A person builds and calibrates an accelerometer using a small mass, a string, an

Question

A person builds and calibrates an accelerometer using a small mass, a string, and a protractor. While riding in a car, the person’s friend observes the string to make an 18.00 angle with the vertical while the car is traveling at 25.0 m/s on an unbanked (horizontal) curve.

a) What is the radial acceleration of the car under these conditions? Draw a FBD of the mass as part of your solution.)

b) What is the radius of the curve?

c) What is the speed of the car if the pendulum hangs at an angle of 12.00 while rounding this same curve?

Explanation / Answer

a)Let magnitude of centripetal acceleration = a

In car's frame, the bob experiences a pseudo force of magnitude ma, where m = mass of the bob.

Forces on the bob are

1. Tension T in the string from which the bob is hanging

2. Weight mg downward

3. Pseudo force ma

Net force in vertical direction = 0

Therefore, T cos 18.0 - mg = 0

Or T = mg/cos 18.0 --------------------------(1)

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 ----------------------------(2)

= 9.8 * 0.268 m/s^2 = 3.18 m/s^2

b)Let r = radius of the curve

Speed v = 25 m/s

a = v^2/r
Or r = v^2/a
Or r = 25^2/3.18 m = 196.54 m
Ans: 196.54 m

c) In equation (2) in the solution to part (a), put 12.0 instead of 18.0

We get a = g*tan(12.0) = 2.08 m/s^2

a = v^2/r

Or v = sqrt(ar)

= sqrt(2.08 * 196.54) m/s

= 20.22 m/s

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