Show My Work roler-coasber cat has a mass of 533 kg when fully loaded with passe

Question

Show My Work roler-coasber cat has a mass of 533 kg when fully loaded with passengers. The path of the coasber from its inieiar point shown in the figure to point s involves only up and-down motion (as seen by the nders), with no motien to the let or right. Assume the roller coaster tracks at points and ane parts of vertical dlrdies of radhus r-10.0 m and r -15.0 m a tr the vehicle han a speed of 19.5 mjs at point &what; the farce eserted by the track on the car at this point a) whet s the maxmum speed he veice can eand stil remain on the track Show My Work

Explanation / Answer

Here ,

mass, m = 513 Kg

a) r1 = 10 m

at the point A

force exerted by tracks = m g + m * v^2/r1

force exerted by tracks = 513 * (9.8 + 19.5^2/10)

force exerted by tracks = 24500 N

the force exerted by tracks is 24500 N

b)

as the highest point B

let the maximum velocity is v

m * g - m * v^2/r2 = 0

9.8 - v^2/15 = 0

solving for v

v = 12.12 m/s

the maximum speed possible is 12.12 m/s

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