## Problem 3: A 1.84 kg school bag hangs in the middle of a clothesline (طناب), causing it to sag (dip) by an angle θ = 3.50°. Find the tension, T in the clothesline.

Solution

Theory: This is a problem of equilibrium. The bag is in equilibrium under the action of tensions (forces) on both sides of the string and weight of the bag. Weight of the bag act vertically down. Resolve the tensions in vertical and horizontal components and apply condition of equilibrium to find T on both sides of the clothesline.

Given

Mass of the bag = 1.84 kg ⇒ Weight of the bag = 1.84 × 9.8 = 18.032 N
Sagging (or bending) angle, θ = 3.50°

Required             Tension T in the string.

Resolve tensions T1 and T2 in rectangular components along vertical and horizontal directions.

Apply first condition of equilibrium,

Now put T2 = T1 in equation (A),

From equation (B), T1 = T2, therefore, tensions on both sides of the string are approximately 148 N.

 Engage

WHAT IF THE BAG WAS NOT HUNG IN THE CENTER OF THE CLOTHESLINE?
(1) WOULD THE SAGGING ANGLE BE SAME ON BOTH ENDS OF THE STRING? (NO)
(2) WOULD THE TENSIONS IN THE STRING ON BOTH SIDES OF THE BAG BE EQUAL? (NO, BECAUSE IT DEPENDS ON THE ANGLE.).
(3) HOW MANY EQUATIONS WOULD WE NEED TO FIND TENSIONS ON BOTH SIDES OF THE BAG? (2, WHY?)