One end of a uniform 4.30-m-long rod of weight F g is supported by a cable at an

Question

One end of a uniform 4.30-m-long rod of weight Fg is supported by a cable at an angle of ? = 37

One end of a uniform 4.30-m-long rod of weight Fg is supported by a cable at an angle of ? = 37A with the rod. The other end rests against the wall, where it is held by friction as shown in the figure below. The coefficient of static friction between the wall and the rod is ?s = 0.545. Determine the minimum distance x from point A at which an additional object, also with the same weightFg, can be hung without causing the rod to slip at point A You will need to work with the equations vector TAu net = 0 and manipulate the equations symbolically to solve for the distance. m vectopr F net = 0 and

Explanation / Answer

along horzantal

N - T*cos? = 0

N = T*cos?

frictional force f = u*N = u*T*cos?

along vertical

Fnety = 0

f + T*sin? = Fg + Fg = 2Fg

u*T*cos? + T*sin? = 2Fg

u*T*cos? + T*sin? = 2Fg

T = Fg / (u*cos? + sin?)

net torque = 0

Fg*(L/2) + Fg*x = T*sin? *L = Fg*sin?*L / (u*cos? + sin?)

(L/2) + x = sin?*L / (u*cos? + sin?)

x = sin?*L / (u*cos? + sin?) - L/2

x = sin37*4.3 / (0.545*cos37 + sin37) - 2.15

2.15 + x = 2.505

x = 0.345m = 34.5 cm

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