Required information A roller-coaster car of mass 307 kg (including passengers) travels around a horizontal curve of radius 38.2 m. Its speed is 22.7 m/s. What is the magnitude of the total force exerted on the car by the track?
Required information A roller-coaster car of mass 307 kg (including passengers) travels around a horizontal curve of radius 38.2 m. Its speed is 22.7 m/s. What is the magnitude of the total force exerted on the car by the track?
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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![### Required Information
A roller-coaster car of mass 307 kg (including passengers) travels around a horizontal curve of radius 38.2 m. Its speed is 22.7 m/s.
**Question:**
What is the magnitude of the total force exerted on the car by the track?
**Answer:**
\[ \_\_\_ \text{ N} \]
### Explanation
This problem involves calculating the centripetal force exerted on the roller-coaster car as it moves around the curve. The centripetal force \( F \) can be calculated using the formula:
\[
F = \frac{mv^2}{r}
\]
Where:
- \( m \) is the mass of the car (307 kg),
- \( v \) is the speed of the car (22.7 m/s),
- \( r \) is the radius of the curve (38.2 m).
This calculation will give you the force in Newtons (N) exerted by the track on the car as it navigates the curve.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8fd20e11-2399-44a5-beb6-e921116d74ba%2F17e52548-302d-4b7a-801b-71bbb463f314%2Fbeyaslf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Required Information
A roller-coaster car of mass 307 kg (including passengers) travels around a horizontal curve of radius 38.2 m. Its speed is 22.7 m/s.
**Question:**
What is the magnitude of the total force exerted on the car by the track?
**Answer:**
\[ \_\_\_ \text{ N} \]
### Explanation
This problem involves calculating the centripetal force exerted on the roller-coaster car as it moves around the curve. The centripetal force \( F \) can be calculated using the formula:
\[
F = \frac{mv^2}{r}
\]
Where:
- \( m \) is the mass of the car (307 kg),
- \( v \) is the speed of the car (22.7 m/s),
- \( r \) is the radius of the curve (38.2 m).
This calculation will give you the force in Newtons (N) exerted by the track on the car as it navigates the curve.
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