# Drop height to acheive known deflection in a beam

A .5m long beam with 29N-m stiffness is attached to a 45kg weight. The beam is inclined 30 degrees from vertical. Assume the beam has no mass, assume the 45kg weight is "sliding" down a vertical pole of infinite stiffness and zero friction.

The mass is dropped and the end of the beam deflects .095m when it contacts the ground.

At what height must the Beam be dropped from to create this deflection? Please arrange the equations so the mass and the beam angle can easily be changed as variables.

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#### Solution Preview

Something is not clear for me in the data you gave, as you have not given the details of the cross-section of the beam.

I shall assume that by "29N-m stiffness" you actually mean the stiffness factor EI = 29 N m^2, according to definitions I found at this web page:

http://darkwing.uoregon.edu/~struct/courseware/461/461_lectures/461_lecture40/461_lecture40.html

However in this case this number is clearly TOO SMALL as I find below.

I can offer you a solution as a formula into which you can substitute the correct numbers or definitions if you find them (one possibility: EI may be 29 KN m^2 = 29000 N m^2 - that is the letter K was lost somewhere).

I shall also assume that the deflection is defined as the shift of the end of the beam in the direction perpendicular ...

#### Solution Summary

The expert drop the height to achieve known deflection in a beam.The infinite stiffness with zero friction is determined.