a)b) **Physics Problem on Spring Compression***A spring with a force constant \( k = 100 \, \text{N/m} \) is fixed vertically to the floor. An object with a mass of \( 0.2 \, \text{kg} \) is dropped directly onto the spring from a height of \( 0.3 \, \text{m} \) above the tip of the spring. What is the maximum compression of the spring before the mass comes to a stop?*### Possible Answers:- \( \boxed{20 \, \text{cm}} \)- \( \boxed{13 \, \text{cm}} \)- \( \boxed{5.6 \, \text{cm}} \)- \( \boxed{2 \, \text{cm}} \)### Explanation:To solve for the maximum compression of the spring, apply the principle of conservation of energy. The potential energy of the object due to gravity will convert into elastic potential energy stored in the spring.1. **Calculate the initial potential energy:** The initial potential energy \( E_p \) due to gravity is given by: \[ E_p = m \cdot g \cdot h \] where: - \( m = 0.2 \, \text{kg} \) - \( g = 9.8 \, \text{m/s}^2 \) - \( h = 0.3 \, \text{m} \) \[ E_p = 0.2 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 0.3 \, \text{m} = 0.588 \, \text{J} \]2. **Equate it to the spring's potential energy at maximum compression:** The elastic potential energy stored in a compressed spring is given by: \[ E_s = \frac{1}{2} k x^2 \] where: - \( k = 100 \, \text{N/m} \) - \( x \) is the compression in meters Setting \( E_p = E_s \), we get: \[ 0.588 \, \text{J} = \frac{1}{2} \times 100 \, \text{ ### Quiz Question: Spring Compression and Mass Speed**Question:** What is the compression of the spring when the mass is travelling at its maximum speed?**Multiple Choice Answers:**- ⃝ 0 cm- ⃝ 5.6 cm- ⃝ 13 cm- ⃝ 2 cmIn this problem, we are examining the relationship between the compression of a spring and the speed of a mass attached to it. To answer this question, consider the principles of energy conservation in a spring-mass system. When the speed of the mass is at its maximum, the spring is neither compressed nor stretched, implying that its compression is 0 cm.

Name: a)b) **Physics Problem on Spring Compression***A spring with a force c
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Description: a)b) **Physics Problem on Spring Compression***A spring with a force constant \( k = 100 \, \text{N/m} \) is fixed vertically to the floor. An object with a mass of \( 0.2 \, \text{kg} \) is dropped directly onto the spring from a height of \( 0.3 \,

Given k = 100 N/m m = 0.2 Kg h =0.3 m g = 10 m/s² Maximum compression = x

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A spring with force constant k=100 N/m is fixed vertically to the floor. An object with mass=0.2kg is dropped directly onto the spring from a height of 0.3m above the tip of the spring. What is the maximum compression of the spring before the mass comes to a stop? 20 cm O 13 çm

A spring with force constant k=100 N/m is fixed vertically to the floor. An object with mass=0.2kg is dropped directly onto the spring from a height of 0.3m above the tip of the spring. What is the maximum compression of the spring before the mass comes to a stop? 20 cm O 13 çm

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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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**Physics Problem on Spring Compression**

*A spring with a force constant \( k = 100 \, \text{N/m} \) is fixed vertically to the floor. An object with a mass of \( 0.2 \, \text{kg} \) is dropped directly onto the spring from a height of \( 0.3 \, \text{m} \) above the tip of the spring. What is the maximum compression of the spring before the mass comes to a stop?*

### Possible Answers:
- \( \boxed{20 \, \text{cm}} \)
- \( \boxed{13 \, \text{cm}} \)
- \( \boxed{5.6 \, \text{cm}} \)
- \( \boxed{2 \, \text{cm}} \)

### Explanation:

To solve for the maximum compression of the spring, apply the principle of conservation of energy. The potential energy of the object due to gravity will convert into elastic potential energy stored in the spring.

1. **Calculate the initial potential energy:**
The initial potential energy \( E_p \) due to gravity is given by:
\[ E_p = m \cdot g \cdot h \]
where:
- \( m = 0.2 \, \text{kg} \)
- \( g = 9.8 \, \text{m/s}^2 \)
- \( h = 0.3 \, \text{m} \)

\[ E_p = 0.2 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 0.3 \, \text{m} = 0.588 \, \text{J} \]

2. **Equate it to the spring's potential energy at maximum compression:**
The elastic potential energy stored in a compressed spring is given by:
\[ E_s = \frac{1}{2} k x^2 \]
where:
- \( k = 100 \, \text{N/m} \)
- \( x \) is the compression in meters

Setting \( E_p = E_s \), we get:
\[ 0.588 \, \text{J} = \frac{1}{2} \times 100 \, \text{

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