Question

In: Physics

Find the magnitude and direction of the resultant of two concurrent forces of 50 and 75...

Find the magnitude and direction of the resultant of two concurrent forces of 50 and 75 N acting on a body at angle of 50 degrees with each other Use the graphical method and the algerbraic method

Solutions

Expert Solution

Concurrent forces means forces acting through a single point.

Therefore,

resultant is given as

R2 = A2 + B2 + 2AB*cos

R2 = 50 2 + 752 + 2*50*75 * cos 50

R2 = 12945.9

R2 = 12946

R = 113.78 N

R = 113.8 N <---------- magnitude

Now,

sin = (75 / 113.8) * sin 50

sin = 0.504862

= arcsin (0.504862)

= 30.3o <-------------------- direction

------------------------------------------------------------------

USING GRAPHICAL METHOD ( YOU CAN DO THIS USING A RULER AND A PROTRACTOR)

Draw 50 N force (take 10 N = 1 cm on a ruler)

then from the head of 50 N, draw another vector fro 75 N (7.5 cm) at an angle of 50 N ( 5.0 cm) (see the diagram above)

Now, draw a resultant line starting from the tail of 50 N vector to the head of 75 N vector. Then measure the length of this line, it will be 11.38 cm means 113.8 N


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