Answer to Question #132195 in Mechanics | Relativity for Bri

Question

 You are on a clothoid roller coster upside down at the top of a loop with an accelerometer.

The radius of the loop's curvature is 18 m. You experience a force of 2.0 times your normal weight from your seat.

a) Identify the forces acting on the accelerometer

b) What reading will you observe at the top of the loop if the accelerometer is calibrated as in the image above?

c) If you actually tried to use an accelerometer like the one shown in the image above on a roller coaster, what likely sources of error would you expect?

2. A clothoid loop in a roller coaster has the same height as a circular loop but half the radius at the top. A rider at the top of either loop typically experiences a net force of 1.5mg. What is the ratio of the speed at the top of the circular loop to the speed at the top of the clothoid loop?

Answer 1

The two forces acting on accelerometer are:

                               i.           The earth gravitational force acting downward.

                              ii.           Centrifugal reaction in upward direction.

b)     Reading of accelerometer would be 4g as it is already at 1g when it was at rest.

the reading when at rest =1g

net acceleration reading =3g

$\therefore$ final reading =reading at rest + net acceleration reading

=1g+3g=4g

c)     Parallel error the speed of accelerometer hinters accurate reading.

Acceleration due to gravity varies with the sea level.

2.

 1.5mg= m${V^{2} \over R}$ ; $\sqrt{1.5}*gR$

      V_clo=$\sqrt{1.5}$ *gR_clo, V_cir==$\sqrt{1.5}$ *gR_cir

 = V_cir/V_clo =${\sqrt{1.5}gRcir \over \sqrt{1.5}gRclo}$

=

$\sqrt{Rcir/Rclo}$ = $\sqrt{2}$ =1.414214 $\implies$ 1.41421