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Chapter 4: Q35P (page 166)

Suppose that you are going to measure Young’s 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’s modulus, Y = (F/A)/(∆L/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 5.03×10−5m2,7.2×10−5m2 and3.6×10−5m2 .

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=πr2=3.14×(0.004)2=5.0265×10−5m2A1≃5.03×10−5m2

03

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

A2=dw=0.012×0.006=7.2×10−5m2

04

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

A3=wd=0.006×0.006=3.6×10−5m2

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Most popular questions from this chapter

Forty-five identical springs are placed side by side (in parallel) and connected to a large massive block. The stiffness of the 45-spring combination is 20,250N/m. What is the stiffness of one of the individual springs?

A block of one mole of a certain material whose atoms are in a cubic array has dimensions of 5 cm by 4 cmby0.5 cm. What is the interatomic distance?

Suppose that we hang a heavy ball with a mass of 10 kg (about 22 lb ) from a steel wire 3m long that is 3 mm in diameter. Steel is very stiff, and Young’s modulus for steel is unusually large, 2×1011N/m2.Calculate the stretchΔL of the steel wire. This calculation shows why in many cases it is a very good approximation to pretend that the wire doesn’t stretch at all (“ideal non extensible wire”).

A hanging wire made of an alloy of iron with diameter 0.09cm is initially 2.2m long. When a 66kg mass is hung from it, the wire stretches an amount of 1.12cm. A mole of iron has a mass of 56g, and its density is 7.87 g/cm3. Based on these experimental measurement, what is Young’s modulus for this alloy iron.

In outer space, a rod is pushed to the right by a constant force F (Figure 4.54). Describe the pattern of interatomic distances along the rod. Include a specific comparison of the situation at locations A, B, and C. Explain briefly in terms of fundamental principles.

Figure 4.54

Hint: Consider the motion of an individual atom inside the rod, and various locations along the rod.

(b) After the rod in part (a) reaches a speed v, the object that had been exerting the force on the rod is removed. Describe the subsequent motion of the rod and the pattern of interatomic distances inside the rod. Include a specific comparison of the situation at locations A, B, and C. Explain briefly.
See all solutions

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