Chapter P.1, Problem 18P

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.

A 70 kg man jumps up and lands on the end of the board, deflecting it by 12 cm. At this instant, what is the approximate magnitude of the upward force the board exerts on his feet? A. 700 A. 700 N

B. 1400 N

C. 2100N

D. 2800 N