Problem 5.110 A road heading due east passes over a small il.You of the hill, wh

Question

Problem 5.110 A road heading due east passes over a small il.You of the hill, where the shape of the roadway is well A road heading due east passes over a small hill. You drive a car of mass m at constant speed v over the top approximated as an arc of a circle with radius R Sensors have been placed on the road surface there to measure the downward force that cars exert on the surface at various speeds. The table gives values of this force versus speed for vour car is shown in the table below. Treat the car as a particle Speed (m/s) 6.00 8.00 10.0 12.0 14.0 16.0 Force (N) 8100 7690 7050 6100 5200 4200

Explanation / Answer

Let us find the equation of this straight line
(F-8100)/ (v^2-36) = (4200-8100) / (256-36)
(F-8100)/ (v^2-36) =-17.73
F-8100 = -17.73V^2 + 638.2
F= 8738.2 - 17.73 V^2

F measure is nothing but reaction.
F = mg- mV^2/R

Part C:

SO,
m*g = 8738.2
m = 8738.2/9.8
m=891.7 Kg

Part D:

m/R = 17.73
R = 891.7/17.73
R= 50.3 m

Part E:

maximum speed is when F=0
F = mg- mV^2/R
0 = mg- mV^2/R
V^2/R = g
V^2 = 9.8*50.3
V = 22.2 m/s
Answer: 22.2 m/s

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