Answer to Question #296363 in Mechanics | Relativity for micheal

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 attaches to the roof of her car. A friend riding in the car

with her observes that the plumb bob hangs at an angle of 15.0° from the vertical

when the car has a speed of 23.0 m/s.

A. What is the radius of the curve? (8 marks)

B. What is the centripetal acceleration of the car rounding the curve? (7 marks)

C. What is the speed of the car if the plumb bob deflection is 9.00° while

rounding the same curve? (5 marks)

Answer 1

a)

$\tan \alpha=\frac{v^2}{rg},$

$r=201~m,$

b)

$a=\frac{v^2}r=2.6~\frac{m}{s^2},$

c)

$v=\sqrt{gr\tan\beta}=17.7~\frac ms.$