Question

4) When sitting in a roller coaster going through a vertical loop of radius of 8.5 meters, your "ap- parent' weight is the normal force provided by the seat, while your "true" weight is the gravitational force (which is unluckily unchangeable at mg) a) How fast must you be moving at the top of the vertical loop to achieve weightlessness (i.e., to have no apparent weight)? b) If moving at the same speed on the bottom of the vertical loop, what is your apparent weight then?

Answer 1

Solution: The net force at the top of the loop (i.e. the weight) F--mg - V (Considering the direction also) , where N is the normal reaction. F--mg+ a). Weightless -mg 0 - 18.5 x 9.8 = 9.12 m/s The required velocity is 9.12 m/s b). Force equation -mg 0 -m (9.8+9.76) = (-m x19.56 ) N Apparent weight at the bottom is (- mx19.56 ) N We can substitute the mass and calculate the weight.