College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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I included the previous parts for context, but I just need help on "Part D" please!

**Learning Goal:**

To apply the law of conservation of energy to an object launched upward in Earth's gravitational field.

In the absence of nonconservative forces such as friction and air resistance, the total mechanical energy in a closed system is conserved. This is one particular case of the law of conservation of energy.

In this problem, you will apply the law of conservation of energy to different objects launched from Earth. The energy transformations that take place involve the object's kinetic energy \( K = (1/2)mv^2 \) and its gravitational potential energy \( U = mgh \). The law of conservation of energy for such cases implies that the sum of the object's kinetic energy and potential energy does not change with time. This idea can be expressed by the equation:

\[ K_i + U_i = K_f + U_f \]

where "i" denotes the "initial" moment and "f" denotes the "final" moment. Since any two moments will work, the choice of the moments to consider is, technically, up to you. That choice, though, is usually suggested by the question posed in the problem.

---

**First**, let us consider an object launched vertically upward with an initial speed \( v \). Neglect air resistance.

**Part A**

As the projectile goes upward, what energy changes take place?

- [ ] Both kinetic and potential energy decrease.
- [ ] Both kinetic and potential energy increase.
- [x] Kinetic energy decreases; potential energy increases.
- [ ] Kinetic energy increases; potential energy decreases.

**Correct.**
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Transcribed Image Text:**Learning Goal:** To apply the law of conservation of energy to an object launched upward in Earth's gravitational field. In the absence of nonconservative forces such as friction and air resistance, the total mechanical energy in a closed system is conserved. This is one particular case of the law of conservation of energy. In this problem, you will apply the law of conservation of energy to different objects launched from Earth. The energy transformations that take place involve the object's kinetic energy \( K = (1/2)mv^2 \) and its gravitational potential energy \( U = mgh \). The law of conservation of energy for such cases implies that the sum of the object's kinetic energy and potential energy does not change with time. This idea can be expressed by the equation: \[ K_i + U_i = K_f + U_f \] where "i" denotes the "initial" moment and "f" denotes the "final" moment. Since any two moments will work, the choice of the moments to consider is, technically, up to you. That choice, though, is usually suggested by the question posed in the problem. --- **First**, let us consider an object launched vertically upward with an initial speed \( v \). Neglect air resistance. **Part A** As the projectile goes upward, what energy changes take place? - [ ] Both kinetic and potential energy decrease. - [ ] Both kinetic and potential energy increase. - [x] Kinetic energy decreases; potential energy increases. - [ ] Kinetic energy increases; potential energy decreases. **Correct.**
## Part D

Using conservation of energy, find the maximum height \( h_{\text{max}} \) to which the object will rise.

Express your answer in terms of \( v \) and \( g \). You may or may not use all of these quantities.

### Input Box
- \( h_{\text{max}} = \) [Input Field]

### Controls
- **Square root button**: Inserts the square root symbol.
- **Greek letters button**: Provides access to Greek symbols.
- **Undo button**: Reverts the last action.
- **Redo button**: Reapplies the last undone action.
- **Reset button**: Clears the current input.
- **Keyboard button**: Displays an on-screen keyboard.
- **Help button**: Provides guidance on using the input box.

### Submission
- **Submit Button**: Finalize your answer.
- **Request Answer Link**: Seek assistance if needed.
expand button
Transcribed Image Text:## Part D Using conservation of energy, find the maximum height \( h_{\text{max}} \) to which the object will rise. Express your answer in terms of \( v \) and \( g \). You may or may not use all of these quantities. ### Input Box - \( h_{\text{max}} = \) [Input Field] ### Controls - **Square root button**: Inserts the square root symbol. - **Greek letters button**: Provides access to Greek symbols. - **Undo button**: Reverts the last action. - **Redo button**: Reapplies the last undone action. - **Reset button**: Clears the current input. - **Keyboard button**: Displays an on-screen keyboard. - **Help button**: Provides guidance on using the input box. ### Submission - **Submit Button**: Finalize your answer. - **Request Answer Link**: Seek assistance if needed.
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