A box is hanging from two strings. String #1 pulls up and left, making an angle of 50° with the horizontal on the left, and string #2 pulls up and to the right with a force of 30 N, making an angle of 75° with the horizontal on the right.

1. FInd the mass of the box.

Hint: Apply ΣFx = 0 and ΣFy = 0

mb = 3.75 kg

Explanation:

System of forces in balance

ΣFx = 0

ΣFy = 0

Forces acting on the box

T₁ : Tension in string 1, at angle of 50° with the horizontal on the left

T₂ = 40 N : Tension in string 2, at angle of 75° with the horizontal on the right.

Wb : Weightt of the box (vertical downward)

x-y T₁ and T₂ components

T₁x = T₁cos50°

T₁y = T₁sin50°

T₂x = 30*cos75° = 7.76 N

T₂y = 30*sin75° = 28.98 N

Calculation of the Wb

ΣFx = 0

T₂x-T₁x = 0

T₂x=T₁x

7.76 = T₁cos50°

T₁ = 7.76 / cos50° = 12.07 N

ΣFy = 0

T₂y+T₁y-Wb = 0

28.98 + 12.07 (cos50°) = Wb

Wb = 36.74 N

Calculation of the mb (mass of the box)

Wb = mb * g

g: acceleration due to gravity = 9.8 m/s²

mb = Wb/g

mb = 36.74 / 9.8

mb = 3.75 kg