How will we figure out the pressure on the ground exerted by a ballerina?

1 Answer
Jose
Feb 17, 2018

#P#= #"(m g )/(A)#

Explanation:

As an object falls from rest, its gravitational potential energy (PE) is converted to kinetic energy (KE).
CASE: Consider a ballerina with mass "m" who is falling #color(blue)"vertically"# under the influence of gravity (g).

The ballarina is falling from highest reached (rest), therefore initial kinetic energy is zero (KE = 0). Once the ballarina hit on the ground, height is zero, therefore no potential energy at ground level (PE = 0).

The work performed by the ballarina is:

#W# = #Delta# #"KE"#

#W# = #"1/2 m nu^2#

But, Work = Force x distance

#W = F h#

Combining "W" equations and solving for F

#"F# = #"(1/2 m nu^2)/h#

By definition, Force = Pressure x Area

#F = P A#

Combining both equations of F and solving for P:

#P# = #"(1/2 mnu^2)/ (h A)#

"#nu#" is obtained from energy transformation balance

PE = KE

#mgh# = #"1/2 mnu^2#

#nu# =. #sqrt2 g h#

Finally,

#P# = #"(m g)/(A)#

Where,

#m#: mass of ballarina
#nu# : ballerina flling speed
#h#: falling high (distance)
#A#: area pressed by the ballarina foot
#g#: gravitational force

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