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# BIO Bone Fracture. Experimental tests have shown that bone

ISBN: 9780321675460 31

## Solution for problem 14E Chapter 8

University Physics | 13th Edition

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Problem 14E

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?

Step-by-Step Solution:

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

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