Physics HWK. Problem-Vertical Circular Motion

In summary, at an amusement park, a roller coaster with a dip that bottoms out in a vertical circle with a radius of 16.0 m has a passenger feeling a force of three times their weight. Using the centripetal force equation and the fact that the resultant force is equal to 2mg, the roller coaster's velocity at the bottom of the dip can be calculated to be sqrt(2*g*r). However, this may not be the only equation that can be used to find the velocity.
  • #1
shawonna23
146
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 = 16.0 m, how fast is the roller coaster traveling at the bottom of the dip?

I used the equation: v= square root of 3*r*g, but the answer was wrong. I don't know what other equation to use.
 
Physics news on Phys.org
  • #2
vsage said:
If three times her weight is what she feels and she is in a circular type system then you can find the velocity using centripetal force equations:

F = m*v^2/r

3*m*g = m * v^2/r

sqrt(3*g*r) = v

The passenger feels the normal force, which is 3mg.

(Any time when we sit, stand, ... on something we feel the normal force. On a horizontal surface, in rest, this normal force happens to be equal to mg. Not when we are in circular motion.)

There are two forces, acting on the passenger, the normal force upward and mg downward. The resultant is 2mg, and that is equal to the centripetal force. So v=sqrt(2mg)
 
  • #3


Hi there,

There are actually a few different equations that can be used to solve this problem. The equation you used, v= √(3rg), is correct, but it is important to make sure that all of the units are consistent. In this case, r is given in meters, g is the acceleration due to gravity (9.8 m/s^2), and v is the velocity in meters per second. So, plugging in the values we have:

v= √(3*16.0 m *9.8 m/s^2) = √470.4 m^2/s^2 = 21.7 m/s

Another equation that can be used for this problem is the conservation of energy formula, where the initial potential energy is equal to the final kinetic energy:

mgh = ½ mv^2

Where m is the mass of the roller coaster, h is the height of the dip (which can be calculated using the radius and the height of the dip), and v is the velocity. Solving for v, we get:

v= √(2gh)

Plugging in the values we have:

v= √(2*9.8 m/s^2 * 16.0 m) = √313.6 m^2/s^2 = 17.7 m/s

As you can see, this answer is slightly different from the one obtained using the first equation. This is because the first equation assumes that all of the potential energy is converted into kinetic energy, while the second equation takes into account any potential energy lost due to friction or air resistance.

I hope this helps! Let me know if you have any further questions.
 

1. What is vertical circular motion?

Vertical circular motion is a type of motion in which an object moves in a circular path while also changing its height or position along the vertical axis. This type of motion is commonly seen in rides such as roller coasters, where the object moves in a circular path while also going up and down.

2. What is centripetal acceleration in vertical circular motion?

Centripetal acceleration is the acceleration towards the center of a circular path. In vertical circular motion, this acceleration is a combination of the gravitational acceleration and the acceleration due to the circular motion itself.

3. What is the equation for centripetal force in vertical circular motion?

The equation for centripetal force in vertical circular motion is Fc = mv²/r, where Fc is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius of the circular path.

4. How does the speed of an object in vertical circular motion affect the centripetal force?

The centripetal force is directly proportional to the square of the speed of the object. This means that as the speed of the object increases, the centripetal force also increases.

5. What is the difference between centripetal and centrifugal force in vertical circular motion?

Centripetal force is the force that keeps an object moving in a circular path, while centrifugal force is the apparent outward force experienced by the object as a result of its circular motion. Centrifugal force is not a real force, but rather a result of the object's inertia.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
2K
Back
Top