What is the speed of the roller coaster at the bottom of the dip?

In summary, the roller coaster at the amusement park has a dip with a radius of 22.0 m. At the bottom of the dip, a passenger experiences a force equal to three times their weight pushing on them. Using the equation Fn -mg= m(v^2/r), and plugging in 3m for Fn, we can calculate the speed of the roller coaster at the bottom of the dip. However, it is important to note that 3m should be multiplied by the force of gravity (g) in order to be correctly used in the equation. Once this correction is made, the calculations are correct and the speed of the roller coaster at the bottom of the dip can be accurately determined.
  • #1
Amber430
15
0
A roller coaster at an amusement park has a dip that bottoms out in a vertical circle of radius r. A passenger feels the seat of the car pushing upward on her with a force equal to three times her weight as she goes through the dip. If r = 22.0 m, how fast is the roller coaster traveling at the bottom of the dip?

At the bottom of the dip, Fn -mg= m(v^2/r). I plugged in 3m for Fn since it's 3 times her weight, and I'm not sure if I'm doing this right.
 
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  • #2
Amber430 said:
At the bottom of the dip, Fn -mg= m(v^2/r).
Good.
I plugged in 3m for Fn since it's 3 times her weight, and I'm not sure if I'm doing this right.
Careful. 3m is a mass, not a force. What's her weight? What's 3 times her weight?
 
  • #3
It looks like everything you have done is correct. When you say that you plugged in 3m for Fn you mean (3m)*g, right? If so, it looks correct.
 
  • #4
No, I was not using 3mg, just 3m. That's where I messed it up. It makes sense now, thank you so much!
 

FAQ: What is the speed of the roller coaster at the bottom of the dip?

What is centripetal acceleration?

Centripetal acceleration is the acceleration that an object experiences as it moves in a circular path. It is always directed towards the center of the circle and is caused by the force that is keeping the object in its circular motion.

What is the formula for calculating centripetal acceleration?

The formula for centripetal acceleration is a = v^2/r, where a is the centripetal acceleration, v is the velocity of the object, and r is the radius of the circular path.

How does centripetal acceleration differ from tangential acceleration?

Centripetal acceleration is always directed towards the center of the circle, while tangential acceleration is directed tangent to the circle. Centripetal acceleration also determines the change in direction of an object's motion, while tangential acceleration determines the change in speed.

What are some real-life examples of centripetal acceleration?

Some examples of centripetal acceleration include a car driving around a curved road, a ball on a string being swung in a circle, and planets orbiting around the sun.

How does centripetal acceleration relate to centripetal force?

Centripetal acceleration and centripetal force are directly related. Centripetal force is the force that causes centripetal acceleration, and they both have the same direction and magnitude. In other words, centripetal force is the force that keeps an object moving in a circular path, resulting in centripetal acceleration.

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