Calculate the tension of the rope.?

Question

A painter is going to use a board for support during a painting job. The board has a weight of 175N and the painter has a weight of 815N. THe left end of the board is supported by a sawhorse and the right end by a lightweight rope attached to an overhead bracket. The overall length of the board is 3.60m. When the painter stands at a distance of 2.70m from the left end of the board, calculate the tension on the rope. Express the result in N.

I'm sorry to sound dense, but what does R stand for?

I would give you a vote if I could vote, but thank you very much! I was so confused as what to do. Thanks for the clarification.

Answer 1

Sum of y forces
T + R= Wp + Wb
T- tension in the rope
R- reaction at the sawhorse
Wp - weight of the painter
Wb - weight of the board

Moment about sawhorse support
R1Wp + R2Wb - LT=0
R1= 3.6 -2.7=0.9m
R2= 3.6/2= 1.8m
L=3.6m

T= (R1Wp + R2Wb )/L
T= (0.9 x 815 + 1.8 x 175)/3.6
T=290 N

Gee we did not even need the Sum of y unless you want to find the sawhorse reaction.

Have fun

Answer 2

Well, we know that if the man were standing in the middle the weight would be 990N in the middle. So half of the weight would be distributed on both sides equally and it would be 495N on both sides. All this tells us is that our answer had better be larger than 495N...since he is closer to the rope.

Now lets begin. The equation I will use are torque equations.

Tb = Torque from weight of board
Tp = Torque from painter
Tt = Torque from the upward tension in the rope.
x = length of board

SInce the rope supports both the man and the weight of the board..we know

Tt = Tb + Tp

The key here is that we have to treat the board as if the weight were concentrated at the center. so that Tb = x/2 * Fb
where Fb is the force downward from the board and x/2 is half the length of the board.

writing out the full equivalent to (Tt) = (Tb) + (Tp) remebering that torque is the length multiplied by the perpendicular force we have:

(x*T) = (x/2*Fb) + (2.7/3.6 * Fm)
Fm = weight of man and T = tension in rope

The ration 2.7/3.6 comes from the fact that
x = 3.6 , x/2 = 1.8 , so x*y = 2.7 (the man stands 2.7m out..and 2.7 is in some ration to the full lenght x. So an equation for this would be "something multiplied by x gives your 2.7m..well we know x is 3.6m..so to get y divide 2.7 by 3.6)

Solving for T you will get a value of 698.75 N pulling up

Answer 3

first artwork out the quantity of the buoy, using (4 x pi x (0.25cubed))/3 then you definately ought to artwork out the mass of the water that should fill this volume, so multiply the quantity via 1020. understanding the most of the two the buoy and the water of the same volume. locate the version, in kg. multiply this distinction via 9.80 one(the acceleration by using gravity) this provides the upward rigidity. to fing the rigidity you subtract the burden (35 x 9.80 one) from the upward rigidity