Roller coaster problem involving velocity

In summary, the problem involves a roller coaster starting at the top of a steep hill with a speed of 7.0 km/h and descending an average angle of 43° below horizontal for a distance of 46.0 m. The coefficient of kinetic friction is given as 0.12. Using the equations Ff= U•Fn, F=ma, and Vf^2-Vo^2=2ad, the final speed at the bottom is calculated to be 7.04 km/h, which is incorrect. The correct answer should be 83.6 km/h. The error in the calculation was due to using the incorrect units for acceleration, which should be m/s^2.
  • #1
y90x
47
0

Homework Statement



A roller coaster reaches the top of the steepest hill with a speed of 7.0 km/h. It then descends the hill, which is at an average angle of 43° below horizontal and is 46.0 m long. What will its speed be when it reaches the bottom? Assume the coefficient of kinetic Friction is 0.12.

Homework Equations


Ff= U•Fn
F=ma
Vf ^2 - Vo^2 = 2ad

The Attempt at a Solution


Ff=U•Fn
Ff= U•mgcos(43)

F=ma
Mgsin(43) - Umgcos(43) =ma
The mass cancels out here so ,
gsin(43) - Ugcos(43) = a
5.82 = a

Vf= (square roof of>>) 2ad + vo ^2
Vf = (square roof of >> ) 2 • 5.82 • 0.046 + 7.0^2
Vf = 7.04 km/h

The answer should be 83.6 km/h
Where did I go wrong
 
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  • #2
y90x said:
5.82 = a
What are the units for this acceleration?
 
  • #3
TSny said:
What are the units for this acceleration?

I just realized it was m/s^2
Thank you
 

FAQ: Roller coaster problem involving velocity

1. How is velocity related to a roller coaster problem?

Velocity is a measure of an object's speed and direction. In a roller coaster problem, velocity is important because it determines how fast the roller coaster is moving and in what direction it is going.

2. What factors affect the velocity of a roller coaster?

The velocity of a roller coaster is affected by several factors, including the angle of the track, the height of the track, and the force of gravity. The design of the roller coaster and the weight of the train also play a role in determining the velocity.

3. How does velocity impact the experience of riding a roller coaster?

The velocity of a roller coaster directly affects the experience of riding it. The faster the roller coaster is moving, the more intense the forces will be on the riders. This can contribute to the thrill and excitement of the ride.

4. How is velocity calculated in a roller coaster problem?

To calculate the velocity of a roller coaster, you will need to use the equation v = √(2gh), where v is velocity, g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the roller coaster at a specific point. By plugging in the values for g and h, you can solve for the velocity of the roller coaster.

5. What is the relationship between velocity and energy in a roller coaster problem?

In a roller coaster problem, velocity and energy are closely related. As the roller coaster gains velocity, it also gains kinetic energy. This energy is then converted into potential energy as the roller coaster reaches the top of a hill, and then back into kinetic energy as it accelerates down the hill. The total amount of energy in the system remains constant, but it is constantly converting between kinetic and potential energies as the roller coaster moves along the track.

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