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A weight of 100 pounds is suspended by two ropes as shown in the accompanying figure. What are the magnitudes of the forces in each of the ropes?

Short Answer

Expert verified

a

Step by step solution

01

Introduction:

  • Consider a 100-pound weight hanging by two ropes.
  • The goal is to determine the force magnitude in each rope.
02

Given Information:

The below given figure shows the weight of 100 pounds suspended by two ropes.

  • Because the weight is stationary, the total of the three vectors is zero.
  • As a result, u+v+w=0.
  • Consider that motion to the right is positive on the x-axis, and upward motion is positive on the y-axis.
  • Decompose each vector into horizontal and vertical components at this point.
03

Explanation

  • Horizontal and vertical components are separated.
  • u=-cos45°ui+sin45°uj
  • v=cos30°vi+sin30°vj
  • w=-100j
04

Explanation

  • u=-12ui+12uj
  • v=32vi+12vj(3)
  • w=-100j(4)
05

Explanation

Using (1), u+v+w=0

As a result

u+v+w=-12ui+12uj+32vi+12vj-100j

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