Question

A woman rides on a Ferris wheel of radius 16m that maintains the same speed throughout its motion. To better understand physics, she takes along a digital bathroom scale (with memory) and sits on it. When she gets off the ride, she uploads the scale readings to a computer and creates a graph of scale reading versus time. (Figure 1) Note that the graph has a minimum value of 510N and a maximum value of 666N . The acceleration due to gravity, g=9.80m/s2.
Figure

Answer 1

Answer:

Mass of the woman is 60 kg and constant speed of the wheel is 4.56 m/s

Explanation:

The maximum reading of the scale is when wheel is at the bottom position

So it is given as

$N_{max} = \frac{mv^2}{R} + mg$

Similarly the minimum value is when she is at the top position of the wheel

So it is given as

$N_{min} = mg - \frac{mv^2}{R}$

so from above two equations we have

$2mg = N_{max} + N_{min}$

$mg = \frac{510 + 666}{2}$

$mg = 588$

$m = 60 kg$

also the speed of the wheel is given as

$2\frac{mv^2}{R} = N_{max} - N_{min}$

$v = \sqrt{\frac{R(N_{max} - N_{min})}{2m}}$

$v = 4.56 m/s$