Question
Please show your work.
Questions 278-281 refer to the diagram below. Which of the following must be true of magnitudes of the tensions given in the diagram? T 1 > T 2 T 2 > T 1 T 1 = T 2 T 3 = T 1 + T 2 If m = 10 kg, theta 1 = 60 degree and theta 2 = 30 degree, the tension T 3 is: 50 N 100 N 137N 237 N If m = 10 kg, theta 1 = 60 degree and theta 2 = 30 degree, the tension T 2 is: 50 N 59 N 100 N The tension T 2 depends upon the length of T 2. If m = 100 kg, theta 1 = 30 degree and theta 2 = 30 degree, the tension T 1 is: 500 N 866 N 1000 N 1732 N
Explanation / Answer
From figure T1 sin1 + T2 sin 2 = T3 and T3 = mg (1). m= 10 kg So, T3 = 10 *10 where g = 10 m / s^ 2 = 100 N And given 1 = 60 degrees 2 = 30 degrees (2).T1 sin 60 +T2 sin 30 = 100 0.866 T1 + 0.5 T2 = 100 -------( 1) Also from figure , T1 cos 60 = T2 cos 30 0.5 T1 = 0.866 T2 T1 = 1.732 T2 ----( 2) subsitute eq( 2) in eq( 1) we get 0.866 x 1.732 T2 +0.5 T2 = 100 1.5 T2 + 0.5 T2 = 100 T2 = 50 N (3). 1 = 30 degrees 2 = 30 degrees m = 100 kg T3 = mg = 100* 10 = 1000 N T1 sin 30 +T2 sin 30 = 1000 0.5 T1 + 0.5 T2 = 1000 T1 + T2 = 2000 -------( 1) Also from figure , T1 cos 30 = T2 cos 30 T1 = T2 ----( 2) subsitute eq( 2) in eq( 1) we get 2T1 = 2000 N T1 = 1000 N 2 = 30 degrees m = 100 kg T3 = mg = 100* 10 = 1000 N T1 sin 30 +T2 sin 30 = 1000 0.5 T1 + 0.5 T2 = 1000 T1 + T2 = 2000 -------( 1) Also from figure , T1 cos 30 = T2 cos 30 T1 = T2 ----( 2) subsitute eq( 2) in eq( 1) we get 2T1 = 2000 N T1 = 1000 N 0.5 T1 + 0.5 T2 = 1000 T1 + T2 = 2000 -------( 1) Also from figure , T1 cos 30 = T2 cos 30 T1 = T2 ----( 2) subsitute eq( 2) in eq( 1) we get 2T1 = 2000 N T1 = 1000 N