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Chapter 14: Q. 32 (page 385)

A 70 kg mountain climber dangling in a crevasse stretches a 50-m-long, 1.0-cm-diameter rope by 8.0 cm. What is Young’s modulus for the rope?

Short Answer

Expert verified

Young's modulus of the rope is $5.5 \times 10^{9} N / m^{2}$ .

Step by step solution

01

Given information

The mass of the climber is $m = 70 k g$

$∆ L = 8 c m = 0.08 m$

The length of the rope is $L = 50 m$

The radius of the rope is $r = \frac{1.0 c m}{2} = 0.5 c m = 0.005 m$

02

Tensile stress

The tensile stress is given by $\frac{F}{A}$ .

role="math" localid="1650295387964" $\frac{F}{A} = \frac{m g}{{πr}^{2}} = \frac{70 \times 9.8}{π {(0.005)}^{2}} = 8.73 \times 10^{6} N / m^{2}$

03

Strain

The strain is given by $\frac{∆ L}{L}$ .

$\frac{∆ L}{L} = \frac{0.08}{50} = 0.0016$

04

Young's modulus of the rope

The Young's modulus of the rope is given by $Y = \frac{\frac{F}{A}}{\frac{∆ L}{L}}$ .

Substitute the obtained values

localid="1650296015704" $Y = \frac{8.73 \times 10^{6}}{0.0016} = 5.5 \times 10^{9} N / m^{2}$

Therefore, Young's modulus of the rope is localid="1650296024948" $5.46 \times 10^{9} N / m^{2}$ .

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Most popular questions from this chapter

A 3.0-cm-diameter tube is held upright and filled to the top with mercury. The mercury pressure at the bottom of the tube— the pressure in excess of atmospheric pressure—is 50 kPa. How tall is the tube?

The $1.0 - m$ -tall cylinder in FIGURE P14.61 contains air at a pressure of $1 a t m_{}$ . A very thin, frictionless piston of negligible mass is placed at the top of the cylinder, to prevent any air from escaping, then mercury is slowly poured into the cylinder until no more can be added without the cylinder overflowing. What is the height h of the column of compressed air?

Hint: Boyle's law, which you learned in chemistry, says $p_{1} V_{1} = p_{2} V_{2}$ for a gas compressed at constant temperature, which we will assume to be the case.

A $355 mL$ soda can is $6.2 cm$ in diameter and has a mass of $20 g$ . Such a soda can half full of water is floating upright in water. What length of the can is above the water level?

A 6.0 m * 12.0 m swimming pool slopes linearly from a 1.0 m depth at one end to a 3.0 m depth at the other. What is the mass of water in the pool?

An aquarium of length $L$ , width (front to back) $W$ , and depth $D$ is filled to the top with liquid of density

a. Find an expression for the force of the liquid on the bottom of the aquarium.

b. Find an expression for the force of the liquid on the front window of the aquarium.

c. Evaluate the forces for a $100 c m$ -long, $35 -cm-wide, 40 - cm$ deep aquarium filled with water.

See all solutions

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