a student builds and calibrates an accelerometer, which she uses to determine th
ID: 2150350 • Letter: A
Question
a student builds and calibrates an accelerometer, which she uses to determine the speed of her car around a certain unbanked highway curve. the accelerometer is a plumb bob with a protractor that she attached to the roof of her car. A friend riding in the car with her observes that the plumb bob hangs at an angle of 18 degrees from the vertical when the car has a speed of 30 m/s.a) what is the centripetal acceleration of the car rounding the curve?
b)what is the radius of the curve?
c) what is the speed of teh car if the plumb bob deflection is 7 degrees while rounding the same curve?
Explanation / Answer
Therefore, T cos 18.0° - mg = 0 Or T = mg/cos 18.0= Net force in horizontal direction = 0 Therefore, ma = T sin 18.0° Using the value of T from equation (1) in the above equation, ma = (mg/cos 18.0°) * sin 18.0° Or ma = mg tan 18.0° Dividing both sides by m, a = g tan 18.0° = 9.8 * 0.0.32 m/s^2 = 3.18 m/s^2 Ans: 2.63 m/s^2 b)Let r = radius of the curve Speed v = 30m/ s a = v^2/r Or r = v^2/a Or r = 30^2/3.18 m = 283.01 m Ans: 283.01 m We get a = g tan 7.00° = 9.8 * 0.122 m/s^2 = 1.19m/s^2 a = v^2/r Or v = sqrt(ar) = sqrt(1.19 * 283.01) m/s = 18.35 m/s
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