1. A bal surface of the Earth, as shown åt Figl he it has a speed v. Ignore air resistance, and assume that any changes in kinetic energy of the Earth are negligible. h, h ----- In this problem, you will analyze this situation by considering two different systems: system BE (the ball and the Earth) and system B (the ball alone). a. Consider system BE, consisting of the ball and the Earth v = v, Earth Earth i As the ball falls from h, to ht, does the total energy of system BE increase, decrease or AS he same? Explain by considering the net work by external forces on system BE. external ii. Consider the following discussion: Student 1: "The changes to system BE are all internal, so its gravitational potential energy doesn't change. Since the kinetic energy of the ball increases, the total energy of system BE increases." Student 2: "I think that the change in potential energy of the system is zero because the distance the ball moves is small compared to the size of the earth. The change in total energy of system BE is equal to the change in kinetic energy of the ball."i id e lolla by yod Joial Identify the incorrect statements made by both students. Explain. iii. Write an expression for each of the following quantities in terms of the given variables and any physical constants. If any of these are zero, state so explicitly. • the change in kinetic energy of system BE • the change in potential energy of system BE • the net external work by external forces on system BE iv. Write an equation that relates the expressions above. * Solve your equation from part iv for the final speed of the ball. Is your result consistent ur what you would obtain using kinematics and your knowledge of the acceleration due to gravity near the Earth's surface? If not, resolve the inconsistency.
1. A bal surface of the Earth, as shown åt Figl he it has a speed v. Ignore air resistance, and assume that any changes in kinetic energy of the Earth are negligible. h, h ----- In this problem, you will analyze this situation by considering two different systems: system BE (the ball and the Earth) and system B (the ball alone). a. Consider system BE, consisting of the ball and the Earth v = v, Earth Earth i As the ball falls from h, to ht, does the total energy of system BE increase, decrease or AS he same? Explain by considering the net work by external forces on system BE. external ii. Consider the following discussion: Student 1: "The changes to system BE are all internal, so its gravitational potential energy doesn't change. Since the kinetic energy of the ball increases, the total energy of system BE increases." Student 2: "I think that the change in potential energy of the system is zero because the distance the ball moves is small compared to the size of the earth. The change in total energy of system BE is equal to the change in kinetic energy of the ball."i id e lolla by yod Joial Identify the incorrect statements made by both students. Explain. iii. Write an expression for each of the following quantities in terms of the given variables and any physical constants. If any of these are zero, state so explicitly. • the change in kinetic energy of system BE • the change in potential energy of system BE • the net external work by external forces on system BE iv. Write an equation that relates the expressions above. * Solve your equation from part iv for the final speed of the ball. Is your result consistent ur what you would obtain using kinematics and your knowledge of the acceleration due to gravity near the Earth's surface? If not, resolve the inconsistency.
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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Transcribed Image Text:### Conservation of Energy
1. **Problem Statement:**
A ball of mass \( m \) falls from height \( h_i \) to height \( h_f \) near the surface of the Earth, as shown in the diagram. When the ball passes \( h_f \), it has a speed \( v_f \). Ignore air resistance, and assume that any changes in kinetic energy of the Earth are negligible.
In this problem, you will analyze this situation by considering two different systems: system BE (the ball and the Earth) and system B (the ball alone).
**a.** Consider system BE, consisting of the ball and the Earth.
- **i.** As the ball falls from \( h_i \) to \( h_f \), does the total energy of system BE increase, decrease, or stay the same? Explain by considering the net work by external forces on system BE.
**ii.** Consider the following discussion:
- **Student 1:** "The changes to system BE are all internal, so its gravitational potential energy doesn’t change. Since the kinetic energy of the ball increases, the total energy of system BE increases."
- **Student 2:** "I think that the change in potential energy of the system is zero because the distance the ball moves is small compared to the size of the Earth. The change in total energy of system BE is equal to the change in kinetic energy of the ball."
Identify the incorrect statements made by both students. Explain.
2. **Tasks:**
**iii.** Write an expression for each of the following quantities in terms of the given variables and any physical constants. If any of these are zero, state so explicitly.
- The change in kinetic energy of system BE
- The change in potential energy of system BE
- The net external work by external forces on system BE
**iv.** Write an equation that relates the expressions above.
**v.** Solve your equation from part iv for the final speed of the ball. Is your result consistent with what you would obtain using kinematics and your knowledge of the acceleration due to gravity near the Earth’s surface? If not, resolve the inconsistency.
### Diagrams:
- The diagram shows two stages of the ball's motion. At height \( h_i \), the ball's velocity \( v = 0 \). At height \( h_f \), the velocity \( v =
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