A 1000 kg car starts from rest at point 1 and moves without friction down the track as shown in the figure. At point 2, the radius od curvature of the track is 6m.

Options

A. the force exerted by the track on the car at point 2 is 4000 kg wt
B. the force exerted by the track on the car at point 2 is 5000 kg wt
C. the minimum safe value of the radius of curvature at point 3 is 15 m
D. the minium safe value of the radius of curvature at point 3 is 10 m

Answer

B, C

Explanation

By work and energy theorem from point 1 to 2
`0+mg(12)=(1)/(2)mv_(2)^(2)` and by NLM at 2
`N-mg=mv_(2)^(2)//R`
N = 5 mg
At point 3
`0+ mg(12-4.5)=(1)/(2)mv_(3)^(2)`
`v_(3)=sqrt(15g)m//s`
NLM at point 3
`mg=m(v_(3)^(2)//r)`
`r = 15 m`