A very famous cat named Razz has a mass of 23.8 kg (Razz is larger one cat). Sud

Question

A very famous cat named Razz has a mass of 23.8 kg (Razz is larger one cat). Suddenly a tornado comes along forcing Razz to seek refuge under a metal manhole cover . Razz holds on to the manhole cover with his claws for dear life. the manhole cover is soild circular disk with a thickness of 2.5 cm, m=211kg and r=61cm. Determine the minimum wind-speed above the manhole cover required to lift the cover with Razz holding on with all his might. comment on the likelihood of such a wind-speed. (you may assume the wind is moving horizontally over the manhole cover and the air under the manhole cover is stationary. The density of air is 1.29kg/m^3.)

Explanation / Answer

let P1 and are the pressure below and above the manhole respectively.

pressure diffrence to lift the man hole,

P1 - P2 = F/A

= (m + M)*g/A

= (m + M)*g/(pi*r^2)

= (23.8 + 211)*9.8/(pi*0.61^2)

= 1968.4 pa

let v2 is the wind speed above the manhole.

use Bernoulli's theorem,

P1 + (1/2)*rho*V1^2 = P2 + (1/2)*rho*v2^2

P1 + 0 = P2 + (1/2)*rho*v2^2

P1 - P2 = (1/2)*rho*v2^2

==> v2 = sqrt(2*(P1-P2)/rho)

= sqrt(2*(1968.4/1.29)

= 55.5 m/s or 200 km/h <<<<<<<<<<--------------Answer

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