A student builds and calibrates an accelerometer and uses it to determine the sp

Question

A student builds and calibrates an accelerometer and uses it to determine the speed of her car around a certain unbanked highway curve. The accelerometer is a plumb bob with a protractor that she attaches to the roof of her car. A friend riding in the car with the student observes that the plumb bob hangs at an angle of 13.0° from the vertical when the car has a speed of 25.0 m/s.

(a) What is the centripetal acceleration of the car rounding the curve?
m/s2
(b) What is the radius of the curve?
m
(c) What is the speed of the car if the plumb bob deflection is 9.00° while rounding the same curve?
m/s

Explanation / Answer

here,

theta = 13 degree

speed , v = 25 m/s

(a)

let the mass of the bob be m and tension in the string be t

t * cos(theta) = m * g ...(1)

and

t * sin(theta) = m * a ...(2)

from (1) and (2)

tan(theta) = a/g

a = g * tan(theta)

a = 9.8 * tan(13) = 2.26 m/s^2

the centripital accelration is 2.26 m/s^2

(b)

let the radius of curve be r

v^2/r = a

25^2 /r = 2.26

r= 276.24 m

the radius of the curve is 276.24 m

(c)

from (1)

ac = g * tan(theta)

let the speed of car be v' when theta = 9 degree

v'^2 /276.24 = 9.8 * tan(9)

v' = 20.71 m/s

the speed of car is 20.71 m/s

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