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## Q. 1.8

The pulley shown in Fig. (a) is subjected to the belt forces P and Q. Using rectangular components, determine the magnitude and direction of the resultant force. ## Verified Solution

Referring to Fig. (b), the rectangular representations of P and Q are

$P=120\cos30^\circ i+120\sin30^\circ j=103.9i+60.0j$ lb

$Q=−100\cos70^\circ i−100\sin70^\circ j=−34.2i−94.0j$ lb

The resultant of P and Q is found by adding their components:

$R=P+Q=(103.9−34.2)i+(60.0−94.0)j=69.7i−34.0j$ lb

Calculating the magnitude and direction of R, we obtain

$R =\sqrt{34.0^{2} + 69.7^{2}}=77.6$ lb            $θ=\tan^{−1}\frac{34.0}{69.7}=26.0^\circ$  