Chapter P.1, Problem 17P

Bending Beams

If you bend a rod down, it compresses the lower side of the rod and stretches the top, resulting in a restoring force. Figure I.4 shows a

FIGURE 1.4

beam of length L, width w, and thickness t fixed at one end and free to move at the other. Deflecting the end of the beam causes a restoring force F at the end of the beam. The magnitude of the restoring force F depends on the dimensions of the beam, the Young’s modulus Y for the material, and the deflection d. For small values of the deflection, the restoring force is

$F=\left[\frac{Yw{t}^3}{4L^3}\right]d$

This is similar to the formula for the restoring force of a spring, with the quantity in brackets playing the role of the spring constant k.

When a 70 kg man stands on the end of a springboard (a type of diving board), the board deflects by 4.0 cm.

If a 35 kg child stands at the end of the board, the deflection is

A. 1.0 cm.

B. 2.0 cm.

C. 3.0 cm.

D. 4.0 cm.