Question

o Show work clearly and logical manner to get maximum credit, additional 10 points: A large and uniform, 173-kg and 18.3 m long utility pole is supported by a rope that is tied at a distance of x= 2.9 m from the top end. The rope is horizontal and the pole makes an angle of = 40 degrees above the horizontal. The lower end of the pole rests on the floor. a) Draw a free-body diagram b) What is the tension in the rope? Hint: choose the axis of rotation at the lower end of the pole. c) What is the x-component of the force that the floor exerts on the pole? d) What is the y-component of the force that the floo exerts on the pole?

Answer 1

Assuming T,f and R to be the tension, frictional force and normal reaction.

a)

T - x R mg o f

Now balancing the forces in horizontal and vertical directions we get;

T = f ................(i)

R = mg ...............(ii)

Now balancing the torque about the lower end of the rope;

mgLcos$\theta$/2 = T(L-x)sin$\theta$

b) Using the data given we have;

T = (173kg x 9.8m/s² x 18.3m x cos40 x 0.5)/((18.3 - 2.9)m x sin40)

=> T = 1200.5 N

Thus tension in rope is 1200.5N

c) And from equation (i) ;

f = 1200.5N

which is the x component of the force that floor exerts on pole.

d) and from equation (ii)

R = 173kg x 9.8m/s² = 1695.4 N

which is the y component of the force that floor exerts on pole.