**Problem 8: Conservation of Energy on a Curved Water-slide***A child of mass \( m \) at rest starts sliding from a height \( h = 3.00 \, \text{m} \) along a curved water-slide without friction. She is launched from a height of \( 0.500 \, \text{m} \) into the pool. Use the law of energy conservation to find the speed of the child at points 2, 3, and 4.***Diagram Explanation:**The diagram shows a vertically curved water-slide. The key points in the diagram are:- **Point P1**: The starting point at the top of the slide, where the height \( h_1 = 3 \, \text{m} \).- **Point P2**: The point where the child is sliding down, located immediately after the start of the slide.- **Point P3**: An intermediate point on the slide located at a height of \( 0.5 \, \text{m} \) above the ground.- **Point P4**: The launch point, where the child is at water level, height \( h = 0 \, \text{m} \).**Objective:**To find the speed \( v \) of the child at points P2, P3, and P4 using the law of energy conservation.**Steps using the Law of Energy Conservation:**1. **Initial Energy at Point P1:** - Potential Energy at P1: \( PE_1 = mgh_1 = mg \times 3 \, \text{m} \) - Kinetic Energy at P1: \( KE_1 = 0 \) (since the child starts at rest)2. **Total Mechanical Energy at Point P1:** - \( E_1 = KE_1 + PE_1 = 0 + mg \times 3 \, \text{m} = 3mg \)3. **Mechanical Energy at Point P2:** - At P2, without friction, mechanical energy remains conserved. - Total Energy \( E_2 = E_1 = 3mg \) - If the potential energy at some height \( h_2 \) is considered: \( PE_2 = mg \times h_2 \) - Then, \( 3mg =

Answered: Image /qna-images/answer/42d3b295-05bb-4b5b-8bb0-99c49d25da1b.jpg

8. Alchild of mass m at rest starts sliding from a height h water-slide without friction. She is launched from a height of 0.500 m into the pool. Use the law of energy conservation to find the speed of the child at points 2, 3, and 4. 3.00 m along a curved |3 PI h=D3m P2 P3 T0.5m

8. Alchild of mass m at rest starts sliding from a height h water-slide without friction. She is launched from a height of 0.500 m into the pool. Use the law of energy conservation to find the speed of the child at points 2, 3, and 4. 3.00 m along a curved |3 PI h=D3m P2 P3 T0.5m

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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