Question

Figure P4.24 shows loads hanging from the ceiling of an elevator that is moving at constant velocity. Find the tension in each of the three strands of cord supporting each load, given that ?1 = 36 degree, ?2 = 54 degree, ?3 = 64 degree, m1 = 3 kg, and m2 = 8 kg.

Figure P4.24 shows loads hanging from the ceiling of an elevator that is moving at constant velocity. Find the tension in each of the three strands of cord supporting each load, given that ?1 = 36°, ?2 = 54°, ?3 = 64°, m1 = 3 kg, and m2 = 8 kg.

Answer 1

Solution: Part A: sin 54 Tsin 36 54 36° 36° 54° 11 cos 36" : cos 54° mi,8 Applying Newton's Second law of motion, Vertical components: T2 sin 54° +T sin 36°-730 T sin 54°+7 sin 36°mg 3x9.8-294N

Substitute, m 3kg and g-9.8 in equation (1) T2 sin 54°+T sin 36°-3x9.8 7, (0.809)+1 (0.587) = 29.4 0.809 0.5871 -29.4 Horizontal components 11 cos 36" = T2 cos 54° cos 36° (0.587) 1- (0.809 T-0725T Substitute, Ti -0.725T, in equation (2) 0.809, 0.587 (0.7255) = 29.4 0.809 +0.42517 -29.4 1.2347 29.4 29.4 1.234 T -23.824N Therefore, =0.725(23.824) 17.27N 17.27N Thus, the tensionT2 -23.824N T,-29.4N

Part B: Tsin 64 64 64 cos64 M1,8

Applying Newton's second law of motion, ertical components T sin 64°-mg Substitute, m2 - 8kg and g-9.8 in equation (3) I sin 64° 8x9.8 8x9.8 sin 64° T,- 87.22 Horizontal components T2 -T cos 64° T,-0.438T Therefore, T2 0.438x87.22 T, -38.202N T-8x9.8 T-784M T, =87 22 N Thus, the tension|T2-38.202AN T, = 78.4 N