Sum of horizontal and vertical components, Mechanical Engineering

Assignment Help:

Sum of horizontal and vertical components:

The two forces shown in the figure, are to be replaced by an equivalent force R applied at P. Locate point P by finding its distance x from AB and specify magnitude of R and the angle O it makes with horizontal. 

720_Sum of horizontal and vertical components.png

Sol.: Let us assume equivalent force R (Resultant force) is acting at an angle of θ with the horizontal. And  ∑H and ∑V be the sum of horizontal and vertical components.

∑H = -1500 cos 30º = -1299N                                   ...(i)

V = 1000 -1500 sin 30º = 250 N                            ...(ii)

R = { ∑H2  + ∑V2  }1/2

For the direction of resultant

R = 1322.87 N                                                                        .......ANS

tanθ  =  ΣV/ ΣH

= 250/-1299

= -10.89º                                                                              .......ANS

Now for finding position of resultant, we make use of Varignon's theorem, that is R × d =∑M , Take moment about point 'O'

1322.878 × x = 1500 cos 30º × 180 + 1500 sin 30º × 50 -1000 × 200

By solving x = 53.92 mm                                                                                                       .......ANS


Related Discussions:- Sum of horizontal and vertical components

Differences between torque and torsion, Differences between torque and tors...

Differences between torque and torsion: Give differences between torque and torsion. List a few examples of torsion in the engineering practice. Sol.: When structural or

Objectives- computer algorithm for on-line scheduling , Objectives After...

Objectives After studying this section, you should be capable to understand: Cell aspects of scheduling, Conventional priority rules, Newer approaches to on line

Evaluate the total deformation of the bar, (a) A member ABC is formed by co...

(a) A member ABC is formed by connecting a steel bar of 20mm diameter to an aluminium bar of 30 mm diameter, and is subjected to forces as shown in figure. Evaluate the total defor

Illustrate the types of special foundations, Illustrate the Types of specia...

Illustrate the Types of special foundations Special foundations find use under following situation: i)  To meet the demands that are arising from uncommon environmental cond

Explain commutator- dc generator, Commutator The function of a commutat...

Commutator The function of a commutator is to change alternating current induced in the armature into unidirectional current. The commutator is of cylindrical shape and is made

energy method, A semi circular frame of flexural rigidity EI is built at A...

A semi circular frame of flexural rigidity EI is built at A and caries a vertical load W at B. calculate the magnitude of the vertical and horizontal deflection at B and hence the

Foil butt seam welding, Foil Butt Seam Welding This is a modification o...

Foil Butt Seam Welding This is a modification of seam welding, in which thin narrow strips of metal arc introduced between one or both of the circular electrodes and the work p

Applications of high temperature materials, Q. Applications of high tempera...

Q. Applications of high temperature materials? A brief description of materials of construction used for common high temperature components in furnaces, boilers, superheaters,

String vibration fixed ends, String Vibration Fixed Ends In case of the...

String Vibration Fixed Ends In case of the vibrations of a string, both its ends at  x = 0  and  x = L  may be permanently fixed;  y (x = 0) = 0 , and  y (x = L) = 0 at all  t

Velocity - area method, Q. What do you mean by Velocity - Area Method? ...

Q. What do you mean by Velocity - Area Method? Out of the above four categories, velocity area method is most widely used and provides more accurate results. Requirements of a

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