Suppose mass (m = 887 g) hanging in the middle divides the string (length L = 59

Question

Suppose mass (m = 887 g) hanging in the middle divides the string (length L = 59.2 cm) exactly in half (and the tension in the two strings are the same), and the distance between the ends of the string (on top) is 45.1 cm, Find the magnitude of the tension in either string. T= N Suppose now that slides to the left (so string 1 is shortened and string 2 is lengthened). What happens to the magnitude of the tension in the strings? T_1 increase, T_2 increases T_1 increases, T_2 decreases T_1 decreases, T_2 decreases T_1 remains the same, T_2 remains the same T_1 decreases, T_2 remains the same T_1 remains the same, T_2 increases T_1 decreases, T_2 increases T_1 increases, T_2 remains the same T_1 remains the same, T_2 decreases Starting again with m in the middle, you now perform two trials: Trial 1: The system is accelerated upward at constant a Trial 2: The system is accelerated to the right at constant a. Which statement is true of the tensions in the strings? In both trials T_1 decreases, in both trials T_2 increases Trial 1: both tensions increase; trial 2: T_1 decreases, T_2 increases Trial 1: both tensions decrease; trial 2: Ti increases, T_2 decreases Trial 1: both tensions decrease; trial 2: T_1 decreases, T_2increases In both trials T_1 increases, in both trials T_2 decreases Trial 1: both tensions increase; trial 2: T_1 increases, T_2 decreases

Explanation / Answer

let the angle string makes with horizontal be theta

so,

45.1 = 2 * (59.2 * cos(theta)/2)

theta = 40.37 degree

since the system is in equilibrium so

net vertical force will be 0

mg - 2 * T * sin(theta) = 0

0.887 * 9.8 = 2 * T * sin(40.37)

T = 6.71 N

if mass slides to the left then angle left string will make with the horizontal will increase and anfle right string will make with horizontal will decrease so

T1 will increase and T2 will decrease

if the system will accelerated upward net downward force will increase so

both T1 and T2 will increase

if the system will accelerated right

T1 will decrease and T2 will increase

so,

Trial 1: both tension increase; trial 2: T1 decrease, T2 increase

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