Halliday, Fundamentals of Physics, 10e ment PRINTER VERSION .BACK NEXT Chapter 1

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Halliday, Fundamentals of Physics, 10e ment PRINTER VERSION .BACK NEXT Chapter 12, Problem 015 Forces F1, F2, and F3 act on the structure of the figure, shown in an overhead view. We wish to put the structure in equilibrium by applying a fourth force, at a point such as P. The fourth force has vector components h and Fv.We are given that a 2.72 m, b 366 m. c- 1.31 m, Fi 46.7N, Fi 10.4 N, and Fr 4.10 N. Find (a) magnitude of Fin (b) magnitude of Fn and (c) d. (a) Number (b) Number (c) Number click if you would like to show work for this question: open Show work

Explanation / Answer

a)

taking forces towards right as positive and forces towards left as negative,

force equation along the horizontal direction is given as

Fh + (- F3) = 0

Fh = F3

Fh = 4.10 N

b)

taking forces towards up as positive and forces towards down as negative,

force equation along the vertical direction is given as

- Fv + F1 + F2 = 0

Fv = F1 + F2

Fv = 46.7 + 10.4

Fv = 57.1 N

c)

taking clockwise torque as negative and counterclocwise torque as positive

using equilibrium of torque about O

- F1 (0) Sin90 + Fv (OP) Sin90 + Fh (OP) Sin0 - F2 (b) Sin90 - F3 (a) Sin90 = 0

- F1 (0) Sin90 + (57.1)(d) + 0 - (10.4)(3.66) Sin90 - (4.10)(2.72) Sin90 = 0

d = 0.862 m

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