If M = 2.0 kg,what is the tension in string 1?
A)1.2 N
B)11 N
C)34 N
D)3.5 N
E)40 N

Question

If M = 2.0 kg,what is the tension in string 1? 
A)1.2 N 
B)11 N 
C)34 N 
D)3.5 N 
E)40 N

Quizplus · Accepted Answer

The tension in string 1 can be found by calculating the net force acting on the system in the vertical direction. Considering upward direction as positive,
T1 - M*g - T2*sin(30) = M*a
where a is the acceleration of the system, g is acceleration due to gravity, T2 is tension in the second string and sin(30) is due to the angle between string 2 and the horizontal. As the system is in equilibrium, a = 0. Therefore,
T1 = M*g + T2*sin(30)
Now, T2 can be found from the equation of torque about the hinge point,
T2*cos(30) * L = M*g * L/2
where L is the length of the horizontal bar. Solving this equation for T2,
T2 = M*g/2cos(30)
Substituting this value in the above equation for T1,
T1 = M*g + M*g/4 = 5M*g/4 = 5*2*9.81/4 = 34.26 N (approx). Therefore, the best choice is C (34 N).

If M = 20 Kg,what Is the Tension in String 1