Moments Question: Plotting Distance Moved vs Resultant of A

[Energize]

Ok I have this question where there is a beam 12m long, there is a pivot 3m along the beam (A) and another 10m along the beam (B). There is an elephant at the left end of the beam that weighs 10,000N and the weight of the beam is 4000N, I need to plot a graph of the distance moved (m) against the resultant of A. Now I know how to get the resultant of A when the object is in between the 2 pivots, but how do I work out the resultant of A when the object is not in between the 2 pivots?

 

[radou]

What exactly do you mean by 'resultant of A'?

 

[Energize]

The force upwards against the beam at that pivot.

 

[radou]

The force upwards against the beam at that pivot.

If I made a correct sketch, the sum of moments around B should give: 4*4000 - 7*A + (10-x)*10000 = 0, so you can get the function A(x) from the equation.

 

[OlderDan]

Ok I have this question where there is a beam 12m long, there is a pivot 3m along the beam (A) and another 10m along the beam (B). There is an elephant at the left end of the beam that weighs 10,000N and the weight of the beam is 4000N, I need to plot a graph of the distance moved (m) against the resultant of A. Now I know how to get the resultant of A when the object is in between the 2 pivots, but how do I work out the resultant of A when the object is not in between the 2 pivots?

There are lots of ways to approach this, but one avoids some sign difficulties you may be having. If you calculate torque about the left end of the beam, the elephant's moment arm goes from 0 to12m with no sign changes, If you assume forces are up at A and B, then a negative force will indicate that the force is actually down. You really don't have to think about the elephant being between the supports or not. The elephant is always to the right of the left end.

 

[Energize]

There are lots of ways to approach this, but one avoids some sign difficulties you may be having. If you calculate torque about the left end of the beam, the elephant's moment arm goes from 0 to12m with no sign changes, If you assume forces are up at A and B, then a negative force will indicate that the force is actually down. You really don't have to think about the elephant being between the supports or not. The elephant is always to the right of the left end.

Sorry I don't understand. I need to move the elephant along the beam 1m at a time and calculate the resultant of A each time for my graph.

 

[civil_dude]

I can tell you this much. This is not a statics problem until the elephant is only 1.2 m left of A. When it is more than 1.2 m left of A, it becomes a kinetics problem.

 

[Energize]

I'm still confused as to how I have to work this out.

 

[OlderDan]

I can tell you this much. This is not a statics problem until the elephant is only 1.2 m left of A. When it is more than 1.2 m left of A, it becomes a kinetics problem.

I can see why you say that, but you are assuming RB has to be upward. There was no visible diagram when I replied, so I did not make that assumption. Thers is no reason why the support at B cannot apply a downward force. The problem says these points are pivots, implying that the beam could only rotate about these points. Since there are two such points, no rotation is possible.

 

[OlderDan]

I'm still confused as to how I have to work this out.

Now that your diagram is visible, it will be easy to follow your attempt at writing and solving the equations. Do what you can and post it.

Pick one point (I suggest the left end of the plank) and calculate all the moments assuming the elephant is a distance m from the left side. The sum of the moments must be zero. The sum of the forces acting (positve up and negative down) must be zero.

 

[civil_dude]

I can see why you say that, but you are assuming RB has to be upward. There was no visible diagram when I replied, so I did not make that assumption. Thers is no reason why the support at B cannot apply a downward force. The problem says these points are pivots, implying that the beam could only rotate about these points. Since there are two such points, no rotation is possible.

Dan you are correct, I did make the assumption that B could not supply a downward reaction.

Thanks for catching that.

 

[OlderDan]

Dan you are correct, I did make the assumption that B could not supply a downward reaction.

Thanks for catching that.

The elephant is the one who should be thankful for the catch