Question

Find theta and W in the figure below where w_1 = 22.0 N, w_2 = 29.0 N, and a = 65.5degree, assuming that the arrangement is at rest.

Answer 1

the formula is given by

W1 = F1Cos( $\alpha$ )---------(1)

F1 = w1 = 22.0N

$\alpha$ =65.5degree

W1 = (22.0)Cos(65.5)

W1 = 9.12N------(2) = FORCE P

W2 = F2Cos( $\alpha$ )

F2=w2 =29.0N

W2 = (29.0)Cos(65.5)

W2 =12.02N--------(3)= FORCE Q

TOTAL FORCE R = W = W1 + W2----------(4)

SUBSTITUTING EQN(2) AND EQN(3) IN EQN(4) WE HAVE

R = W = 9.12 + 12.02 = 21.14N-------(5)

FROM THE LAW OF EQUILIBRIUM OF CONCURRENT COPLANAR FORCES WE HAVE THE RESULTANT FORCE GIVEN BY

R= $\sqrt{}$ P^2 + Q^2 + 2PQCos $\Theta$ ---------(6)

squaring eqn(6) on both the sides we have

(R)^2 = (P)^2 + (Q)^2 +2PQCos $\Theta$

substituting the values of R ,P,Q in the above equation we have

(21.14)^2 = (22.0)^2 + (29.0)^2 + 2(22.0)(29.0)Cos $\Theta$

Cos $\Theta$ = 0.6881

$\Theta$ = Cos^-1[0.6881]

=46degree 30 minutes