College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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**Problem Statement:** 1. Refer to figures 1 and 2. Calculate the magnitude of force needed to displace the block by 12.0 cm. What is the maximum kinetic energy this object can attain? What is its maximum potential energy? What is the amplitude? Where would you find the maximum and minimum potential and kinetic energies? If the angular frequency is 10.0 rad/sec, calculate the mass of the object. --- **Figure 1:** The image shows a block attached to a spring on a flat surface. The spring is coiled and attached to one end, with the block on the other, indicating a classic spring-mass system. --- **Hooke's Constant Plot:** - **Graph Explanation:** - The graph is labeled "Hooke's Constant Plot." - The y-axis represents the Force (N), ranging from 0.00 to 6.00 N. - The x-axis represents the Displacement (cm), ranging from 0.00 to 5.00 cm. - The plot is a straight line indicating a linear relationship between force and displacement, consistent with Hooke's Law (F = kx). This graph can be used to determine the spring constant (k) by calculating the slope of the line (change in Force divided by change in Displacement). --- To solve the problem: - **Force Calculation:** - Use Hooke's Law: F = kx. - Determine the spring constant (k) from the slope of the graph. - **Maximum Kinetic and Potential Energy:** - Maximum Potential Energy at maximum displacement: PE_max = (1/2)kx^2. - Maximum Kinetic Energy when all potential energy is converted: KE_max = PE_max. - **Angular Frequency and Mass:** - Use the formula for angular frequency in terms of mass and spring constant: ω = sqrt(k/m). - Rearrange to solve for mass (m): m = k/ω^2. These steps will guide the calculation of the required physical quantities.
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Transcribed Image Text:**Problem Statement:** 1. Refer to figures 1 and 2. Calculate the magnitude of force needed to displace the block by 12.0 cm. What is the maximum kinetic energy this object can attain? What is its maximum potential energy? What is the amplitude? Where would you find the maximum and minimum potential and kinetic energies? If the angular frequency is 10.0 rad/sec, calculate the mass of the object. --- **Figure 1:** The image shows a block attached to a spring on a flat surface. The spring is coiled and attached to one end, with the block on the other, indicating a classic spring-mass system. --- **Hooke's Constant Plot:** - **Graph Explanation:** - The graph is labeled "Hooke's Constant Plot." - The y-axis represents the Force (N), ranging from 0.00 to 6.00 N. - The x-axis represents the Displacement (cm), ranging from 0.00 to 5.00 cm. - The plot is a straight line indicating a linear relationship between force and displacement, consistent with Hooke's Law (F = kx). This graph can be used to determine the spring constant (k) by calculating the slope of the line (change in Force divided by change in Displacement). --- To solve the problem: - **Force Calculation:** - Use Hooke's Law: F = kx. - Determine the spring constant (k) from the slope of the graph. - **Maximum Kinetic and Potential Energy:** - Maximum Potential Energy at maximum displacement: PE_max = (1/2)kx^2. - Maximum Kinetic Energy when all potential energy is converted: KE_max = PE_max. - **Angular Frequency and Mass:** - Use the formula for angular frequency in terms of mass and spring constant: ω = sqrt(k/m). - Rearrange to solve for mass (m): m = k/ω^2. These steps will guide the calculation of the required physical quantities.
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Step 1: Determine the given variable
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Step 2: Calculate the force needed to displace the block by 12 cm
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Step 3: Calculate the maximum kinetic energy that the object can attain :
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Step 4: Calculate the maximum potential energy that the object can attain :
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Step 5: Determine where you can find maximum and minimum of kinetic energy and potential energy
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Step 6: Find mass of object
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Solution
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