A roller-coaster car has a mass of 490 kg when fully loaded with passengers. The

Question

A roller-coaster car has a mass of 490 kg when fully loaded with passengers. The path of the coaster from its initial point shown in the figure to point B involves only up-and-down motion (as seen by the riders), with no motion to the left or right. Assume the roller-coaster tracks at points and are parts of vertical circles of radius r_1 = 10.0 m and r_2 = 15.0 m, respectively. If the vehicle has a speed of 20.5 m/s at point what is the force exerted by the track on the car at this point? What is the maximum speed the vehicle can have at and still remain on the track?

Explanation / Answer

a) Applying Newton’s second law to the car,

Fn- mg = Fc

Fn- mg = mv^2/r

Fn = mg + mv^2/r

Fn = 490*9.8 + 490*20.5^2/10 = 25394.25 N

b) Applying Newton’s second law to the car,

-Fn- mg =- Fc

-Fn- mg = -mv^2/r

At max speed Fn =0 N

- mg = -mv^2/r

mg = mv^2/r

g=v^2/r

v=sqrt(gr) = sqrt(9.8*15) = 12.12m/s

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