Question

3. A car with mass m travels over a hill with a radius of curvature of r at a speed of 15 m/s. What is the normal force on the car when the car is at the top of the hill? (6 pts) the car has a mass of 1200 Kilograms and the radius of curvature is 25 meters 4. A student with a mass of m rides a roller coaster with a loop with a radius of curvature of r. What is the minimum speed the rollercoaster can maintain and still make it all the way around the loop? (6 pts) the radius of curvature is 6.0 meters, the mass of the rider is 60 Kg

Answer 1

Given, mano of car m = 1200 Radius of cuivature of roller coaster in n = 6.om. Radius of curvature of hell B= 25 m of cart V = 15 mis. The Care han circular motion. The gravitational force on car in The relocity fg = mg. טדס mg care in ac = The normal force on the car in N. The centripetal acceleration of V 2 The normal force in smaller than fg using newton's law of motion. = mac fg -N = N = mva =) mg = N = mg n 2 m (g-v2 = 1200 (9,8 152 25 :) 1200 (9.8-9) =) N = 960 Netwon. The normal force on the car when it at the top of the hill in 960N. m = 60 kg of rider in Mann of the nider m= 60 at the minimum ve relocity Umin. The normal krce on the rider in also directed down wardr. Ety - mac =) -N-mg =-mac =) (Nting) m = ac ng =) ~2 +g

To still make the rider all the way around the hoop the normal force on rider must be zero. g = 2a Zarg = = rng - 6.0x0.8 av = 7.67 mis mis 22 Vmen - I .67 mis. The minimum speed in 4,67 mis