lil 19 A 10 kg mass is placed on a spring with a spring constant of 25 N/m. (a) Calculate the force with which the spring pulls back on the mass. Show all work, including the cquation and substitution with units B iU AA E E X T- A: UPLOAD FILE (b) How far is the spring stretchcd by the mass? Show all work, including the cquation and substitution with units B i D AA▼ 三 A:

Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
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Chapter7: Energy Of A System
Section: Chapter Questions
Problem 7.11CQ: A certain uniform spring has spring constant k. Now the spring is cut in half. What is the...
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### Application of Hooke's Law

**Problem Statement:**

** (a)**
A 10 kg mass is placed on a spring with a spring constant of 25 N/m. Calculate the force with which the spring pulls back on the mass. Show all work, including the equation and substitution with units.

** (b)**
How far is the spring stretched by the mass? Show all work, including the equation and substitution with units.

**Explanation:**

In this problem, we are dealing with a scenario involving a mass attached to a spring. The spring stretches or compresses in response to the attached mass, illustrating Hooke's Law, which states:

\[ F_{spring} = -kx \]

Where:
- \( F_{spring} \) is the force exerted by the spring in Newtons (N).
- \( k \) is the spring constant in Newtons per meter (N/m).
- \( x \) is the displacement of the spring from its equilibrium position in meters (m).

**Solution (Part a):**

To find the force with which the spring pulls back on the mass, we will calculate the gravitational force acting on the mass and then apply Newton's third law, which states that the force exerted by the spring is equal and opposite to the gravitational force:

\[ F_{gravity} = mg \]

Where:
- \( m \) is the mass (10 kg).
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, m/s^2 \)).

**Solution (Part b):**

To find the displacement \( x \) of the spring, we rearrange Hooke’s Law to solve for \( x \):

\[ x = \frac{F_{spring}}{k} \]

This equation will be used to determine how far the spring is stretched by solving the values we get from part (a).
Transcribed Image Text:### Application of Hooke's Law **Problem Statement:** ** (a)** A 10 kg mass is placed on a spring with a spring constant of 25 N/m. Calculate the force with which the spring pulls back on the mass. Show all work, including the equation and substitution with units. ** (b)** How far is the spring stretched by the mass? Show all work, including the equation and substitution with units. **Explanation:** In this problem, we are dealing with a scenario involving a mass attached to a spring. The spring stretches or compresses in response to the attached mass, illustrating Hooke's Law, which states: \[ F_{spring} = -kx \] Where: - \( F_{spring} \) is the force exerted by the spring in Newtons (N). - \( k \) is the spring constant in Newtons per meter (N/m). - \( x \) is the displacement of the spring from its equilibrium position in meters (m). **Solution (Part a):** To find the force with which the spring pulls back on the mass, we will calculate the gravitational force acting on the mass and then apply Newton's third law, which states that the force exerted by the spring is equal and opposite to the gravitational force: \[ F_{gravity} = mg \] Where: - \( m \) is the mass (10 kg). - \( g \) is the acceleration due to gravity (approximately \( 9.81 \, m/s^2 \)). **Solution (Part b):** To find the displacement \( x \) of the spring, we rearrange Hooke’s Law to solve for \( x \): \[ x = \frac{F_{spring}}{k} \] This equation will be used to determine how far the spring is stretched by solving the values we get from part (a).
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