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Chapter 10: Q. 71 (page 260)

It鈥檚 your birthday, and to celebrate you鈥檙e going to make your first bungee jump. You stand on a bridge $100 m$ above a raging river and attach a $30 m$ -long bungee cord to your harness. A bungee cord, for practical purposes, is just a long spring, and this cord has a spring constant of $40 N / m$ . Assume that your mass is $80 k g$ . After a long hesitation, you dive off the bridge. How far are you above the water when the cord reaches its maximum elongation?

Short Answer

Expert verified

The distance between you and water when the bungee cord is at maximum elongation $= 10.9 m$ .

Step by step solution

01

Given information

Height of the bridge, $h = 100 m$

Length of bungee cord $L = 30 m$

The spring constant of the cord $k = 40 N / m$

02

Explanation

The potential energy of the cord:

$Potentialenergy = m g h w h e r e m = 80 k g, g = 9.8 m / s^{2} Potentialenergy = (80 k g) (9.8 m / s^{2}) h = 784 h J$

The elastic energy of the cord,

role="math" localid="1649402893356" $U_{x} = \frac{1}{2} k y^{2} = \frac{1}{2} (40 N / m) y^{2} = (20 N / m) y^{2}$

role="math" localid="1649402871543" $Distance = h + y = (30 m) + y$

By conservation of energy, equate potential energy and elastic energy.

role="math" localid="1649403050726" $(20 N / m) y^{2} = (784 k g . m / s^{2}) h h = (100 m) + y (20 N / m) y^{2} = (784 k g . m / s^{2}) (100 + y) 20 y^{2} = 784 y + 78400 20 y^{2} - 784 y - 78400 = 0 鈰� 鈰� 鈰� (1) Bysolvingtheequation (1) y = 85.21 m$

Distance of the cord $= (100 m) - (30 m + 85.21 m) = - 15.21 m$

The distance of the cord is $15.21 m$ below the water.

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Most popular questions from this chapter

A particle moves from A to D in $F I G U R E E X 10.35$ while experiencing force $\overset{鈫�}{F} = (6 \hat{i} + 8 \hat{j}) N$ . How much work does the force do if the particle follows path (a) ABD, (b) ACD, and (c) AD? Is this a conservative force? Explain.

a. A $50 g$ ice cube can slide without friction up and down a $30^{o}$ slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring $10 c m$ . The spring constant is $25 N / m$ . When the ice cube is released, what total distance will it travel up the slope before reversing direction?

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b. How much work is done by external forces?

The potential energy for a particle that can move along the x-axis is $U = A x^{2} + B \sin (\frac{蟺 x}{L})$ where A, B, and L are constants. What is the force on the particle at

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b. The particle moves from the origin to the point with coordinates $(a, b)$ by moving first along the y-axis to $(0, b)$ , then parallel to thex-axis. How much work does the force do?

c. Is this a conservative force?

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