Lesson_4.6_Homework_Solution

Lesson_4.6_Homework_Solution - Lesson 4.6 Homework...

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Lesson 4.6 Homework Solutions 1. A 200-kg mass is suspended from the end of a 2.5-m cable with a diameter of 1.6 cm. (i) Calculate the stress in the cable. (ii) If the wire stretches by 0.48 mm under this stress, what is the strain produced? (iii) What is the Young’s modulus of the material of the wire? The force pulling the cable is 200 kg × 9.8 ms -2 = 1960 N The radius of the cable is: r = 0.8 cm = 0.008 m The area of cross section of the cable is: A = π r 2 = π × (0.008) 2 = 2.01 × 10 -4 m 2 4 6 2 1960 N (i) 2.01 10 9.75 10 Nm F Stress A - - = = = × × (ii) L = 2.5 m, L = 0.48 mm = 0.48 × 10 -3 m 5 3 0.48 10 1.92 10 m 2.5 L Strain L m - - × = × = = 6 -2 1 5 1 2 Stress 9.75 10 Nm (iii) Strain 1.9 5.08 10 2 10 Nm y - - × × = = = × 2. When a cylindrical plastic strip 22 cm long is stretched by a force of 15.8 N applied at one of its ends, its length increases by 5.9 mm. If the average diameter of the strip is 6.8 mm, calculate the Young’s modulus of elasticity of the material of the strip. Area of cross section = π r 2 = π (3.4 x 10 -3 ) 2 = 3.6 x 10 -5 m 2 5 2 5 3 2 2 7 2 5 15.8 4.4 10 3.6 10 5.9 10 0.027 22 1.6 10 10 4.4 10 0.027 F Stress Nm A L Strain L stes Nm s Nm Y strain - - - - - - = = = × × × = = = = × × × = =
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3. How much pressure is needed to compress the volume of an
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Lesson_4.6_Homework_Solution - Lesson 4.6 Homework...

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