Question

Could someone check if I did this correctly? I also need help with f, g and h.

1. You are decorating your bedroom and want to hang your new 5kg framed poster of Isaac Newton in an artistic manner, as a nod to his beautiful laws of motion. You attach 3 strings in the configuration shown below. You need to determine the magnitude and direction of the force a 4th string attached at the remaining hook would need to exert to keep the poster in equilibrium. 250 T,-60N T1 50N 40° hook where 4th T3-30N string will be attached a) Draw your first free body diagram in the box on the left, showing ALL the forces acting on the poster with their respective an (include the unknown force of the 4th string and define the angle it makes with the horizontal). You can assume that all of these strings are pulling on the poster (not pushing). FBD #1 FBD #2 FT 4 Fixi Fre T4 x

Answer 1

Part A and C)

Part A and C) Part D and E) Using equilibrium along x axis as the system is at rest net must be zero. sigma F_x = 0 38.3N - 25.36N - 30N + T_4, x = 0 T_4, x = 17.06 N Part F and G) sigma F_y = 32.14N + 54.38N - 49N + T_4, y = 0 T_4, y = -37.52N T_4 = squareroot T^2_4, x + T^2_4, y = squareroot (17.06 N)^2 + (-37.52 N)^2 = 41.22 N Angle theta = tan^-1 (17.06/-37.52) = 335.55 degree with +x axis or theta = tan^-1 (17.6/37.52) = 24.45 degree with -ve Y axis.

Part B)

Part D and E) Using equilibrium along x axis as the system is at rest net must be zero.

$\sum F_{x} = 0$

$38.3 N - 25.36 N - 30 N + T_{4,x} = 0$

$T_{4,x} = 17.06 N$

Part F and G)

$\sum F_{y} = 32.14 N + 54.38 N - 49 N + T_{4,y} = 0$

$T_{4,y} = -37.52 N$

Part H)

$T_{4}= \sqrt{T_{4,x}^{2}+ T_{4,y}^{2}} = \sqrt{(17.06 N)^{2}+(-37.52 N)^{2}} = 41.22 N$

Angle

$\theta = \tan^{-1}\left ( \frac{17.06}{-37.52} \right )= 335.55^{0}$  with + x axis or

$\theta = \tan^{-1}\left ( \frac{17.06}{37.52} \right )=24.45^{0}$  with -ve Y axis.