Newton's second law:

$\overline{){\mathbf{F}}{\mathbf{=}}{\mathbf{m}}{\mathbf{a}}}$

**(a)**

Let the x-axis pint to the left and the y-axis upward.

The weight points downwards.

The component of the tension, F_{Ty}, points opposite to the weight, thus making the adjacent side.

cos θ = adjacent/hypotenuse = F_{Ty}/F_{T}

F_{Ty} = F_{T} cos θ

(A) A 20-kg loudspeaker is suspended 2.0 m below the ceiling by two ropes that are each 30° from vertical.

Find the value of *T*, the magnitude of the tension in either of the ropes.

Express your answer in newtons.

T=

(B) Suppose that the loudspeaker in the problem had a mass of 500 kg and the ropes hung 20° from the vertical. Into which of the following intervals would you expect *T* to fall? You do not have to calculate *T *exactly to answer this question; just make an estimate.

a) 500 to 1000 N

b) 1000 to 2000 N

c) 2000 to 4000 N

d) 4000 to 8000 N

e) 8000 to 16,000 N

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Forces in 2D concept. You can view video lessons to learn Forces in 2D. Or if you need more Forces in 2D practice, you can also practice Forces in 2D practice problems.