College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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### Conservation of Energy #### 5. Is it possible to rank the changes in total energy of the three systems by simply comparing the rankings of the change in potential and kinetic energy for the systems (i.e., without comparing the net work on the systems)? Explain. #### D. In order for the equation \( K_i + U_i = K_f + U_f \) to be true for a given system, what must be true about the net work on that system? Explain. (Hint: Rearrange the terms to express the equation in terms of \(\Delta K\) and \(\Delta U\). How are these related to the change in total energy of the system?) --- ### II. Systems A block of mass \( m \) on a frictionless surface is attached to an ideal massless spring of constant \( k \), as shown in the diagram below. **Diagram Description:** - The block is initially at \( x = 0 \), the spring is neither stretched nor compressed. - At time \( t_i \), the block is released from rest at \( x = x_i \). - At time \( t_f \), the block passes \( x = 0 \) moving to the left with speed \( v_f \). - **Just Before Diagram** shows the block at \( x = x_i \) with the spring compressed/stretched. - **t = t_f, x = 0** shows the block passing the equilibrium position. --- #### A. Consider system A, which consists of the block and the spring. **1. List all the forces acting on system A during the interval from \( t_i \) to \( t_f \). For each force, indicate the object exerting the force and the type of force.** - Gravitational force (by Earth) - Normal force (by surface) - Spring force (by spring) **Notes** (as per handwritten annotations): - Gravitational force perpendicular to gravitational work is zero. - Work done by spring: \( W = \int_{x_i}^{0} -kx\, dx = -\frac{1}{2}kx_i^2 \) **2. For each force that you listed above, state whether that force does positive, negative, or zero work on system A during the interval from \( t_i \) to \( t_f \). Explain.** - Gravitational force: zero work. - Normal force: zero
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Transcribed Image Text:### Conservation of Energy #### 5. Is it possible to rank the changes in total energy of the three systems by simply comparing the rankings of the change in potential and kinetic energy for the systems (i.e., without comparing the net work on the systems)? Explain. #### D. In order for the equation \( K_i + U_i = K_f + U_f \) to be true for a given system, what must be true about the net work on that system? Explain. (Hint: Rearrange the terms to express the equation in terms of \(\Delta K\) and \(\Delta U\). How are these related to the change in total energy of the system?) --- ### II. Systems A block of mass \( m \) on a frictionless surface is attached to an ideal massless spring of constant \( k \), as shown in the diagram below. **Diagram Description:** - The block is initially at \( x = 0 \), the spring is neither stretched nor compressed. - At time \( t_i \), the block is released from rest at \( x = x_i \). - At time \( t_f \), the block passes \( x = 0 \) moving to the left with speed \( v_f \). - **Just Before Diagram** shows the block at \( x = x_i \) with the spring compressed/stretched. - **t = t_f, x = 0** shows the block passing the equilibrium position. --- #### A. Consider system A, which consists of the block and the spring. **1. List all the forces acting on system A during the interval from \( t_i \) to \( t_f \). For each force, indicate the object exerting the force and the type of force.** - Gravitational force (by Earth) - Normal force (by surface) - Spring force (by spring) **Notes** (as per handwritten annotations): - Gravitational force perpendicular to gravitational work is zero. - Work done by spring: \( W = \int_{x_i}^{0} -kx\, dx = -\frac{1}{2}kx_i^2 \) **2. For each force that you listed above, state whether that force does positive, negative, or zero work on system A during the interval from \( t_i \) to \( t_f \). Explain.** - Gravitational force: zero work. - Normal force: zero
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