Question

A weight, with mass M_w = 26kg hangs x= 2.0m from the end of an L= 6.0m beam. The beam itself has mass M_B = 88kg and is supported by ropes at each end. Find the values of the two tensions, T_L and T_R.

Please show all steps, even the most basic ones. Thank you!

Answer 1

tension in the left rope is TL and tension in right rope be TR.

let both the tension are in vertically upward direction.

other forces acting on the beam area:

weight of hanging mass=26*9.8=254.8 N, in vertically downward direction

weight of the beam=88*9.8=862.4 N, in vertically downward direction

let left end be x=0

then TL is acting at x=0

TR is acting at x=6 m

hanging mass weight is acting at x=2 m

weight of the beam is acting at x=6/2=3 m

balancing forces in vertical direction:

TL+TR=254.8+862.4=1117.2 N...(1)

balancing torque about x=0:

254.8*2+862.4*3=TR*6

==>TR=(254.8*2+862.4*3)/6=516.13 N

then TL=1117.2-516.13=601.07 N