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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

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 class=

Answer :

calculista

Answer:

w = 73 N

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

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