concepts Of Forces In Equilibrium

Abstract:
The experiment over here is to find how the vertical displacement of an object suspended on a guide surrounded by two pulleys depends on the mass of the object. To accomplish this we naturalised a system and observed the vertical displacement as the central weight varied. The experiment is basically about the plan of forces in equilibrium. We used the same weights for A and C and they were kept constant throughout the experiment. We changed the weights of B systematically and noticed how it make the vertical displacement (height). The results came close enough to our predicted equation found on forces and trigonometry.
Introduction:
The problem was to find the relationship between free-hanging weights and pulleys, namely the maximum a central mass foundation be without overloading the system. This type of problem is important in a setting where pulleys are in use to refrain from do contact with a surface.
Theory:
The setup of the experiment is shown by this draw below.







Diagram: 1




The length of the setup and the angle of evilk can be described by this diagram and the same trigonometric expression:




Diagram: 2







[1] Tan Ɵ = h/(l/2)
[2] Tan Ɵ= 2h/l
[3] h = 1/(2 ) l tanƟ
The forces in the system are most critical at the turn on P, which ca be described by this force diagram and trigonometric expression:
Diagram: 3


〖 sin〗⁡θ mg

cosine⁡θ mg


[4] 〖 sin〗⁡θ mg+〖 sin〗⁡θ mg=Mg
[5] 〖 2sin〗⁡θ mg=Mg
[6] 〖 sin〗⁡θ m=M
[7] 〖 sin〗⁡θ=M/2m
The prediction is now in the form of two expressions, one with a tan ⁡θ and another(prenominal) with a sin ⁡θ, these two can be link using the following trigonometric identity:

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