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A RDN B 1. Rank the three systems according to the absolute value of the net work by external forces, from largest to smallest. If the net work on any of the systems is zero, state so explicitly. Explain. A -d, -d, lod 2. Rank the three systems according to the absolute value of the change in total energy, from largest to smallest. If the change in energy of any of the systems is zero, state so to explicitly. Explain. 20 Rank the three systems according to the absolute value of the change in potential energy, from largest to smallest. If the change in potential energy of any of the systems 1is zero, state so explicitly. Explain.

A RDN B 1. Rank the three systems according to the absolute value of the net work by external forces, from largest to smallest. If the net work on any of the systems is zero, state so explicitly. Explain. A -d, -d, lod 2. Rank the three systems according to the absolute value of the change in total energy, from largest to smallest. If the change in energy of any of the systems is zero, state so to explicitly. Explain. 20 Rank the three systems according to the absolute value of the change in potential energy, from largest to smallest. If the change in potential energy of any of the systems 1is zero, state so explicitly. Explain.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Could you help with C1,2 and 3?

**Conservation of Energy** **I. Relating Work and Changes in Energy** Two experiments are conducted involving identical blocks on a level, frictionless surface. Each block starts from rest and is pushed through a distance \( d_1 \) by a hand that exerts a constant horizontal force of magnitude \( F_0 \). **Experiment 1:** The blocks are connected by an ideal massless spring of constant \( k_1 \), which is initially neither stretched nor compressed. At the end of the interval shown, each block has a speed of zero. **Experiment 2:** Each block has a speed of \( v_2 \) at the end of the interval shown. **A. Consider system 1 (which consists of the two blocks and the spring in experiment 1) and system 2 (which consists of the two blocks in experiment 2).** In the table below, indicate whether each of the quantities is positive, negative, or zero for systems 1 and 2. Explain. (Note: \( \Delta U \) represents the change in potential energy of the system.) | | \( W_{\text{net ext}} \) | \( \Delta K \) | \( \Delta U \) | \( \Delta E_{\text{tot}} \) | | ------------- | --------------- | --------- | --------- | --------------- | | System 1 | + | 0 | + | + | | System 2 | + | + | 0 | + | **B. State whether each of the statements below is consistent with your results above. If not, cite a specific case from the table that contradicts the student’s statement.** 1. *Student 1: "The net work done on a system is always equal to the change in kinetic energy of that system."* **Incorrect.** As noted in system 1, the net work done on the system is not always equal to the change in kinetic energy (\( \Delta K \)). There is also a change in potential energy (\( \Delta U \)). 2. *Student 2: "In the absence of friction, the total energy of a system must remain constant. In other words, \( K_i + U_i = K_f + U_f \)."* **True.** If there's no dissipative force (like friction) present in the system, the
Transcribed Image Text:**Conservation of Energy** **I. Relating Work and Changes in Energy** Two experiments are conducted involving identical blocks on a level, frictionless surface. Each block starts from rest and is pushed through a distance \( d_1 \) by a hand that exerts a constant horizontal force of magnitude \( F_0 \). **Experiment 1:** The blocks are connected by an ideal massless spring of constant \( k_1 \), which is initially neither stretched nor compressed. At the end of the interval shown, each block has a speed of zero. **Experiment 2:** Each block has a speed of \( v_2 \) at the end of the interval shown. **A. Consider system 1 (which consists of the two blocks and the spring in experiment 1) and system 2 (which consists of the two blocks in experiment 2).** In the table below, indicate whether each of the quantities is positive, negative, or zero for systems 1 and 2. Explain. (Note: \( \Delta U \) represents the change in potential energy of the system.) | | \( W_{\text{net ext}} \) | \( \Delta K \) | \( \Delta U \) | \( \Delta E_{\text{tot}} \) | | ------------- | --------------- | --------- | --------- | --------------- | | System 1 | + | 0 | + | + | | System 2 | + | + | 0 | + | **B. State whether each of the statements below is consistent with your results above. If not, cite a specific case from the table that contradicts the student’s statement.** 1. *Student 1: "The net work done on a system is always equal to the change in kinetic energy of that system."* **Incorrect.** As noted in system 1, the net work done on the system is not always equal to the change in kinetic energy (\( \Delta K \)). There is also a change in potential energy (\( \Delta U \)). 2. *Student 2: "In the absence of friction, the total energy of a system must remain constant. In other words, \( K_i + U_i = K_f + U_f \)."* **True.** If there's no dissipative force (like friction) present in the system, the
### Conservation of Energy A fundamental principle of physics is that the total energy of a system changes only through interactions with objects outside that system. One way to change the total energy of a system is through work done by external forces. The net work done on a system by external forces and the change in energy of that system are related by the principle of conservation of energy. In mechanics, this principle can be expressed as: \[ W_{\text{ext}} = \Delta E_{\text{tot}} \] #### Experiment 3 In Experiment 3, each block is pushed by a constant force \( F_o \). **Diagram Description:** - The diagram shows two blocks, labeled A and B, connected by a spring with a spring constant \( k_3 \). - At \( t = t_s \), the blocks are initially at rest and are a distance \( d_o \) apart. - At \( t = t_6 \), the blocks have moved closer together, compressing the spring. #### Systems **System 3** consists of the two blocks and the spring in Experiment 3. ### Exercises 1. **Rank the three systems according to the net work by external forces, from largest to smallest. If the net work on any of the systems is zero, state so explicitly. Explain.** 2. **Rank the three systems according to the absolute value of the change in total energy, from largest to smallest. If the change in energy of any of the systems is zero, state so explicitly. Explain.** 3. **Rank the three systems according to the absolute value of the change in potential energy, from largest to smallest. If the change in potential energy of any of the systems is zero, state so explicitly. Explain.** 4. **Rank the three systems according to the absolute value of the change in kinetic energy, from largest to smallest. If the change in kinetic energy of any of the systems is zero, state so explicitly. Explain.**
Transcribed Image Text:### Conservation of Energy A fundamental principle of physics is that the total energy of a system changes only through interactions with objects outside that system. One way to change the total energy of a system is through work done by external forces. The net work done on a system by external forces and the change in energy of that system are related by the principle of conservation of energy. In mechanics, this principle can be expressed as: \[ W_{\text{ext}} = \Delta E_{\text{tot}} \] #### Experiment 3 In Experiment 3, each block is pushed by a constant force \( F_o \). **Diagram Description:** - The diagram shows two blocks, labeled A and B, connected by a spring with a spring constant \( k_3 \). - At \( t = t_s \), the blocks are initially at rest and are a distance \( d_o \) apart. - At \( t = t_6 \), the blocks have moved closer together, compressing the spring. #### Systems **System 3** consists of the two blocks and the spring in Experiment 3. ### Exercises 1. **Rank the three systems according to the net work by external forces, from largest to smallest. If the net work on any of the systems is zero, state so explicitly. Explain.** 2. **Rank the three systems according to the absolute value of the change in total energy, from largest to smallest. If the change in energy of any of the systems is zero, state so explicitly. Explain.** 3. **Rank the three systems according to the absolute value of the change in potential energy, from largest to smallest. If the change in potential energy of any of the systems is zero, state so explicitly. Explain.** 4. **Rank the three systems according to the absolute value of the change in kinetic energy, from largest to smallest. If the change in kinetic energy of any of the systems is zero, state so explicitly. Explain.**
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