1. A 90.0 kg crate is being pushed across a level floor at a constant speed by a 260 N force at an angle of 28.0° below the horizontal. The surface is not frictionless. a) Draw a free body diagram that includes all of the forces exerted on the crate, including a labeled system coordinate. FN FC0328 mg b) What are the algebraic expressions for the normal force (FN) and the coefficient of kinetic friction between the crate and the floor? EF $28
1. A 90.0 kg crate is being pushed across a level floor at a constant speed by a 260 N force at an angle of 28.0° below the horizontal. The surface is not frictionless. a) Draw a free body diagram that includes all of the forces exerted on the crate, including a labeled system coordinate. FN FC0328 mg b) What are the algebraic expressions for the normal force (FN) and the coefficient of kinetic friction between the crate and the floor? EF $28
Physics for Scientists and Engineers: Foundations and Connections
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ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter6: Applications Of Newton’s Laws Of Motion
Section: Chapter Questions
Problem 76PQ: Chris, a recent physics major, wanted to design and carry out an experiment to show that an objects...
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![### Physics Problem: Force and Motion on a Crate
#### Problem Statement
A 90.0 kg crate is being pushed across a level floor at a constant speed by a 260 N force at an angle of 28.0° below the horizontal. The surface is not frictionless.
#### Question a
**a)** Draw a free-body diagram that includes all of the forces exerted on the crate, including a labeled system coordinate.
**Free-Body Diagram:**
- **Diagram Description:**
- There is a rectangular block labeled "m" to represent the crate.
- A force, \( F \), is applied at an angle of 28° below the horizontal.
- The components of the applied force are broken down into \( F \cos 28° \) (horizontal component) and \( F \sin 28° \) (vertical component pointing downwards).
- The normal force, \( F_N \), is acting upwards.
- The gravitational force, \( mg \), is acting downwards.
#### Question b
**b)** What are the algebraic expressions for the normal force (\( F_N \)) and the coefficient of kinetic friction between the crate and the floor?
\[ \sum F = 0 \]
#### Question c
**c)** Calculate the magnitude of the normal force and the coefficient of kinetic friction between the crate and the floor.
#### Solution Explanation
1. **Free-Body Diagram Analysis:**
- From the free-body diagram, list all forces acting on the crate:
- Normal Force (\( F_N \))
- Gravitational Force (\( mg \))
- Applied Force (\( F \)) divided into \( F \cos 28° \) and \( F \sin 28° \)
2. **Equilibrium Conditions:**
- Since the crate is moving at a constant speed, the acceleration is zero, meaning the sum of forces in both the x (horizontal) and y (vertical) directions must be zero.
- Horizontal Direction:
\[ \sum F_x = F \cos 28° - F_{\text{friction}} = 0 \]
- So, the frictional force \( F_{\text{friction}} = F \cos 28° \).
- Vertical Direction:
\[ \sum F_y = F_N + F \sin 28° - mg = 0 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88cd9656-9419-481b-bc0b-e9aadd0312cb%2Fff8e1114-b215-4e69-85b5-41404ecc2e6a%2Fnj7iww7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Physics Problem: Force and Motion on a Crate
#### Problem Statement
A 90.0 kg crate is being pushed across a level floor at a constant speed by a 260 N force at an angle of 28.0° below the horizontal. The surface is not frictionless.
#### Question a
**a)** Draw a free-body diagram that includes all of the forces exerted on the crate, including a labeled system coordinate.
**Free-Body Diagram:**
- **Diagram Description:**
- There is a rectangular block labeled "m" to represent the crate.
- A force, \( F \), is applied at an angle of 28° below the horizontal.
- The components of the applied force are broken down into \( F \cos 28° \) (horizontal component) and \( F \sin 28° \) (vertical component pointing downwards).
- The normal force, \( F_N \), is acting upwards.
- The gravitational force, \( mg \), is acting downwards.
#### Question b
**b)** What are the algebraic expressions for the normal force (\( F_N \)) and the coefficient of kinetic friction between the crate and the floor?
\[ \sum F = 0 \]
#### Question c
**c)** Calculate the magnitude of the normal force and the coefficient of kinetic friction between the crate and the floor.
#### Solution Explanation
1. **Free-Body Diagram Analysis:**
- From the free-body diagram, list all forces acting on the crate:
- Normal Force (\( F_N \))
- Gravitational Force (\( mg \))
- Applied Force (\( F \)) divided into \( F \cos 28° \) and \( F \sin 28° \)
2. **Equilibrium Conditions:**
- Since the crate is moving at a constant speed, the acceleration is zero, meaning the sum of forces in both the x (horizontal) and y (vertical) directions must be zero.
- Horizontal Direction:
\[ \sum F_x = F \cos 28° - F_{\text{friction}} = 0 \]
- So, the frictional force \( F_{\text{friction}} = F \cos 28° \).
- Vertical Direction:
\[ \sum F_y = F_N + F \sin 28° - mg = 0 \]
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