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A company has asked you to design a new Gravitron ride. They have a motor that will spin the passengers at 26.1 m/s. How large the would the machine need to be in order for the passengers to feel 8g's of acceleration?

Answer 1

Adrian Ayala

I found: #8.7m#

I would say that the acceleration (centripetal) #a_c# should be equal to:

#8g=8*9.9=78.4#

So: #a_c=v^2/r=78.4# and: #r=v^2/78.4=(26.1)^2/78.4=8.68~~8.7m#

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Answer 2

Parker Abbott

To calculate the radius (r) of the Gravitron ride, you can use the formula: ( a = \frac{v^2}{r} ), where ( a ) is acceleration (in this case, 8g), ( v ) is the speed (26.1 m/s), and ( r ) is the radius. Rearrange the formula to solve for ( r ): ( r = \frac{v^2}{a} ). Substituting the given values, ( r = \frac{(26.1 , \text{m/s})^2}{8 \times 9.8 , \text{m/s}^2} ). Calculate the result.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.