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
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Author:Raymond A. Serway, Chris Vuille
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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.
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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