What is the minimum kinetic energy for this roller coaster ride?

In summary, the question asks for the minimum kinetic energy required at point A on a rollercoaster with a loop of radius 12m, a travel distance of 50m, and an average frictional force of 40N. With a mass of 50kg, the total energy required at the top of the loop can be calculated using the equations for kinetic energy, potential energy, and friction. However, without further information on the location of point A and the mass of the coaster, it is difficult to determine the exact minimum kinetic energy required.
  • #1
rrosa522
48
0

Homework Statement


A rollercoaster has a loop with a radius of 12m. The coaster travels 50m and at point A, enters the loop. The average frictional force on the coaster is 40N. The mass of passenger is 50kg. What is the minimum kinetic energy required at point A to generate a velocity of 27m/s at the top of the loop.

Homework Equations

The Attempt at a Solution


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Is my solution correct?

total distance to the top of the loop = (2*pi*r)/2+50= 87.68
total Energy required = Ek+Ep+ Ff
=((1/2)(27.)^2(50))+(9.81*50*24)+ (40*87.6)
=33636.25
 
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  • #2
Is there a diagram to accompany this question? It's difficult to tell from your description where exactly "point A" is located with respect to the loop's circumference, or what effect if any the 50 m travel distance up to point A has on subsequent motion. Is the mass of the coaster given?
 
  • #3
Check the rounding.
rrosa522 said:
What is the minimum kinetic energy required at point A to generate a velocity of 27m/s at the top of the loop.
A is a point on the loop, why did you take friction before point A into account?
 

Related to What is the minimum kinetic energy for this roller coaster ride?

1. What is kinetic energy?

Kinetic energy is the energy that an object possesses due to its motion. It is a form of energy that is dependent on an object's mass and velocity.

2. Why is kinetic energy important in roller coaster rides?

Kinetic energy is important in roller coaster rides because it is the energy that allows the roller coaster to move and perform various motions and stunts. Without sufficient kinetic energy, the roller coaster would not be able to complete its ride.

3. How is the minimum kinetic energy for a roller coaster ride determined?

The minimum kinetic energy for a roller coaster ride is determined by considering the height, mass, and maximum velocity of the roller coaster. The ride must have enough kinetic energy to overcome the force of gravity and complete its path without stopping.

4. What factors can affect the minimum kinetic energy for a roller coaster ride?

The factors that can affect the minimum kinetic energy for a roller coaster ride include the height of the ride, the mass of the roller coaster, and any forces acting upon the roller coaster such as friction or air resistance.

5. How does the minimum kinetic energy for a roller coaster ride impact the experience of riders?

The minimum kinetic energy for a roller coaster ride can impact the experience of riders by determining the speed and intensity of the ride. A higher minimum kinetic energy can result in a more thrilling and exciting ride, while a lower minimum kinetic energy may result in a slower and less intense ride.

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