Roller coaster problem A roller coaster shown below is built in your town. The r

ID: 2263996 • Letter: R

Question

Roller coaster problem

A roller coaster shown below is built in your town. The radius of the circular part is 20 meters. As a

physics student, you are invited to take the first ride. You found that the speed of the car at the

bottom of the circular motion is 35 m/s. A full load car weighs 5000kg. Assume energy is not

dissipated in the process.

(a) Find the normal force on the car due to the track at the bottom of the

track.

(b) Find the speed of the car at the top of the circle. (Hint: consider energy)

(d) What is the minimum height H required for the car to reach the top of

the circle? (Assume the car starts with zero velocity at the top of the hill.)

a) mg+mv^2/r = 5000*9.8 + 5000*35^2/20 = 355250N

b) 2mgr = 0.5mv^2 - 0.5mV^2

4gr = v^2 - V^2

V^2 = 35^2 - 4*9.8*20 = 441

V = 21m/s

c) N = mV^2/r - mg = 5000*21^2/20 - 5000*9.8 = 61250N

d) let minimum speed needed at the top of circle be v1

mv1^2/r = mg

v1 = sqrt(gr) = sqrt(9.8*20) = 14m/s

Conserving energy,

mgH - mg(2r) = 0.5mv1^2

gH = 0.5v1^2 + 2gr = 0.5*14^2 + 2*9.8*20 = 490

H = 50m

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