A student builds andcalibrates an accelerometer, which she uses to determine the

Question

A student builds andcalibrates an accelerometer, which she uses to determine the speedof her car around a certain highway curve. The accelerometer is aplumb bob with a protrator that she attaches to the roof of hercar. A friend riding in the car with her observes that the plumbbob hangs at an angle of 8o from thevertical when the car has a speed of 24.6 m/s. The acceleration of gravityis 9.8 m/s2 .At this instant, what is the centripetalacceleration of the car rounding the curve? Answer in units ofm/s2. b)what is the radius of the curve(m). A student builds andcalibrates an accelerometer, which she uses to determine the speedof her car around a certain highway curve. The accelerometer is aplumb bob with a protrator that she attaches to the roof of hercar. A friend riding in the car with her observes that the plumbbob hangs at an angle of 8o from thevertical when the car has a speed of 24.6 m/s. The acceleration of gravityis 9.8 m/s2 .At this instant, what is the centripetalacceleration of the car rounding the curve? Answer in units ofm/s2. b)what is the radius of the curve(m). b)what is the radius of the curve(m).

Explanation / Answer

the horizatal force acting on the bob          F = mgsin       m = mass of the bob        g = accleration due togravity        = angle made withthe verticle    the force on the bob is due to the centripetalforce acting on it in circular motion               C.F = mv^2 / r = F = mg sin                               from the above relation we can solve for the radius of circularmotion of the car .                           r = v^2/g sin               v = speed of the car               r = radius of the track       centripetal accleration ofthe car , a = v^2 /r                                        

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