Three forces act on particle - mechanics, Mechanical Engineering

Assignment Help:

Three forces act on particle:

Three forces act on particle 'O' as shown in the figure given below. Determine the value of 'P' such that resultant of these three forces is horizontal. Find magnitude and direction of the fourth force which when acting along with the given forces, will keep 'O' in equilibrium.

 

288_Three forces act on particle.png

Sol.: As resultant(R) is horizontal so the vertical component of resultant is zero, that is,

ΣV = 0, ΣH = R

ΣV = 200sin10° + Psin50° + 500sin150° = 0

On solving,      ΣP = -371.68N                                                                                                                      ...(i)

ΣH = 200cos10° + Pcos50° + 500cos150° = 0

By putting value of 'P', we get

ΣH = -474.96N                                                                                                                     ...(ii)

Let Unknown force be 'Q' and subtends an angle of ? With horizontal x axis. Additional force makes system in equilibrium now,

ΣH = Qcos   -474.96N = 0 that is,          Qcosθ   = 474.96N------(3)

As ΣV is already zero, on addition of force Q, the body is in equilibrium so again            V is zero.

ΣV = 200sin10° -371.68sin50° + 500sin150° + Qsinθ = 0

But 200sin10° - 371.68sin500 + 500sin1500 = 0 by equation (1) So,    Qsinθ = 0, that means Q = 0or sinθ   = 0,

ΣQ is not zero so sinθ = 0,  Q= 0

By putting  = 0 in equation (iii),

Q = 474.96N,     = 0º                                  .......ANS

 


Related Discussions:- Three forces act on particle - mechanics

Internal energy - thermodynamics, Internal Energy (U): It is the energ...

Internal Energy (U): It is the energy possessed by the system on account of its configurations, and motion of atoms and molecules. Not like potential energy and kinetic energy

Kinetics of Rectilinear motion, Advantages of work energy principle over D'...

Advantages of work energy principle over D''alambert''s principal.Explain in detail

Maximum bending stress , Obtain the equations of the elastic curve and use ...

Obtain the equations of the elastic curve and use them to determine the deflection and rotation at point B  in terms of E, I, F and L. Determine the maximum bending stress in the

Slider crank mechanism, What is the mathematical displacement equation and ...

What is the mathematical displacement equation and its derivatives?

Venturi tube-main components of a carburettor , Venturi Tube: A ventu...

Venturi Tube: A venturi is basically an air passage that has a shape similar to that shown in Figure that is narrower at the middle known as venturi tube. As air travels thro

Jig and fixture, design summarised of milling fixture

design summarised of milling fixture

Value of the maximum shear stress , Value of the maximum shear stress: ...

Value of the maximum shear stress: Illustrates that for a given maximum shear stress the minimum diameter needed for a solid circular shaft to transmit P kW at N rpm may be ex

Polymerization, Polymerization Whether similar molecules join in long ...

Polymerization Whether similar molecules join in long chain is termed as polymerization and resulting outcome is a polymer in a chemical reaction. Each plastic are polymers. T

Evaluate the temperature of the centre of the bar, A copper bar 80 mm by 60...

A copper bar 80 mm by 60 mm in cross-section (k = 370 W/m ºC) is lying in a insulated trough so that the heat transfer from one face both the edges is negligible. It is seen that w

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd