find the resultant force F and sag \"s\" https://session.mastering engineering.c

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find the resultant force F and sag "s" https://session.mastering engineering.com/myct/itemView?assignment ProblemID-407 ENGR 2210 Fall 2015 Chapter 3HW Signed in as George Fournier Help : Problem 3.31 Resources « previous 5 of 8 I nex Problem 3.31 Part A Blocks D and E have a mass of 4 kg and 7 kg , respectively. Take z-2 mFigure!) Determine the magnitude of the force F Express your answer to three significant figures and include the appropriate units. FValue N 6 m Submit Incorrect; Try Again; 2 atte remaining Part B Determine the sag s for Express your answer to three significant figures and

Explanation / Answer

given,

mass of D and E = 4 kg and 7 kg

in equalibrium

sum of horizontal force = 0 and

sum of vertical force = 0

so,

tension on the left rope

T_left = mass of D * g

T_left = 4 * 9.8

T_left = 39.2 N

tension on the right rope

T_right = mass of E * g

T_right = 7 * 9.8

T_right = 68.6 N

let tha angle left rope is making with vertical at F be theta

let tha angle roght rope is making with vertical at F be phi

horizontal forces

T_left * sin(theta) = T_right * sin(phi)

39.2 * sin(theta) = 68.6 * sin(phi)

vertical forces

39.2 * cos(theta) + 68.6 * cos(phi) = F

sin(theta) = (6 - x) / sqrt((6 - x)^2 + s^2)

cos(theta) = s / sqrt((6 - x)^2 + s^2)

sin(phi) = x / sqrt(x^2 + s^2)

cos(phi) = s / sqrt(x^2 + s^2)

putting the values

39.2 * ((6 - x) / sqrt((6 - x)^2 + s^2)) = 68.6 * (x / sqrt(x^2 + s^2))

39.2 * (s / sqrt((6 - x)^2 + s^2)) + 68.6 * (s / sqrt(x^2 + s^2)) = F

since x = 2

so

39.2 * ((6 - 2) / sqrt((6 - 2)^2 + s^2)) = 68.6 * (2 / sqrt(2^2 + s^2))

39.2 * (s / sqrt((6 - 2)^2 + s^2)) + 68.6 * (s / sqrt(2^2 + s^2)) = F

on solving we'll get

F = 97.5088 N

s = 5.93296 m

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