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A scaffold of mass 40 kg and length 4.5 m is supported in a horizontal position by one vertical cable at each end. A window washer of mass 86 kg stands at a point 1.1 m from one end. What is the tension in the cable?

Respuesta :

Answer:

[tex]R_A=402.018\ N[/tex]

[tex]R_B=832.782\ N[/tex]

Explanation:

Given:

  • mass of scaffold, [tex]m_s=40\ kg[/tex]
  • length of scaffold, [tex]l=4.5\ m[/tex]
  • point mass of window washer, [tex]m=86\ kg[/tex]
  • distance of point mass from one end, [tex]d=1.1\ m[/tex]

Here we consider the mass of the beam as uniformly distributed load concentrated at mid-span.

Using the schematic diagram:

Balancing forces:

[tex]\sum F=0[/tex]

[tex]R_A+R_B=(40+86)\times 9.8[/tex] ..............................(1)

Balancing moment about point A:

[tex]\sum M_A=0[/tex]

[tex]4.5\times R_B=9.8\times (86\times 3.4+40\times \frac{4.5}{2})[/tex]

[tex]R_B=832.782\ N[/tex] ......................................(2)

Putting value from eq. (2) into eq. (1)

[tex]R_A+832.782=1234.8\ N[/tex]

[tex]R_A=402.018\ N[/tex]

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