Find Tension in Ropes Supporting a 6m Uniform Plank w/ 300N Weight

[kubombelar]

hey guys i nid help with this problem: A uniform plank AB is 6m long and has a weight of 300N,
it is supported horizontally at its ends by two vertical ropes. A weight of 50N rests on the plank at C where AC is 2m. Find the tension in each rope. THANKS

 

[HallsofIvy]

hey guys i nid help with this problem: A uniform plank AB is 6m long and has a weight of 300N,
it is supported horizontally at its ends by two vertical ropes. A weight of 50N rests on the plank at C where AC is 2m. Find the tension in each rope. THANKS

Have you done nothing on this yourself? Surely you know that you are expected to show what you have tried and where you got stuck.
To start you off:
Let T_A and T_B be the tensions in the ropes at end A and B respectively.

Now there are 3 forces acting on the plank, the two forces at A and B and the weight of the plank which we can take to be concentrated at the center. There are two "laws" here- since the plank is not moving up or down, the total vertical force must be 0. Since the plank is not rotating, the total torque must be 0. It is probably simplest to calculate the torques due to the three forces about point A and set their sum equal to 0. Remember that the torque at point A, due to force F acting at distance d from A, measured perpendicularly to the force vector, is Fd. Here, since all forces act vertically, that just means "measured horizontally".

 

[kubombelar]

ok i tried my best. Since the question focuses on equilibrium,we can see that the downward 300N has to balanced by an equal upward force in order to be in equilibrium. so for the first rope i multiplied the 2m by 50which gave me 100N. Which leaves me with the other rope which the weight on it was not specifed. So i presumed it to be 50N. I multiplied it by 4 which gave me 200N. So for the upward forces i added them which gave me 300N which was equal to the downward 300N. Thus the plank was now in equilibrium. Am i correct?