A car with a mass of 1000 kg is traveling in a mountainous area with a constant

Question

A car with a mass of 1000 kg is traveling in a mountainous area with a constant speed of 73.6 km/h. The road is horizontal and flat at point A, horizontal and curved at points B and C.

https://s4.lite.msu.edu/res/msu/nagytibo/Mechanics/CircularMotion/Graphics/002a.gif

The radii of curvatures at B and C are: rB = 135 m and rC = 115 m. Calculate the normal force exerted by the road on the car at point A.

Now calculate the normal force exerted by the road on the car at point B. Incorrect.

And finally calculate the normal force exerted by the road on the car at point C.

Explanation / Answer

normal force exerted by road on the car at point A = weight of car = 1000*9.81 = 9810 N = W

at point B =W- ( mV^2) /R OR W + (m V^2)/R where m= 1000 kg V = 73.6 Km/h = 20.44 m/sec R = 135 m

(m*V^2)/ R= ( 1000* 20.44^2 )/135 = 3094.77 N

so normal reaction = 9810 +3094.77 = 12904.77 N ( curved surface is concave) OR N = 9810- 3094.77 = 6715 N (if curved surface convex)

at point C

(m*V^2)/ R = ( 1000* 20.44^2)/115 = 3632.98= 3633 N

normal reaction = 9810+3633 = 13443 N ( curved surface is concave) 0R N = 9810-3633 = 6177 N (if curved surface convex)

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