Law Of Parallelogram

Question 1

Define

Answer 1

If two forces P and Q acting on a partical,be represented in magnitude and direction by the two sides of parallelogram, then their resultant is represented both in magnitude and direction by the diagnol of parallelogram which is passing through the intersection point of these two forces P and Q.

Question 2

Proof

Answer 2

Consider a parallelogram 0ACD. Let sides oa and ob represent the forces P and Q acting at a point 0.

Question 3

From geometry of the figure

Answer 3

AC=OB=Q
AngleCAD=AngleBOA= theta

Question 4

Right angle triangle

Answer 4

∆ODC
∆ADC

Question 5

From ∆ ADC

Answer 5

AD=ACcostheta=Qcostheta
CD=ACsintheta=Qsintheta

Question 6

From ∆ ODC,using pythagoras theorm

Answer 6

OC²=OD²+CD²
=(OA+AD)²+CD²
=(OA)²+(AD)²+2OA(AD)+CD²

Question 7

Resultant

Answer 7

R²=P²+Q²+2PQcostheta

Question 8

R

Answer 8

√P²+Q²+2PQcostheta

Question 9

Resultant angle

Answer 9

Tan alpha=F2sintheta/F1+F2costheta

Question 10

Case i
Theta=90 degree

Answer 10

P and Q are right angle

Question 11

R

Answer 11

R=√P²+Q²+PQcos90

Question 12

R

Answer 12

R=√P²+Q²

Question 13

Tan alpha

Answer 13

Qsin90/P+Qcos90
Tan alpha= Q/P

Question 14

Case ii theta=0

Answer 14

P and Q are in same direction

Question 15

R

Answer 15

R=√P²+Q²+2PQ
R=√(P+Q)²
R=P+Q

Question 16

Tan alpha

Answer 16

0

Question 17

Case iii
Theta=180

Answer 17

P and Q are in opposite direction

Question 18

R

Answer 18

Cos 180 =-1
Sin180 = 0
R=P-Q

Question 19

Tan alpha

Answer 19

0