Please fine the mass of the shirt hanging on the line shown below

Question

Left side of clothes line: Ft=20N and the angle it makes with the shirt is 18 degree. Right side of clothes line: Ft=22.7N and the angle it makes with the shirt is 33 degrees. The mass of the shirt is unknown.

Answer 1

 

This problem is solved by resolving the two sides of the clothes line into two right triangles.

Since the T-shirt is in equilibrium, or not moving, we can say that the net force on the T-shirt is equal to zero. That means that the sum of the vertical forces (up/down) that act on the T-shirt is zero. And the sum of the horizontal forces (left/right) is equal to zero. 

The left side triangle has a hypotenuse with a value of 20N. The right side triangle has a hypotenuse with a value of 22.7N. Each triangle will have a vertical force component and a horizontal force component. The horizontal components do not support the weight of the T-shirt. The horizontal components stabilize the position of the T-shirt in the left and right directions. The sum of the vertical components of each triangle must be equal to the weight of the T-shirt in order to support it on the clothes line. By using SOHCAHTOA, we can find the value of the vertical components and thus the weight of the T-shirt. We can then use w = mg to find the mass of the T-shirt.

GIVEN:

F_1T = 20 N

θ₁ = 18°

F_2T = 22.7

θ₂ = 33°

 

UNKNOWN:

Vertical components of F_1T and F_2T

F_1yT = ?

F_{2yT = ?}

Weight of the t-shirt = (F_1yt + F_2yT) = ?

m = ? mass of the t-shirt

 

EQUATIONS:

SOHCAHTOA

 

sinθ = (O/H) where O = vertical component (F_yT) of the line's tension and H = the hypotenuse or tension (F_T) in the clothes line.

Thus the vertical component equations for triangle1 and triangle2 are:

F_1yT = (F_1T • sinθ)

F_2yT = (F_2T • sinθ)

Weight of the t-shirt = F_1yT + F_2yT

m = W/g

 

SOLUTION:

 

F_1yT = (20 N • sin 18°) = 6.18 N

F_2yT = (22.7 N • sin 33°) = 12.36 N

Weight of the t-shirt = 6.18 N + 12.36 N = 18.54 N

m = (18.54 N / 9.81 m/s²) = 1.89 kg, which is the mass of the t-shirt. Which is about 4 lbs. That may mean it is wet since few or no t-shirts weigh 4 lbs.

 

P.S. I tried to copy/paste a free body diagram of the problem. It did not work. Sorry :((