Question

A box is held at rest by two ropes that form 30° angles with the vertical. The tension T in either rope is 42 N. What is the weight (w) of the box?

73 N

36 N

79 N

86 N

62 N

Answer 1

w = 73 N

Step-by-step explanation:

Since the box is held by the ropes it means that the resulting tension is equal to the weight of the box

T_res = w

Now, the resulting tension is a combination of the tension of each rope.

Since we want to find the vertical component we must multiply by the cosine of 30 degrees the value of T

T_res = T*cos(30) + T*cos(30)

T_res = 2*(42 N)*(0.866)

T_res = 72.746 N

T_res = w = 72.746 N