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Chapter 4: Q35P (page 166)

Suppose that you are going to measure Young鈥檚 modulus for three rods by measuring their stretch when they are suspended vertically and weights are hung from them (Figure 4.56)

(Figure 4.56)

Rod 1 is 2.7 m long and cylindrical with radius 4 mm (1 mm is 0.001 m). Rod 2 is 3.2 m long by 12 mm wide by 6 mm deep. Rod 3 is 3 m long by 6 mm wide by 6 mm deep. The definition of Young鈥檚 modulus, Y = (F/A)/(鈭哃/L), includes the quantity A, the cross-sectional area.

(a) What is the cross-sectional area of rod 1?

(b) What is the cross-sectional area of rod 2?

(c) What is the cross-sectional area of rod 3?

Short Answer

Expert verified

The results are 5.03脳10鈭�5m2,7.2脳10鈭�5m2 and3.6脳10鈭�5m2 .

Step by step solution

01

Given data

Rod 1,

L = 2.7 m

R = 4mm = 0.004 m

Rod 2,

L = 3.2 m

w = 12mm = 0.012 m

d = 6mm = 0.006 m

Rod 3,

L = 3 m

w = 0.006 m

d = 0.006 m

02

(a)Determine the cross-sectional area of rod 1 

A1=蟺谤2=3.14脳(0.004)2=5.0265脳10鈭�5m2A1鈮�5.03脳10鈭�5m2

03

(b) Determine the cross-sectional area of rod 2 

A2=dw=0.012脳0.006=7.2脳10鈭�5m2

04

(c)Determine the cross-sectional area of rod 3

A3=wd=0.006脳0.006=3.6脳10鈭�5m2

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Most popular questions from this chapter

One mole of tungsten (6.02脳1023atoms) has a mass of 184 g, as shown in the periodic table on the inside front cover of the textbook. The density of tungsten is19.3g/cm3. What is the approximate diameter of a tungsten atom (length of a bond) in a solid block of the material? Make the simplifying assumption that the atoms are arranged in a cubic array.

A certain spring has stiffness 190N/m. The spring is then cut into two equal lengths. What is the stiffness of one of these half-length springs?

: Two wires with equal lengths are made of pure copper. The diameter of wire A is twice the diameter of wire B. When 6kg masses are hung on the wires, wire B stretches more than wire A. You make careful measurements and compute young鈥檚 modulus for both wires. What do you find? (a) YA>YB, b) YA=YBc) YA<YB

Lead is much softer than aluminum, and can be more easily deformed or pulled into a wire. What difference between the two materials best explains this? (a) Pb and Al atoms have different sizes. (b) Pb and Al atoms have different masses. (c) The stiffness of the interatomic bonds is different in Pb and Al.

An object of mass m is attached by two stretched springs (stiffnessKs and relaxed lengthL0 ) to rigid walls, as shown in figure 4.60. The springs are initially stretched by an amount (L-L0). When the object is displaced to the right and released, it oscillates horizontally. Starting from the momentum principle, find a function of the displacement xof the object and the timet describes the oscillatory motion.

(a) What is the period of the motion?

(b) If L0 were shorter (so the springs are initially stretched more), would the period be larger, smaller, or the same?
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