**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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Description: **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? Wher

The given graph is :The formula for the potential energy is also

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1. Refer and use figure 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 you would find the maximum and minimum potential and kinetic energies? If the angular frequency is 10.0 rad-sec¹, calculate the mass of the object. Figure 1: Hooke's Constant Plot

1. Refer and use figure 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 you would find the maximum and minimum potential and kinetic energies? If the angular frequency is 10.0 rad-sec¹, calculate the mass of the object. Figure 1: Hooke's Constant Plot

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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Concept explainers

Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.

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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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