Question

ers use a hill for riders to gain speed followed by an upside down loop. The loops are i large radius bottoms and small radius tops, and such a shape is called a clothoid. Answer designed with 1 out why the clothoid is used. ou answe The speed of the rollercoaster is 22 m/s at the bottom of the loop and 8 m/s at the top of the loop 1 10 m 2 5.0 m m 1.0 x 1o3 kg 03 g a Use quantitative force diagrams to determine the size of the force on the rider by the seat at the top and bottom of the loop. Now suppose the rollercoaster had been designed with the small 5 meter radius at the bottom and the large 10 meter radius at the top. Use quantitative force diagrams to determine the size of the force on the rider by the seat at the top and bottom of the loop. b. Why is the clothoid shape used in rollercoasters? c.

Answer 1

(a)

Let, Force on rider by seat = F

Net force = mv^2 / r

At bottom,

F - mg = mv^2 / r

F = mv^2 / r + mg

Force on rider by seat at the bottom,

F1 = (1000*22^2 / 10) + (1000*9.8)

F1 = 58200 N

Force on rider by seat at the top,

F2 = mv^2 / r - mg

Put all the values and use 9.8 m/s^2 for value of g.

F2 = (1000*8^2 / 5) - (1000*9.8)

F2 = 3000 N

(b)

Force on rider by seat at the bottom,

F1 = (1000*22^2 / 5) + (1000*9.8)

F1 = 106600 N

Force on rider by seat at the top,

F2 = mv^2 / r - mg

F2 = (1000*8^2 / 10) - (1000*9.8)

F2 = -3400 N

(c)

Clothoid shape is used in rollercoasters to maintain the forces on rollercoasters.

The radius of curvature at the top should be small. so that, the net force is larger than the force of gravity to continue the ride

on top. if the radius of curvature is too small at the bottom, the upward force on the person can be more than they can

tolerate.