### Non-Conservative Work**1. A 1.75 kg ball rolls down an incline into a spring. The ball starts from rest at a height of 3.10 m above the spring, and the spring constant is 185 N/m.****a. If the spring is compressed 65 cm when the ball comes to rest against the spring, was energy conserved?****b. How much work was done by non-conservative forces in this case?****c. How far would the spring be compressed if the work done by non-conservative forces was zero?****d. In a new situation, with zero non-conservative forces, the spring is compressed by 0.50 m? What height was the ball dropped from this time?**---### Explanation of Concepts:#### Non-Conservative ForcesNon-conservative forces are those that cause energy to be lost from the system in the form of heat, sound, or other forms of internal energy. Unlike conservative forces (such as gravity and spring force), they do not store energy within the system which means that total mechanical energy is not conserved.#### Spring Constant (k)The spring constant (k) is a measure of the stiffness of the spring. It is given as 185 N/m.### Problem-Solving Steps:1. **Energy Conservation Check (Question a):** - Calculate the initial potential energy of the ball. - Calculate the spring potential energy when the spring is compressed. - Compare the initial potential energy with the spring potential energy to check conservation of energy.2. **Work Done by Non-Conservative Forces (Question b):** - Determine the difference between the initial potential energy and the spring potential energy. - This difference is the work done by non-conservative forces.3. **Spring Compression without Non-Conservative Forces (Question c):** - Use energy conservation principles to calculate the spring compression if no energy is lost to non-conservative forces.4. **New Height Calculation (Question d):** - Given the spring compression in the new scenario, use energy conservation principles to determine the new height of the ball's drop.--- Students can use these principles to solve real-world physics problems involving potential energy, work, and conservation of energy. For a deeper understanding, it is suggested to draw diagrams depicting energy transformations and forces at play.

Since you have asked question with multiple sub-parts in a single request, we would be answering…

1. A 1.75 kg ball rolls down an incline into a spring. The ball starts from rest at a height of 3.10 m above the spring and the spring constant is 185 m a. If the spring is compressed 65 cm when the ball comes to rest against the spring, was energy conserved? b. How much work was done by non-conservative forces in this case? c. How far would the spring be compressed if the work done by non-conservative forces was zero?

1. A 1.75 kg ball rolls down an incline into a spring. The ball starts from rest at a height of 3.10 m above the spring and the spring constant is 185 m a. If the spring is compressed 65 cm when the ball comes to rest against the spring, was energy conserved? b. How much work was done by non-conservative forces in this case? c. How far would the spring be compressed if the work done by non-conservative forces was zero?

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

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

### Non-Conservative Work

**1. A 1.75 kg ball rolls down an incline into a spring. The ball starts from rest at a height of 3.10 m above the spring, and the spring constant is 185 N/m.**

**a. If the spring is compressed 65 cm when the ball comes to rest against the spring, was energy conserved?**

**b. How much work was done by non-conservative forces in this case?**

**c. How far would the spring be compressed if the work done by non-conservative forces was zero?**

**d. In a new situation, with zero non-conservative forces, the spring is compressed by 0.50 m? What height was the ball dropped from this time?**

---

### Explanation of Concepts:

#### Non-Conservative Forces
Non-conservative forces are those that cause energy to be lost from the system in the form of heat, sound, or other forms of internal energy. Unlike conservative forces (such as gravity and spring force), they do not store energy within the system which means that total mechanical energy is not conserved.

#### Spring Constant (k)
The spring constant (k) is a measure of the stiffness of the spring. It is given as 185 N/m.

### Problem-Solving Steps:

1. **Energy Conservation Check (Question a):**
- Calculate the initial potential energy of the ball.
- Calculate the spring potential energy when the spring is compressed.
- Compare the initial potential energy with the spring potential energy to check conservation of energy.

2. **Work Done by Non-Conservative Forces (Question b):**
- Determine the difference between the initial potential energy and the spring potential energy.
- This difference is the work done by non-conservative forces.

3. **Spring Compression without Non-Conservative Forces (Question c):**
- Use energy conservation principles to calculate the spring compression if no energy is lost to non-conservative forces.

4. **New Height Calculation (Question d):**
- Given the spring compression in the new scenario, use energy conservation principles to determine the new height of the ball's drop.

---

Students can use these principles to solve real-world physics problems involving potential energy, work, and conservation of energy. For a deeper understanding, it is suggested to draw diagrams depicting energy transformations and forces at play.

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