Answer
(a) $4$
(b) $4.905N/cm^2$
(Other estimates are also possible.)
Work Step by Step
(a) We can find the required number of geckos as follows:
$m=250g=0.25Kg$
$W=mg$
$\implies W=(0.25Kg)(9.8m/s^2)=2.45N$
It is given that each foot pad of a gecko can attach to the ceiling with a force of $11N$
$\implies n=\frac{11N}{2.45N}$
$n=4.489\approx 4$
(b) The required force per square centimeter can be calculated as follows:
Let the dimensions of the shoes be $12cm$ and $5cm$
and the area of shoe sole: $=(12cm)(5cm)=60cm^2$
Thus the area of two soles: $=120cm^2$
Let the mass of the body be $60Kg$
Then $W=mg=(60Kg)(9.8m/s^2)=588.6N$
Now the force per square centimeter that the body exerts on the soles is given as
$\frac{588.6N}{120cm^2}=4.905N/cm^2$
This force is much smaller than $11N/cm^2$ that is exerted by the gecko.
