Please show work and equations used munt.ed 1 of 9 Problem A car travels at a sp

Question

Please show work and equations used munt.ed 1 of 9 Problem A car travels at a speed of 21 m/s around a curve of 27 m. m- 1500 kg Gi) What is the net centripetal force needed to keep the car from skidding sideways? (ii) Were there no friction between the car's tires and the road, what centripetal force would be provided just by banking the road at 29o? (iii) Now, suppose a friction force is also present and prevents the car from skidding. Calculate the magnitude of the normal force exerted on the car by the road's surface. (iv) Calculate the magnitude of the friction force Ca

Explanation / Answer

Given,

v = 21 m/s ; r = 27 m ; m = 1500 kg

i)We know that,

Fc = m v^2/R = 1500 x 21^2/27 = 24500 N

Hence, Fc = 2.45 x 10^4 N

ii)theta = 29 deg

Now the velocity will be:

v = sqrt (r g tan(theta))

v = sqrt (27 x 9.81 x tan29) = 12.11 m/s

Fc = m v^2/R = 1500 x 12.11^2/27 = 8.15 x 10^3 N

Hence, Fc = 8.15 x 10^3 N

iii)N = mg cos(theta)

N = 1500 x 9.81 x cos(theta) = 1.29 x 10^4 N

N = 1.29 x 10^4 N

iv)Ff = Fc - w

Ff = m v^2/R - N sin(theta)

Ff = 8.15 x 10^3 - 1.29 x 10^4 x sin30 = 1.7 x 10^3 N

Hence, Ff = 1.7 x 10^3 N

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