BIO Bone Fracture.? Experimental tests have shown that bone will rupture if it is subjected to a force density of 1.03 X 108 N/m2. Suppose a 70.0-kg person carelessly roller-skates into an overhead metal beam that hits his forehead and completely stops his forward motion. If the area of contact with the person’s forehead is 1.5 cm2, what is the greatest speed with which he can hit the wall without breaking any bone if his head is in contact with the beam for 10.0 ms?
Solution 14E Step 1: Given data: 8 2 Force density F d 1.03 × 10 N/m . 2 4 Area in contact A = 1.50 cm = 1.50 × 10 m. Mass of skater m = 70 kg. Speed v = 10 m/s Step 2: Assume that the stopping event is a constant declaration over the time interval specified. v = a * a = v/t The force is F = m a * F = m v/t * Maximum force is given by F = F Area in contact max d * F = 1.03 × 10 N/m 2 1.50 × 104m 2 max * F max= 15450 N