Particle Equilibrium with Non-Coplanar Forces: ISBM College of Engineering Experiment, Study notes of Mechanics

An experiment conducted at ISBM College of Engineering to study the equilibrium of a particle subjected to non-coplanar concurrent forces. the title, aim, apparatus description, theory, procedure, observation, calculation, and result of the experiment. Students can use this document as study notes, summaries, or schemes and mind maps to understand the concept of equilibrium of a particle under non-coplanar concurrent forces.

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Peoples Empowerment Group
ISBM COLLEGE OF ENGINEERING, NANDE, PUNE
DEPARTMENT OF APPLIED SCIENCE
Academic Year 2019-20-21
ENGINEERING MECHANICS
Experiment no.4
Title: To study the equilibrium of particle subjected to non-coplanar
concurrent forces.
Aim: To study the equilibrium of particle subjected to non-coplanar concurrent forces.
Apparatus: A space frame, spring balance weight, scale and thread.
Description of apparatus : The experimental setup consist of space frame in fig. is a rigid
jointed space frame as shown in fig 1 .Three balance carrying a thread at one end,can be hooked
on to any of the holes. At the end of the three string make a knot at P from which a load W can
be hung.
Theory: The forces acting at point P are shown in fig. 2,these forces are vertically represented
as T1=T1e1, T2=T2e2, T3=T3e3 ,W = WK where T1, T2, T3 are magnitude of tensions ,e1, e2 ,and e3
are unit vector along respective of P direction for equilibrium of point P.
T1+T2+T3 +W =0
Unit vectors e1, e2 and e3 can be derived by knowing the position co-ordinates of points 1, 2, 3
and P and tension T1, T2, T3 can be obtained analytically by solving vector equation through
equivalence of i, j and k coefficients.
Procedure:
1) The three string carrying the spring balance are hooked on three space frame 1, 2 and 3
are ends to form a knot at point P carrying a hook.
2) The initial readings on balance are noted.
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Peoples Empowerment Group

ISBM COLLEGE OF ENGINEERING, NANDE, PUNE

DEPARTMENT OF APPLIED SCIENCE

Academic Year 2019-20-

ENGINEERING MECHANICS

Experiment no.

Title: To study the equilibrium of particle subjected to non-coplanar

concurrent forces.

Aim: To study the equilibrium of particle subjected to non-coplanar concurrent forces.

Apparatus: A space frame, spring balance weight, scale and thread.

Description of apparatus: The experimental setup consist of space frame in fig. is a rigid

jointed space frame as shown in fig 1 .Three balance carrying a thread at one end,can be hooked on to any of the holes. At the end of the three string make a knot at P from which a load W can be hung.

Theory: The forces acting at point P are shown in fig. 2,these forces are vertically represented

as T 1 =T 1 e 1 , T 2 =T 2 e 2 , T 3 =T 3 e 3 ,W = WK where T 1 , T 2 , T 3 are magnitude of tensions ,e 1 , e 2 ,and e 3 are unit vector along respective of P direction for equilibrium of point P. T 1 +T 2 +T3 +W = Unit vectors e 1 , e 2 and e 3 can be derived by knowing the position co-ordinates of points 1, 2, 3 and P and tension T 1 , T 2 , T 3 can be obtained analytically by solving vector equation through equivalence of i, j and k coefficients.

Procedure:

  1. The three string carrying the spring balance are hooked on three space frame 1, 2 and 3 are ends to form a knot at point P carrying a hook.
  2. The initial readings on balance are noted.
  1. The load โ€˜Wโ€™ is attached at point โ€˜Pโ€™ and new in three strings are noted ensuring the stability and precision of three strings noted tension.
  2. The final readings in spring balance are noted and experimentally obtained tensions in strings are noted.
  3. Space co-ordinates of 1,2,3 are noted in the observation table.
  4. The position of 1, 2, 3 are changed, all 3 to 5 steps are repeated for two more load.

Observation:

Sr.No Load in N Tension in the Spring (Experimental) Space Co-ordinates Tension in the spring Remark % error in T 1 (N)

T 2

(N)

T 3

(N) Points X(m) Y(x) Z(m) T 1 (N)

T 2

(N)

T 3

(N)

T 1 T 2 T 3

P

P

P

Calculation:

Formula to define a unit vector,

e =

( x 2 โˆ’ xp ) i +( y 2 โˆ’ yp ) j +( z 2 โˆ’ zp ) k

โˆš(^ x^^2 โˆ’ xp^ )^2 +(^ y^^2 โˆ’^ yp^ )^2 +(^ z^^2 โˆ’ zp^ )^2

Co-ordinates of point are,

Result: The experimental value of a tensile force is compared with analytical value presented

in table.

Conclusion: It is concluded that the experimental and analytical value of the tension in spring

are near by same.

Experiment no: 5

Title: To study the equilibrium of particle subjected to

non-coplanar concurrent forces.

Div:__________

Roll No: ________

Date: ___________