Prove the parallelogram law of forces - mechanics, Mechanical Engineering

Prove the parallelogram law of forces:

Assume that the two forces P and Q act at a point 'O' as shown in figure given below. The force P can be represented in magnitude and direction by vector OA, While force Q is represented in magnitude and direction by vector OB, Angle between the two force is 'a'. The resultant can be denoted by vector OC as shown in the figure given below. Drop perpendicular from C on OA.


P,Q = Forces whose resultant is needed to be found out.

θ= Angle that the resultant forces makes with one of the forces

α= Angle between the forces P and Q

1071_Prove the parallelogram law of forces.png

It is the magnitude of resultant 'R'


2383_Prove the parallelogram law of forces1.png

Direction ( θ ):

865_Prove the parallelogram law of forces2.png



(i) Resultant R is max when two forces collinear and are in the same direction.

 2380_Prove the parallelogram law of forces3.png

(ii) Resultant R is min when two forces collinear but acting in the opposite direction.

That is  α = 1800    =>   Rmin = P- Q

(iii) If a = 900, that is when the forces act at right angle, then

R =   P2  + Q2

(iv) If the two forces are equal that is, when P = Q  =>R = 2P.cos(θ/2)


Posted Date: 10/16/2012 1:27:54 AM | Location : United States

Related Discussions:- Prove the parallelogram law of forces - mechanics, Assignment Help, Ask Question on Prove the parallelogram law of forces - mechanics, Get Answer, Expert's Help, Prove the parallelogram law of forces - mechanics Discussions

Write discussion on Prove the parallelogram law of forces - mechanics
Your posts are moderated
Related Questions

Wheels:  The wheel, along with the tyre has to take the vehicle load, provide a cushioning effect (to protect against force or shock) and cope with the steering control. The wheel

Q. Application of cold service insulation? Cold insulation shall be installed specifically in accordance with the Manufacturer's recommendations, and generally as outlined belo

What different of blow hole and pin hole

Remove cover left crank case and check for leakage: Before attending oil seal leakage check if any leak is there in the highlighted points - Neutral switch "o" ring leak, Shifter

Coil: A coil is used in ignition system to increase the voltage supplied by the battery or magneto. Coil

Explain about structural design of combined footing. Structural Design of Combined Footing The rectangular and trapezoidal combined footings are designed assuming uniform so

Compression Ratio (r): It is the ratio of the total cylinder volume when the piston is at the bottom dead centre, V t to the clearance volume, V C . R= v t /v c

Prove that the ratio of belt tension is given by the T 1 / T 2   = e μθ Let  T1 = Tension in belt on the tight side T2 = Tension in belt on the slack side θ = Angle

Find out extension: Q: A bar having length 25mm has varying cross section. It carries load of 14KN. Find out extension if cross section is given by (6 + x 2 /100) mm 2