Question

An engineer wishes to design a roller coaster so that

Answer 1

To prevent cars from falling, the radius at the top of the circle should be

small such cars inverted at the top remain attached during motion.

Correct response;

The radius of the coaster can be C) 20 m

Method by which the above option is selected

Mass of roller coaster car, m = 500 kg

Speed at the top of the circle, v = 20 m/s

Required:

The maximum radius of the circular path the roller coaster car.

Solution:

$\displaystyle Centrifugal \ force, \, F_{c} = \mathbf{\frac{m \cdot v^2}{r}}$

Where;

r = The radius of the circular path.

Weight of the roller coaster car = m·g = The centripetal force

Where;

g = Acceleration due to gravity = 9.81 m/s²

At equilibrium, we have;

Centrifugal force = Centripetal force

$\displaystyle \frac{m \cdot v^2}{r} = \mathbf{ m \cdot g}$

Therefore;

$\displaystyle r = \mathbf{ \frac{v^2}{g}}$

Which gives;

$\displaystyle r = \frac{20^2}{9.81} \approx 40.77$

The maximum radius for safety of a roller coaster, r ≈ 40.77 meters

$\displaystyle Range \ of \ radius \ of \ the \ circle = \frac{40.77}{4} \leq Radius \ of \ circle \leq 40.77$

Which gives;

Range of the radius of the circle = 10.2 ≤ Radius of circle ≤ 40.77

The correct option for safety considerations is therefore;

• C) 20 m

The possible question options are;

A) 5 m  B) 10 m  C) 20 m  D) 40 m  E) 80 m

Learn more about centripetal force here:

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