How can I calculate the tension force?

[elleo]

Homework Statement

Find the tension force that the rope is doing to the bridge (see attached image)

Relevant Equations

T=mg
I don´t know if others apply

This is my attemp of solution:

Since the formula to calculate the tension is T=mg
I first calcualted the weight of the bridge with the ecuation
W= mg m=W/g
m= 18,000 N / 9.81 m/s
m= 1834 kg

So T=(1834)(9.81)= 17,991 N

But this seems no logical to me because the Tension force is a bit less than the weight force of the bridge, I think it should de more

 

[haruspex]

the formula to calculate the tension is T=mg

That would only be for the simple case of a mass hanging statically and vertically, with no other support for the mass.
The diagram is unclear without more explanation. Is it a uniform load of 3kN/m (in which case, the arrows are showing torque about the joint)?

There is a standard procedure for solving just about any 2D mechanics problem:
- pick a rigid component;
- consider the sum of forces and resulting acceleration (ΣF=ma) in each of two directions, usually at right angles;
- pick an axis and consider the sum of torques and resulting acceleration (Στ=Iα) about the axis.
Since this is a statics question, a=α=0.

 

[elleo]

Yes, it’s a uniform 3 KN/m
And the diagram doesn’t give the angle between the bridge and the wall, so I don’t know if it’s possible to calculate the resulting force

 

[gneill]

Pretty sure you should assume that the angle between the bridge and wall is 90°. If in doubt, specify your assumption in your submitted answer. If the problem statement leaves out critical information, it's your choice to specify your assumptions. Markers can't (well, shouldn't) penalize for missing information.

 

[Orodruin]

Yes, it’s a uniform 3 KN/m

Please submit the entire actual problem statement. Arrows in that form generally means a linearly increasing load, not a uniform load unless what is shown is the resulting torque at each point (which would be incompatible with the 3 kN/m quoted at the end).

 

[Herman Trivilino]

m= 18,000 N / 9.81 m/s
m= 1834 kg

So T=(1834)(9.81)= 17,991

Don't you see that you've just gone in a circle? You took 18 000 N, divided it by $g$, and then multiplied the result by $g$. Apart from the round-off error, you end up with exactly what you started with, 18 000 N.

Can you draw a free-body diagram of the beam and then use the 1st and 2nd conditions for equilibrium to set up your equations? Hint, $T=mg$ will not be one of those equations. And your intuition that $T$ should be greater than the magnitude of the weight force is correct. Note that the magnitude of the weight force is $mg$.