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A hA B hB C hc D hp E

A hA B hB C hc D hp E

College Physics
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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--- **Roller Coaster Physics: Analyzing Mechanical Energy** In the diagram below, an object of mass \( m \) starts from rest on a roller coaster with negligible friction. The roller coaster track has various segments represented by points labeled A, B, C, D, and E. The heights at each point are noted as \( h_A, h_B, h_C, \) and \( h_D \). ### Diagram Explanation - **Point A:** The object starts at this point with a height \( h_A \). - **Point B:** The object descends to a lower height \( h_B \). - **Point C:** The object continues to a height \( h_C \). - **Point D:** The object reaches a height \( h_D \). - **Point E:** The object arrives at this point with constant height, indicating no further vertical displacement. ### Questions (a) **What terms are present in the object's mechanical energy?** Choose from: - Gravitational potential energy, Spring potential energy, Kinetic energy, Work done against friction - Gravitational potential energy, Spring potential energy, Kinetic energy - Spring potential energy, Kinetic energy, Work done against friction - Gravitational potential energy, Kinetic energy (b) **Mechanical energy is ____ because there is ____ only.** Fill in the blanks regarding the state of mechanical energy and other forces acting on the system. --- This educational content helps learners analyze mechanical energy transformations as the object moves along the roller coaster track, emphasizing the concepts of gravitational potential energy and kinetic energy.
Transcribed Image Text:--- **Roller Coaster Physics: Analyzing Mechanical Energy** In the diagram below, an object of mass \( m \) starts from rest on a roller coaster with negligible friction. The roller coaster track has various segments represented by points labeled A, B, C, D, and E. The heights at each point are noted as \( h_A, h_B, h_C, \) and \( h_D \). ### Diagram Explanation - **Point A:** The object starts at this point with a height \( h_A \). - **Point B:** The object descends to a lower height \( h_B \). - **Point C:** The object continues to a height \( h_C \). - **Point D:** The object reaches a height \( h_D \). - **Point E:** The object arrives at this point with constant height, indicating no further vertical displacement. ### Questions (a) **What terms are present in the object's mechanical energy?** Choose from: - Gravitational potential energy, Spring potential energy, Kinetic energy, Work done against friction - Gravitational potential energy, Spring potential energy, Kinetic energy - Spring potential energy, Kinetic energy, Work done against friction - Gravitational potential energy, Kinetic energy (b) **Mechanical energy is ____ because there is ____ only.** Fill in the blanks regarding the state of mechanical energy and other forces acting on the system. --- This educational content helps learners analyze mechanical energy transformations as the object moves along the roller coaster track, emphasizing the concepts of gravitational potential energy and kinetic energy.
### Educational Exercise: Mechanical Energy and Speed Calculation #### Instructions: **(b)** Mechanical energy is \_\_\_\_\_ because there is \_\_\_\_\_. **(c)** Calculate the speed of the object at point D (\( v_D \)) in terms of the following variables: \( (g, h_A, h_D) \) - **Write an algebraic expression**; do not use numerical values. To type your equations, click the MathType popup button (red radical) in the answer box. **Hint**: To enter subscripts, press the right-facing arrow next to the superscript/exponent button. For example, if you want to enter \( mg \), type "m^g". \[ v_D = \_\_\_ \] **(d)** What is the relationship between \( v_D \) and mass \( m \)? - ⬤ velocity at D is proportional to the mass - ⬤ velocity at D is proportional to the square root of mass - ⬤ velocity at D is independent of the mass **(e)** How does the speed of the object at point D change if the object at A starts with a speed \( v_A \) instead of starting from rest? Write your answer in terms of: \( v_A, g, h_A, h_D \). - **Write an algebraic expression**; do not use numerical values. To type your equations, click the MathType popup button (red radical) in the answer box. **Hint**: To enter subscripts, press the right-facing arrow next to the superscript/exponent button. For example, if you want to enter mg type "m^g". **Note:** Subscripts are case-sensitive so make sure to enter capital letters for the subscripts. \[ v_D = \_\_\_ \] **Note:** This question has 7 attempts.
Transcribed Image Text:### Educational Exercise: Mechanical Energy and Speed Calculation #### Instructions: **(b)** Mechanical energy is \_\_\_\_\_ because there is \_\_\_\_\_. **(c)** Calculate the speed of the object at point D (\( v_D \)) in terms of the following variables: \( (g, h_A, h_D) \) - **Write an algebraic expression**; do not use numerical values. To type your equations, click the MathType popup button (red radical) in the answer box. **Hint**: To enter subscripts, press the right-facing arrow next to the superscript/exponent button. For example, if you want to enter \( mg \), type "m^g". \[ v_D = \_\_\_ \] **(d)** What is the relationship between \( v_D \) and mass \( m \)? - ⬤ velocity at D is proportional to the mass - ⬤ velocity at D is proportional to the square root of mass - ⬤ velocity at D is independent of the mass **(e)** How does the speed of the object at point D change if the object at A starts with a speed \( v_A \) instead of starting from rest? Write your answer in terms of: \( v_A, g, h_A, h_D \). - **Write an algebraic expression**; do not use numerical values. To type your equations, click the MathType popup button (red radical) in the answer box. **Hint**: To enter subscripts, press the right-facing arrow next to the superscript/exponent button. For example, if you want to enter mg type "m^g". **Note:** Subscripts are case-sensitive so make sure to enter capital letters for the subscripts. \[ v_D = \_\_\_ \] **Note:** This question has 7 attempts.
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