Explanation Given: Height of the bridge, y 1 = 100 m Length of bungee cord, L = 30 m The spring constant of the cord , k = 40 N/m Assume your mass, k = 40 N/m The data given can be visualized as below: Note that the end of the upstretched cord is at y 0 = height of bridge − length or cord = 100 m − 30 m = 70 m Formula used: The conservation of energy equation, K 2 + U s 2 + U g 2 = K 1 + U s 1 + U g 1 K = kinetic energy = 1 2 m v 2 U s = the potential energy of the cord = 1 2 k ( Δ s ) 2 U g = gravitational potential energy = mgh Where; V = velocity k =spring constant Δ s = elongation of cord Calculation: Choose yourself + spring + earth as the system. There are no forces from outside this system, so it is an isolated system. The interaction forces within the system are the spring force of the bungee cord and the gravitational force. These are both conservative forces, so mechanical energy is conserved. One can equate the system’s initial energy, as one step off the bridge, to its final energy when one reaches the lowest point. One does not need to compute speed at the point where the cord starts to stretch. Use the energy conservation equation. K 2 + U s 2 + U g 2 = K 1 + U s 1 + U g 1 The initial potential energy of the cord, U s 1 = 0. Since the cord is not stretched. Initial kinetic energy K 1 = Final kinetic energy, K 2 = 0 The final potential energy of the cord U s 2 = 1 2 k ( Δ s ) 2 , where, elongation be y 2 as shown in the figure. K 2 + U s 2 + U g 2 = K 1 + U s 1 + U g 1 ⇒ 0 J + 1 2 k ( y 2 − y 0 ) 2 + m g y 2 = 0 J + 0 J + m g y 1 m g 2 + 1 <

Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)

4th Edition

ISBN: 9780134110684

Author: Randall D. Knight (Professor Emeritus)

Publisher: PEARSON

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Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The p…

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Chapter 10, Problem 71EAP

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The distance between you and water, when the bungee jump cord reaches its maximum elongation.

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Chapter 10, Problem 70EAP

Chapter 10, Problem 72EAP

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Chapter 10 Solutions

Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)

Ch. 10 - Prob. 1CQ Ch. 10 - Can kinetic energy ever be negative? Can...Ch. 10 - Prob. 3CQ Ch. 10 - 4. The three balls in FIGURE Q1O.4, which have...Ch. 10 - Rank in order, from most to least, the elastic...Ch. 10 - 6. A spring is compressed 1.0 cm. How far must you...Ch. 10 - Prob. 7CQ Ch. 10 - A particle with the potential energy shown in...Ch. 10 - A compressed spring launches a block up an...Ch. 10 - 10. A process occurs in which a system’s potential...

Ch. 10 - A process occurs in which a system’s potential...Ch. 10 - FIGURE Q10.12 is the energy bar chart for a...Ch. 10 - Prob. 13CQ Ch. 10 - Object A is stationary while objects B and C are...Ch. 10 - Prob. 2EAP Ch. 10 - 3. The lowest point in Death Valley is 85 m below...Ch. 10 - Prob. 4EAP Ch. 10 - Prob. 5EAP Ch. 10 - 6. What height does a frictionless playground...Ch. 10 - 7. A 55 kg skateboarder wants to just make it to...Ch. 10 - Prob. 8EAP Ch. 10 - A pendulum is made by tying a 500 g ball to a...Ch. 10 - A 20 kg child is on a swing that hangs from...Ch. 10 - A 1500 kg car traveling at 10 m/s suddenly runs...Ch. 10 - Prob. 12EAP Ch. 10 - A cannon tilted up at a 30° angle fires a cannon...Ch. 10 - In a hydroelectric dam, water falls 25 m and then...Ch. 10 - How far must you stretch a spring with k = 000 N/m...Ch. 10 - A stretched spring stores 2.0 J of energy. How...Ch. 10 - A student places her 500 g physics book on a...Ch. 10 - A block sliding along a horizontal frictionless...Ch. 10 - A 10 kg runaway grocery cart runs into a spring...Ch. 10 - As a 15,000 kg jet plane lands on an aircraft...Ch. 10 - The elastic energy stored in your tendons can...Ch. 10 - The spring in FIGURE EX10.22a is compressed by ?x....Ch. 10 - The spring in FIGURE EXIO.23a is compressed by ?x....Ch. 10 - FIGURE EX10.24 is the potential-energy diagram for...Ch. 10 - Prob. 25EAP Ch. 10 - In FIGURE EX10.26, what is the maximum speed of a...Ch. 10 - Prob. 27EAP Ch. 10 - FIGURE EX10.28 shows the potential energy of a 500...Ch. 10 - In FIGURE EX10.28, what is the maximum speed a 200...Ch. 10 - A system in which only one particle can move has...Ch. 10 - A system in which only one particle can move has...Ch. 10 - A particle moving along the y-axis is in a system...Ch. 10 - A particle moving along the x-axis is in a system...Ch. 10 - FIGURE EX10.34 shows the potential energy of a...Ch. 10 - A particle moves from A to D in FIGURE EX10.35...Ch. 10 - A force does work on a 50 g particle as the...Ch. 10 - A system loses 400 J of potential energy. In the...Ch. 10 - What is the final kinetic energy of the system for...Ch. 10 - How much work is done by the environment in the...Ch. 10 - A cable with 20.0 N tension pulls straight up on a...Ch. 10 - A very slippery ice cube slides in a vertical...Ch. 10 - A 50 g ice cube can slide up and down a...Ch. 10 - You have been hired to design a spring-launched...Ch. 10 - It’s been a great day of new, frictionless snow....Ch. 10 - Prob. 45EAP Ch. 10 - A 1000 kg safe is 2.0 m above a heavy-duty spring...Ch. 10 - You have a ball of unknown mass, a spring with...Ch. 10 - Sam, whose mass is 75 kg, straps on his skis and...Ch. 10 - A horizontal spring with spring constant 100 N/m...Ch. 10 - Truck brakes can fail if they get too hot. In some...Ch. 10 - Prob. 51EAP Ch. 10 - Use work and energy to find an expression for the...Ch. 10 - Prob. 53EAP Ch. 10 - The spring shown in FIGURE 10.54 is compressed 50...Ch. 10 - Prob. 55EAP Ch. 10 - Prob. 56EAP Ch. 10 - A system has potential energy U(x) = x + sin ((2...Ch. 10 - Prob. 58EAP Ch. 10 - Prob. 59EAP Ch. 10 - Prob. 60EAP Ch. 10 - The potential energy for a particle that can move...Ch. 10 - A particle that can move along the x-axis...Ch. 10 - An object moving in the xy-plane is subjected to...Ch. 10 - An object moving in the xy-plane is subjected to...Ch. 10 - Prob. 65EAP Ch. 10 - In Problems 66 through 68 you are given the...Ch. 10 - Prob. 67EAP Ch. 10 - Prob. 68EAP Ch. 10 - A pendulum is formed from a small ball of mass m...Ch. 10 - Prob. 70EAP Ch. 10 - Prob. 71EAP Ch. 10 - Prob. 72EAP Ch. 10 - The spring in FIGURE CP10.73 has a spring constant...Ch. 10 - A sled starts from rest at the top of the...

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