A 1,730 KG car traveling at a rate of 166Kph is racing around a flat circular tr

ID: 1414917 • Letter: A

Question

A 1,730 KG car traveling at a rate of 166Kph is racing around a flat circular track, maintaining a perfectly circular 2 Km path.

Please SHOW STEP BY STEP AS CLEAR AND SIMPLE AS POSSIBLE

a. What is the centripetal force acting on the car?

b. What is the minimum coefficient of statistic friction between the tires and the track that will maintain this situation?

c. If the tires have a radius of 1.2m, what is the angular velocity of the tire?

d. How many rotation do the tires make on a single loop around the track?

here,

mass of car , m = 1730 kg

speed of car , v = 166 kph

v = 46.11 m/s

radius , R = 2000 m

centripital force acting on the car , F = m* v^2 /R

F = 1730 * 46.11^2 /2000

F = 1839.19 N

let the minimum coefficient of friction be uk

uk * m * g = F

uk * 1730 * 9.8 = 1839.39

uk = 0.108

radius of tires , r = 1.2 m

angular velocity , w= v/r

w = 46.11 /1.2 = 38.43 rad/s

let the number of rotation be n

n * 2 * pi * r = 2 * pi * R

n * 1.2 = 2000

n = 1666.67

number of rotations are 1666.67

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