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

## 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.

## 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

gneill
Mentor
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?

mfb
Mentor
Check the rounding.
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?