Question

A uniform rod 120 N beam with length 12 m (ignore length in tin the picture below) is supported in a horizontal position by a pin and cable at 37 degrees as shown in the figure. What is the magnitude of the normal exerted by the pin on the beam? 70 N 75 N 60 N 80 N 120 N

Answer 1

Ty ARy 37° Ry Tx In 120 N

Using translational equilibrium

$R_{ x} - T_{x} = 0 N \Rightarrow R_{x} = T_{x}$

Using rotational equilibrium about the pin

$T_{y}\times 12 m - 120 N\times 6 m = 0$

$T\cos 37^{0}\times 12 m - 120 N\times 6 m = 0$

$T =\frac{120 N\times 6 m }{\cos 37^{0}\times 12 m}= 75N$

Now

$R_{y} =120 N - 75 N\times \cos 37^{0} = 60 N$

$R_{x} = T\sin 37^{0} = 75 N \times \sin 37^{0} = 45 N$

Net reaction at the pin

$R = \sqrt{R^{2}_{x}+R^{2}_{y}} = \sqrt{ (45 N)^{2}+(60N)^{2}}= 75 N$