Question

Problems (6) and (7). Please be detailed with your answers.

6. The apparent weight of passengers (average mass of 75kg) on a roller coaster can decrease to zero as the car goes upside down in a loop-the-loop of 30.Om radius of curvature. Find the car's speed at the top of the loop if the passengers are to feel weightless. (12pts) 7. A new sports car is tested on a 500m diameter track. If the car speeds up at a steady 1.50m/s2, how long after starting is the magnitude of its centripetal acceleration equal to the tangential acceleration? For full credit draw a clear diagram showing both the centripetal and tangential accelerations. (15pts)

Answer 1

6) when centripetal acceleration is equal to acceleration due to gravity the apparent weight of the passengers becomes zero.

a_rad = g

v^2/r = g

v^2 = g*r

v = sqrt(g*r)

= sqrt(9.8*30)

= 17.1 m/s <<<<<<<<------------------------Answer

7) radius of the track, r = d/2 = 500/2 = 250 m

tangetnial acceleration, a = 1.50 m/s^2

let v is the speed of the car when the car's centripetal acceleration is equal to tangential acceleration.

a_centripetal = v^2/r

v^2 = a_centripetal*r

v = sqrt(a_centripetal*r)

= sqrt(1.5*250)

= 19.36 m/s

initial velocity, u = 0

let t is the time taken.

now use, t = (v - u)/a

= (19.36 - 0)/1.5

= 12.9 s <<<<<<<<<<----------------------Answer