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 µ= 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? 2 m y E
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 µ= 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? 2 m y E
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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![**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 Description:**
- The diagram shows a curved, quarter-circle path starting at a height of 2 meters.
- The box slides from the top of this path onto a horizontal surface labeled with a reddish-brown line. This level surface has a length of 2 meters.
- The right end of the level surface leads to another quarter-circle curved surface.
- The height the box reaches on the second curve is marked as \( y \).
**Physics Concepts:**
1. **Conservation of Energy:**
- Initial Potential Energy on the first curve is converted to Kinetic Energy at the bottom.
- Some energy is lost due to friction on the level surface.
2. **Friction Calculations:**
- Work done by friction \( = \text{friction force} \times \text{distance} \).
- Friction force \( = \mu \times \text{normal force} = \mu \times m \times g \).
3. **Final Height Calculation:**
- After overcoming friction, the remaining kinetic energy allows the box to move up the second curve to height \( y \).
This problem helps in understanding energy conservation and the effect of friction on motion.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F632065a4-87e4-4db9-9a16-90da95c730a4%2F45fe34be-797a-420f-97bd-86723b6085e6%2F9vwo0va_processed.png&w=3840&q=75)
Transcribed Image Text:**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 Description:**
- The diagram shows a curved, quarter-circle path starting at a height of 2 meters.
- The box slides from the top of this path onto a horizontal surface labeled with a reddish-brown line. This level surface has a length of 2 meters.
- The right end of the level surface leads to another quarter-circle curved surface.
- The height the box reaches on the second curve is marked as \( y \).
**Physics Concepts:**
1. **Conservation of Energy:**
- Initial Potential Energy on the first curve is converted to Kinetic Energy at the bottom.
- Some energy is lost due to friction on the level surface.
2. **Friction Calculations:**
- Work done by friction \( = \text{friction force} \times \text{distance} \).
- Friction force \( = \mu \times \text{normal force} = \mu \times m \times g \).
3. **Final Height Calculation:**
- After overcoming friction, the remaining kinetic energy allows the box to move up the second curve to height \( y \).
This problem helps in understanding energy conservation and the effect of friction on motion.
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