If $\alpha$ = 40$\degree$,$\beta$ = 60$\degree$,and M = 4.0 kg,determine the tension in string 1.
A)15 N
B)22 N
C)17 N
D)20 N
E)36 N

Question

If $\alpha$ = 40$\degree$,$\beta$ = 60$\degree$,and M = 4.0 kg,determine the tension in string 1. 
A)15 N 
B)22 N 
C)17 N 
D)20 N 
E)36 N

Quizplus · Accepted Answer

From the given equation, we can solve for the unknown tension in string 1:
F1F1F1S1F1F1F10 = 40F1F1F1S1F1F1F10  →  F1F1F1S1 = 40F1F1F10
F1F1F1S1F1F1F10 = 60F1F1F1S1F1F1F10  →  F1F1F1S1 = 60F1F1F10

Using the law of cosines, we can find the tension in string 1:
Mg = F1F1F1S1cos(60°) + F1F1F1S1cos(40°)
F1F1F1S1 = (Mg - F1F1F1S1cos(60°)) / cos(40°)

Substituting the given values, we get:
F1F1F1S1 = (4.0 kg)(9.81 m/s^2 - 60F1F1F10cos(60°)) / cos(40°)
F1F1F1S1 = 20.02 N ≈ 20 N

Therefore, the correct answer is D) 20 N.

If α\alphaα = 40 °\degree° β\betaβ = 60 °\degree° ,And M = 4

If $\alpha$ = 40 $\degree$ $\beta$ = 60 $\degree$ ,And M = 4