Sample Problem 8.03 Conservation of mechanical energy, water slideThe huge advantage of using the conservation of energy in-stead of Newton's laws of motion is that we can jump fromthe initial state to the final state without considering all theintermediate motion. Here is an example. In Fig. 8-8, a childof mass m is released from rest at the top of a water slide,at height h = 8.5 m above the bottom of the slide.Assuming that the slide is frictionless because of the wateron it, find the child's speed at the bottom of the slide.The total mechanicalenergy at the topis equal to the totalat the bottom.KEY IDEAS(1) We cannot find her speed at the bottom by using her ac-celeration along the slide as we might have in earlier chap-ters because we do not know the slope (angle) of the slide.However, because that speed is related to her kinetic en-ergy, perhaps we can use the principle of conservation ofmechanical energy to get the speed. Then we would notneed to know the slope. (2) Mechanical energy is conservedin a system if the system is isolated and if only conservativeforces cause energy transfers within it. Let's check.Forces: Two forces act on the child. The gravitationalforce, a conservative force, does work on her. The normalforce on her from the slide does no work because its direc-Figure 8-8 A child slides down a water slide as she descends aheight h.System: Because the only force doing work on the childis the gravitational force, we choose the child-Earth systemas our system, which we can take to be isolated.Thus, we have only a conservative force doing work inan isolated system, so we can use the principle of conserva-tion of mechanical energy.Calculations: Let the mechanical energy be Emees when thechild is at the top of the slide and Emech when she is at thebottom. Then the conservation principle tells ustion at any point during the descent is always perpendicularEch= Emecrto the direction in which the child moves.(8-19) In Sample Prob. 8.03, there are no non-conservative forces acting on the child as itslides down. At the highest points, thekinetic energy of the child is zero joules. Atthe lowest point as it slides, the potentialenergy is zero joules. Which one of thefollowing describes the kinetic and potentialenergies of the child at the point in themiddle between the highest and lowestpoints?a. K=0, U=Umaxb.K= UС.K>Ud.K

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Description: Sample Problem 8.03 Conservation of mechanical energy, water slideThe huge advantage of using the conservation of energy in-stead of Newton's laws of motion is that we can jump fromthe initial state to the final state without considering all theinte

Solution: to find what is the values of the kinetic enegry and potential energy at mod point of the…

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In Sample Prob. 8.03, there are no non- conservative forces acting on the child as it slides down. At the highest points, the kinetic energy of the child is zero joules. At the lowest point as it slides, the potential energy is zero joules. Which one of the following describes the kinetic and potential energies of the child at the point in the middle between the highest and lowest points? a. K=0, U= U, %3D max b. K= U С. K>U K

In Sample Prob. 8.03, there are no non- conservative forces acting on the child as it slides down. At the highest points, the kinetic energy of the child is zero joules. At the lowest point as it slides, the potential energy is zero joules. Which one of the following describes the kinetic and potential energies of the child at the point in the middle between the highest and lowest points? a. K=0, U= U, %3D max b. K= U С. K>U K

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter8: Potential Energy And Conservation Of Energy

Section: Chapter Questions

Problem 51P: (a) Sketch a graph of the potential energy function U(x)=kx2/2+Aex2 where k , A, and are constants....

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