Question

1. you have been asked to determine if a concept for a roller coaster is safe for people to ride. the safety guidelines state you cannot exceed 2000 n of force for a 70 kg rider. the current blueprint states the radius of the smallest loop decreases to 8 meters, and the cart will have a velocity of 21 m/s. what is the centripetal force and will the ride be safe?

Explanation:

Step1: Recall centripetal force formula

The formula for centripetal force is \(F = \frac{mv^{2}}{r}\), where \(m = 70\space kg\), \(v = 21\space m/s\), and \(r=8\space m\).

Step2: Substitute values into the formula

Substitute the values: \(F=\frac{70\times(21)^{2}}{8}\). First, calculate \((21)^{2}=441\). Then \(70\times441 = 30870\). Now, \(F=\frac{30870}{8}=3858.75\space N\).

Answer:

No, it is significantly over 2000 N