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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Question
Please help solve for Fnet
![## Scenario
A 1530 kg race car is driving around a circular track with a radius of \( r = 104 \) m. In the instant shown in the figure, the vehicle has a forward speed of \( v = 28.9 \) m/s and is slowing down at a rate of \( 4.30 \) m/s². We need to calculate:
- The magnitude of the net force, \( F_{\text{net}} \), acting on the vehicle at this time.
- The angle, \( \theta \), between the net force vector and the direction of motion.
## Diagram Analysis
The image depicts a race car maneuvering along a curved track. The following elements are notable:
- **Circular Track**: The track is shown with a radius \( r \), with the car positioned on its circular path.
- **Velocity Vector**: An arrow labeled \( v \) indicates the direction of the car's instantaneous velocity.
- **Central Force Vector**: An arrow pointing towards the center of the circle indicates the direction of the centripetal force.
## Calculations
### Known Values
- Mass, \( m = 1530 \) kg
- Radius, \( r = 104 \) m
- Speed, \( v = 28.9 \) m/s
- Deceleration, \( a = 4.30 \) m/s²
### Net Force, \( F_{\text{net}} \)
1. **Centripetal Force**:
\[
F_c = \frac{mv^2}{r}
\]
2. **Tangential Force**:
\[
F_t = ma
\]
3. **Net Force** (combination of radial and tangential forces):
\[
F_{\text{net}} = \sqrt{F_c^2 + F_t^2}
\]
### Angle, \( \theta \)
- Use trigonometric relations to determine the angle:
\[
\theta = \tan^{-1}\left(\frac{F_t}{F_c}\right)
\]
## Input Fields
- \( F_{\text{net}} = \) [Input Box N] (incorrect answer given: \( 2857.5 \) N)
- \( \theta = \) [Input Box °] (incorrect answer)
This interactive component allows learners to input their](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02b0d8dd-74c4-474c-82fb-c33b821e5fe0%2F868a97ff-12d4-4759-90e9-04529fa9d0d2%2Fbczco3k_processed.png&w=3840&q=75)
Transcribed Image Text:## Scenario
A 1530 kg race car is driving around a circular track with a radius of \( r = 104 \) m. In the instant shown in the figure, the vehicle has a forward speed of \( v = 28.9 \) m/s and is slowing down at a rate of \( 4.30 \) m/s². We need to calculate:
- The magnitude of the net force, \( F_{\text{net}} \), acting on the vehicle at this time.
- The angle, \( \theta \), between the net force vector and the direction of motion.
## Diagram Analysis
The image depicts a race car maneuvering along a curved track. The following elements are notable:
- **Circular Track**: The track is shown with a radius \( r \), with the car positioned on its circular path.
- **Velocity Vector**: An arrow labeled \( v \) indicates the direction of the car's instantaneous velocity.
- **Central Force Vector**: An arrow pointing towards the center of the circle indicates the direction of the centripetal force.
## Calculations
### Known Values
- Mass, \( m = 1530 \) kg
- Radius, \( r = 104 \) m
- Speed, \( v = 28.9 \) m/s
- Deceleration, \( a = 4.30 \) m/s²
### Net Force, \( F_{\text{net}} \)
1. **Centripetal Force**:
\[
F_c = \frac{mv^2}{r}
\]
2. **Tangential Force**:
\[
F_t = ma
\]
3. **Net Force** (combination of radial and tangential forces):
\[
F_{\text{net}} = \sqrt{F_c^2 + F_t^2}
\]
### Angle, \( \theta \)
- Use trigonometric relations to determine the angle:
\[
\theta = \tan^{-1}\left(\frac{F_t}{F_c}\right)
\]
## Input Fields
- \( F_{\text{net}} = \) [Input Box N] (incorrect answer given: \( 2857.5 \) N)
- \( \theta = \) [Input Box °] (incorrect answer)
This interactive component allows learners to input their
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