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 rollerskates 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?

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 rollerskates 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?

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter14: Static Equilibrium, Elasticity, And Fracture

Section: Chapter Questions

Problem 67PQ

See similar textbooks

Similar questions

Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.100 μm, what is the length of the fiber?
A tunnel of length L =150 m, height H = 7.2 m, and width 5.8 m (with a flat roof) is to be constructed at distance d = 60 m beneath the ground. The tunnel roof is to be supported entirely by square steel columns, each with a cross-sectional area of 960 cm2.The mass of 1.0 cm3 of the ground material is 2.8 g. (a) What is the total weight of the ground material the columns must support? (b) How many columns are needed to keep the compressive stress on each column at one-half its ultimate strength?
A tow truck is pulling a car out of a ditch by means of a steel cable that is 9.2 m long and has a radius of 0.50 cm. When the car just begins to move, the tension in the cable is 279.6 N. How much has the cable stretched from its initial length? Assume Ysteel is 2x1011 N/m2
A tunnel of length L = 130 m, height H = 9.4 m, and width 5.6 m (with a flat roof) is to be constructed at distance d = 68 m beneath the ground. (See the figure.) The tunnel roof is to be supported entirely by square steel columns, each with a cross-sectional area of 906 cm2. The mass of 1.0 cm3 of the ground material is 2.3 g. (a) What is the total weight of the ground material the columns must support? (b) How many columns are needed to keep the compressive stress on each column at one-half its ultimate strength?
A child slides across a floor in a pair of rubber-soled shoes. The frictional force acting on each foot is 20.0 N. The footprint area of each shoe sole is 15.0 cm2, and the thickness of each sole is 4.70 mm. Find the horizontal distance by which the upper and lower surfaces of each sole are offset. The shear modulus of the rubber is 3.00 ✕ 106 N/m2.
The normal force of the ground on the foot can reach three times a runner’s body weight when the foot strikes the pavement. By what amount does the 52-cm-long femur of an 80 kg runner compress at this moment? The cross-section area of the bone of the femur can be taken as 5.2 x 10-4 m2.
A 6.1-g bullet has a velocity of 475 m/s when it penetrates a wooden door to a depth of 3.5 cm. Assuming the frictional force that stops the bullet is constant, how long does it take from the time the bullet hits the door till it comes to a stop?
A 40.0-m-long steel elevator cable has a cross-sectional area of 4.0 × 10^(-4 )m^2and is able to stretch 1.0 cm before breaking. If the elevator itself has a mass of1000. kg, how many 70.0-kg people can safely ride in the elevator?(Ysteel = 2.0 × 10^ 11 N/m^2) a. 14 b. 16 c. 12 d. 18 e. NOTA
An axial pull of 1.5 kN is acting on a bar of consisting two equal lengths as shown but of diameter 10cm and 20 cm respectively. What will be the stresses in the two sections respectively in N/mm2? A. 0.153 and 0.0036 B. 0.290 and 0.046 C. 0.190 and 0.0046 D. 0.124 and 0.124
A 50-N force is applied to a metal rod with a length of 10 m and a cross-sectional area of 1.0 x 10^(−5) m^2. Supposing that the shear modulus of the rod is 2.5 x 10^10 N/m^2, what would be the shear distance?
A child slides across the floor in a pair of rubber-soled shoes. The frictional force acting on each foot is 20.0 N. The footprint area of each sole is 11.6 cm ^ 2 and the thickness of each sole is 6 mm. Find the horizontal distance that the upper and lower surfaces of each sole run. The shear modulus of rubber is 3.00 MN / m ^ 2.
A wire of length “Lo” and cross-sectional area S supports a weight W vertically. a) This fine wire has a Young’s modulus = E and participates in the elastic zone as if it were a very small spring of constant force. Determine the force constant of the spring b) the behavior of the wire is represented in the graph. What would be the force constant for a copper wire 75.0 cm long and 1.291 mm in diameter? c) What weight W would the wire in part b) have if it were stretched 1.25 m