Solving for Speed on a Roller Coaster's Top of Hill

In summary, the conversation discusses the calculation of the velocity of a roller coaster moving over a circular rise with a radius of 18 meters. The passengers on the coaster "feel light" at the top of the hill, with an apparent weight of only 60% of their true weight. The correct solution involves using Newton's second law for circular motion to find the net force at the top of the hill, which is 40% of the passengers' weight. The final answer for the velocity is 8.4 m/s.
  • #1
SilverAu
9
0

Homework Statement


A roller coaster car is going over the top of a 18-m- radius circular rise. At the top of the hill, the passengers "feel light," with an apparent weight only 60% of their true weight. How fast is the coaster moving?

Homework Equations


I think F=mv^2/ (r)
F=ma

The Attempt at a Solution


Attempt:
F=mv^2/r
(.6)g=v^2/r
(9.8*.6)r=v^2
5.88*18=v^2
v=10.3 m/s My answer is said to be wrong
 
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  • #2
This is not advanced physics, so moving to the intro physics section.
 
  • #3
SilverAu said:

Homework Statement


A roller coaster car is going over the top of a 18-m- radius circular rise. At the top of the hill, the passengers "feel light," with an apparent weight only 60% of their true weight. How fast is the coaster moving?

Homework Equations


I think F=mv^2/ (r)
F=ma

The Attempt at a Solution


Attempt:
F=mv^2/r
(.6)g=v^2/r
(9.8*.6)r=v^2
5.88*18=v^2
v=10.3 m/s My answer is said to be wrong
You did not calculate what the question asks.
It's not the centripetal force which is 60% of the weight.
Draw a diagram with all the forces.
 
  • #4
OK well if I am solving for the velocity of the moving coaster, how would I do that because I've drawn the diagram with forces and I don't see it.
 
  • #5
Write Newton's second law for circular motion. The acceleration is the centripetal acceleration.
What is the expression for the net force at the top of the hill?
 
  • #6
If they only felt 0.6 of their weight then the centripetal force on them is 1- 0,6= 0.4 of their weight.
 
  • #7
Yeah I actually just figured it out, that is the only thing I messed up... Should be
F=mv^2/r
(.4)g=v^2/r
(9.8*.4)r=v^2
3.92*18=v^2
v=8.4m/s
Thanks for helping you guys
 

1. How is the speed on a roller coaster's top of hill calculated?

The speed on a roller coaster's top of hill is calculated using the formula v = √(2gh), where v is the final velocity, g is the acceleration due to gravity, and h is the height of the hill.

2. What factors affect the speed on a roller coaster's top of hill?

The factors that affect the speed on a roller coaster's top of hill include the height of the hill, the angle of the track, the mass of the roller coaster and its passengers, and any external forces such as friction or air resistance.

3. Why is it important to solve for speed on a roller coaster's top of hill?

Solving for speed on a roller coaster's top of hill is important because it helps engineers and designers ensure that the roller coaster is safe and exciting for riders. It also allows them to optimize the design for the desired speed and experience.

4. Can the speed on a roller coaster's top of hill be changed?

Yes, the speed on a roller coaster's top of hill can be changed by adjusting the height of the hill or the angle of the track. Other factors such as the mass of the roller coaster and external forces can also affect the speed.

5. How does the speed on a roller coaster's top of hill affect the rest of the ride?

The speed on a roller coaster's top of hill affects the rest of the ride by determining the amount of kinetic energy that the roller coaster has at the top of the hill. This energy is then converted into different forms as the roller coaster continues along the track, creating the thrilling twists, turns, and drops that make roller coasters so exciting.

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