A woman rides on a Ferris wheel of radius 16m that maintains the same speed thro

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.

What is the woman's mass?

Express your answer in kilograms. Show all work.

Explanation / Answer

Refer above figure,

In figure Fn= normal force, Fc= centripetal force , mg= weight

Scale reads the normal force(Fn) of the woman’s feet

Applying Newton’s second law to point a

-Fn-mg= -Fc

Fn+mg= Fc

Fn= Fc-mg

Fn= mv^2/r –mg ---------------(1)

Applying Newton’s second law to point b

Fn-mg= Fc

Fn= Fc+mg

Fn= mv^2/r +mg ---------------(2)

eqn (1) and (2) indicate Fn is greatest at point b and least at point a

From data maximum value for Fn = 666N and minimum Fn = 510N

Hence

Fn= mv^2/r +mg

Fn= m[v^2/r +g]

666= m[v^2/16+9.8]

v^2=16(666/m -9.8) ------------(3)

and

Fn= mv^2/r - mg

510= m[v^2/r –9.8]--------------(4)

Plug (3) in (4)

510= m[v^2/16 –9.8]

510=m[16(666/m -9.8)/16-9.8]          => m= 8kg

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