Work energy momentum ### Problem StatementA 0.40 kg small box starts from rest and slides down a frictionless curved surface (¼ of a circle) with a radius of 2.00 meters. At the bottom of the ramp, there is a level surface of length 2.00 meters with a coefficient of friction \( \mu = 0.4 \). After the level surface, the box slides up another frictionless curved surface on the other side (¼ of a circle). How high up the second curved surface does the box go?### Diagram ExplanationThe diagram illustrates the following:1. **Curved Surface 1 (Left Side)**: - The left quarter circle represents the initial frictionless curved surface. The box starts at the top of this curve.2. **Level Surface (Middle)**: - This is a straight section of length 2 meters. The box moves across this surface before reaching the next curve.3. **Curved Surface 2 (Right Side)**: - Another quarter circle on the right side shows the frictionless curved surface where the box ascends.4. **Heights**: - The radius of the curved surfaces is 2 meters, indicating the maximum height of the curves. - The height \( y \) represents how far up the second curve the box ascends after crossing the level surface.### Analytical Approach1. **Energy Conservation Principle**: - Calculate the initial potential energy at the top of the first curve. - Determine the work done against friction on the level surface.2. **Friction Work Calculation**: - Use the relation \( \text{Work} = \mu \times \text{normal force} \times \text{distance} \).3. **Final Potential Energy**: - Analyze how the change in mechanical energy affects the final height \( y \).This problem combines principles of energy conservation and the effects of friction to determine movement across different surfaces.

According to work energy theorem Work done = change in kinetic energy

4. A 0.40 kg small box starts from rest and slides down a frictionless curved surface ( % of a circle ) of radius = 2.00 meters, at the bottom of the ramp there is a level surface , length = 2.00 meters, with a coefficient of friction u= 0.4, after the level surface it slide up another frictionless curved surface on the other side (1/4 of a circle). How high up the second curved surface does the box go?

4. A 0.40 kg small box starts from rest and slides down a frictionless curved surface ( % of a circle ) of radius = 2.00 meters, at the bottom of the ramp there is a level surface , length = 2.00 meters, with a coefficient of friction u= 0.4, after the level surface it slide up another frictionless curved surface on the other side (1/4 of a circle). How high up the second curved surface does the box go?

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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Work energy momentum

### Problem Statement

A 0.40 kg small box starts from rest and slides down a frictionless curved surface (¼ of a circle) with a radius of 2.00 meters. At the bottom of the ramp, there is a level surface of length 2.00 meters with a coefficient of friction \( \mu = 0.4 \). After the level surface, the box slides up another frictionless curved surface on the other side (¼ of a circle). How high up the second curved surface does the box go?

### Diagram Explanation

The diagram illustrates the following:

1. **Curved Surface 1 (Left Side)**:
- The left quarter circle represents the initial frictionless curved surface. The box starts at the top of this curve.

2. **Level Surface (Middle)**:
- This is a straight section of length 2 meters. The box moves across this surface before reaching the next curve.

3. **Curved Surface 2 (Right Side)**:
- Another quarter circle on the right side shows the frictionless curved surface where the box ascends.

4. **Heights**:
- The radius of the curved surfaces is 2 meters, indicating the maximum height of the curves.
- The height \( y \) represents how far up the second curve the box ascends after crossing the level surface.

### Analytical Approach

1. **Energy Conservation Principle**:
- Calculate the initial potential energy at the top of the first curve.
- Determine the work done against friction on the level surface.

2. **Friction Work Calculation**:
- Use the relation \( \text{Work} = \mu \times \text{normal force} \times \text{distance} \).

3. **Final Potential Energy**:
- Analyze how the change in mechanical energy affects the final height \( y \).

This problem combines principles of energy conservation and the effects of friction to determine movement across different surfaces.

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