Question

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

Answer 1

`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