3. A 2.00-m long air track rests on a horizontal surface with a 10.0-cm high support under one end. A 50.0-g glider (a cart-like object that floats on a cushion of air) is released from rest et the elevated end of the air track. For the purposes of this problem, use the approximation of 10.0 m/s² for the acceleration due to gravity near Earth's surface. ituetion described in the problem stotom
3. A 2.00-m long air track rests on a horizontal surface with a 10.0-cm high support under one end. A 50.0-g glider (a cart-like object that floats on a cushion of air) is released from rest et the elevated end of the air track. For the purposes of this problem, use the approximation of 10.0 m/s² for the acceleration due to gravity near Earth's surface. ituetion described in the problem stotom
College Physics
11th Edition
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Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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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 Inclined Plane and Air Track
#### Problem Statement:
A 2.00-m long air track rests on a horizontal surface with a 10.0-cm high support under one end. A 50.0-g glider (a cart-like object that floats on a cushion of air) is released from rest at the elevated end of the air track. For the purposes of this problem, use the approximation of 10.0 m/s² for the acceleration due to gravity near Earth's surface.
#### Tasks:
a. **Draw a pictorial representation of the situation described in the problem statement.**
*Hint: Sketch an inclined plane with a 2.00-meter length and one end elevated by 10.0 cm.*
b. **Determine the angle of elevation of the air track.**
*Hint: Use trigonometric ratios (sin, cos, tan) based on the height and length of the track.*
c. **Find the acceleration of the glider.**
*Hint: Consider the component of gravitational acceleration acting along the inclined plane.*
d. **How fast will the glider be moving when it has traveled 100 cm down the inclined plane?**
*Hint: Use kinematic equations to determine the final velocity, considering initial velocity and constant acceleration.*
e. **How long will it take the glider to travel 100 cm down the inclined plane?**
*Hint: Use kinematic equations to find time, based on distance, initial velocity, and acceleration.*
#### Solutions:
1. **Pictorial Representation of the Situation:**
Illustrate an inclined plane with a length of 2.00 meters. The lower end of the track is on the ground, while the upper end is elevated by 10.0 cm.
2. **Angle of Elevation (θ):**
\[
\text{tan}(\theta) = \frac{\text{height}}{\text{base}} = \frac{10.0 \, \text{cm}}{200 \, \text{cm}} = \frac{0.1}{2} = 0.05
\]
\[
\theta = \text{tan}^{-1}(0.05) \approx 2.86^\circ
\]
3. **Acceleration of the Glider (a):**
\[
a = g \cdot \sin(\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3524539-73d7-4b1e-9607-006acd5ee568%2Ff4425e83-5975-4e96-9539-5687862029be%2Fj0vj20t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Physics Problem on Inclined Plane and Air Track
#### Problem Statement:
A 2.00-m long air track rests on a horizontal surface with a 10.0-cm high support under one end. A 50.0-g glider (a cart-like object that floats on a cushion of air) is released from rest at the elevated end of the air track. For the purposes of this problem, use the approximation of 10.0 m/s² for the acceleration due to gravity near Earth's surface.
#### Tasks:
a. **Draw a pictorial representation of the situation described in the problem statement.**
*Hint: Sketch an inclined plane with a 2.00-meter length and one end elevated by 10.0 cm.*
b. **Determine the angle of elevation of the air track.**
*Hint: Use trigonometric ratios (sin, cos, tan) based on the height and length of the track.*
c. **Find the acceleration of the glider.**
*Hint: Consider the component of gravitational acceleration acting along the inclined plane.*
d. **How fast will the glider be moving when it has traveled 100 cm down the inclined plane?**
*Hint: Use kinematic equations to determine the final velocity, considering initial velocity and constant acceleration.*
e. **How long will it take the glider to travel 100 cm down the inclined plane?**
*Hint: Use kinematic equations to find time, based on distance, initial velocity, and acceleration.*
#### Solutions:
1. **Pictorial Representation of the Situation:**
Illustrate an inclined plane with a length of 2.00 meters. The lower end of the track is on the ground, while the upper end is elevated by 10.0 cm.
2. **Angle of Elevation (θ):**
\[
\text{tan}(\theta) = \frac{\text{height}}{\text{base}} = \frac{10.0 \, \text{cm}}{200 \, \text{cm}} = \frac{0.1}{2} = 0.05
\]
\[
\theta = \text{tan}^{-1}(0.05) \approx 2.86^\circ
\]
3. **Acceleration of the Glider (a):**
\[
a = g \cdot \sin(\
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