32. A roller-coaster track has six semicircular "dips" with different radii of curvature. The same roller-coaster cart rides through each dip at a different speed. For the different values given for the radius of curvature R and speed v, rank the magnitude of the force of the roller-coaster track on the cart at the bottom of each dip. Rank from largest to smallest. To rank items as equivalent, overlap them. v= 4 v = 12 v = 16 m/s レ=8 レ=4 m/s v = 16 m/s m/s m/s m/s R= 15 R= 15 R= 15 R= 30 R= 30 R= 60 m m m
32. A roller-coaster track has six semicircular "dips" with different radii of curvature. The same roller-coaster cart rides through each dip at a different speed. For the different values given for the radius of curvature R and speed v, rank the magnitude of the force of the roller-coaster track on the cart at the bottom of each dip. Rank from largest to smallest. To rank items as equivalent, overlap them. v= 4 v = 12 v = 16 m/s レ=8 レ=4 m/s v = 16 m/s m/s m/s m/s R= 15 R= 15 R= 15 R= 30 R= 30 R= 60 m m m
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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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Number 32
![**Exercise 32: Roller Coaster Track Physics**
A roller-coaster track has six semicircular "dips" with different radii of curvature. Each dip is navigated at different speeds. For the various values of radius \( R \) (in meters) and speed \( v \) (in meters per second) at the bottom of each dip, rank the magnitude of the force. Rank from largest to smallest, noting ties with equal overlap.
### Values for Dips:
1. \( R = 15 \, \text{m} \), \( v = 4 \, \text{m/s} \)
2. \( R = 15 \, \text{m} \), \( v = 8 \, \text{m/s} \)
3. \( R = 15 \, \text{m} \), \( v = 12 \, \text{m/s} \)
4. \( R = 30 \, \text{m} \), \( v = 16 \, \text{m/s} \)
5. \( R = 30 \, \text{m} \), \( v = 16 \, \text{m/s} \)
6. \( R = 60 \, \text{m} \), \( v = 16 \, \text{m/s} \)
### Diagram:
- The diagram shows a semicircular dip with a radius \( R \) and a cart at the lowest point.
Each dip has a different combination of radius and speed, which affects the force experienced by the coaster at the bottom of each dip. Your task is to rank these forces, understanding that the centripetal force experienced depends on both the speed and radius of curvature.
Keep in mind the formula for centripetal force:
\[ F = \frac{mv^2}{R} \]
Where \( F \) is the centripetal force, \( m \) is the mass of the object, \( v \) is the velocity, and \( R \) is the radius of the circular path.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc609cf24-1b53-4e12-a93f-3be4e30d8479%2Fc4b9e88d-ed14-45be-b6c7-a3fede185d91%2Fn9cmsp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise 32: Roller Coaster Track Physics**
A roller-coaster track has six semicircular "dips" with different radii of curvature. Each dip is navigated at different speeds. For the various values of radius \( R \) (in meters) and speed \( v \) (in meters per second) at the bottom of each dip, rank the magnitude of the force. Rank from largest to smallest, noting ties with equal overlap.
### Values for Dips:
1. \( R = 15 \, \text{m} \), \( v = 4 \, \text{m/s} \)
2. \( R = 15 \, \text{m} \), \( v = 8 \, \text{m/s} \)
3. \( R = 15 \, \text{m} \), \( v = 12 \, \text{m/s} \)
4. \( R = 30 \, \text{m} \), \( v = 16 \, \text{m/s} \)
5. \( R = 30 \, \text{m} \), \( v = 16 \, \text{m/s} \)
6. \( R = 60 \, \text{m} \), \( v = 16 \, \text{m/s} \)
### Diagram:
- The diagram shows a semicircular dip with a radius \( R \) and a cart at the lowest point.
Each dip has a different combination of radius and speed, which affects the force experienced by the coaster at the bottom of each dip. Your task is to rank these forces, understanding that the centripetal force experienced depends on both the speed and radius of curvature.
Keep in mind the formula for centripetal force:
\[ F = \frac{mv^2}{R} \]
Where \( F \) is the centripetal force, \( m \) is the mass of the object, \( v \) is the velocity, and \( R \) is the radius of the circular path.
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