What is the tension in the rope? And the horizontal and vertical forces exerted by the pivot?

Question

A uniform board of length 2.4m and mass 4kg is pivoted at one end and has a rope attached at the other end, as shown in Fig. 12.56. A bucket of mass 2kg is suspended 40cm from the rope.

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Answer 1 · 2018-04-23T00:41:37

Tension : 26.8 N
Vertical component : 46.6 N
Horizontal component : 23.2 N

Let the vertical and horizontal components of the force exerted on the bar at the pivot be #V# and #H#, respectively.

For the bar to be in equilibrium, the net force and the net torque on it must be zero.

The net torque must vanish about any point. For convenience we take the net moment about the pivot, leading to (here we have taken #g=10" ms"^-2#)

# T times 2.4" m" times sin75^circ = 40" N"times 1.2" m"times sin45^circ#
#qquad qquad qquad +20" N" times "2 m" times sin45^circ implies#

#color(red)(T = 26.8" N")#

For the vertical component of the net force to vanish, we have

#Tcos 60^circ+V = (4+2)" Kg"times 10" ms"^-2 = 60" N" implies#

#color(red)(V =46.6" N" )#

For the horizontal component of the net force to vanish, we have

#Tsin60^circ = H implies#

#color(red)(H =23.2" N") #