Solved: A block of weight W is dropped from a height h

Chapter 11, Problem 11.57

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A block of weight W is dropped from a height h onto the horizontal beam AB and hits point D. (a) Denoting by \(y_{m}\) the exact value of the maximum deflection at D and by \(y_{m}^{\prime}\) the value obtained by neglecting the effect of this deflection on the change in potential energy of the block, show that the absolute value of the relative error is \(\left(y_{m}^{\prime}-y_{m}\right) / y_{m}\), never exceeding \(y_{m}^{\prime} / 2 h\). (b) Check the result obtained in part a by solving part a of Prob. 11.52 without taking \(y_{m}\) into account when determining the change in potential energy of the load, and comparing the answer obtained in this way with the exact answer to that problem.

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