A new coffee shop is opening in your neighborhood. The owners have ordered a lar

Question

A new coffee shop is opening in your neighborhood. The owners have ordered a large sign that will hang outside of the shop. The sign will consist of a giant, 10 kg coffee mug that will hang vertically downward from the end of a narrow, horizontal steel beam that sticks out a distance of 2 m from the shop. The 5 kg beam is supported by a wire that is attached to the shop wall on one end, and the far end of the beam on the other, making an angle of 30° from the horizontal. The owners want to know how strong the wire has to be to support the sign. PLEASE USE DETAILS

Explanation / Answer

here,

mass of giant , m = 10 kg

length of beam , l = 2 m

mass of beam , mb = 5 kg

theta = 30 degree

let the tension in the wire be t

taking moment of force about the pivot point

t * sin(theta) * l - mb * g * l/2 - m * g * l = 0

t * sin(30) * 5 - 5 * 9.8 * 2.5 - 10 * 9.8 * 5 = 0

t = 245 N

the wire should can withstand for tension of 245 N

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