Question

To prevent damage to floors (and to increase friction), a crutch will often have a rubber tip attached to its end. If the end of the crutch is a circle of radius 1.2 cm without the tip, and the tip is a circle of radius 2.8 cm, by what factor does the tip reduce the pressure exerted by the crutch?

Answer 1

In this case, the force would remain constant, as the force is due to the weight of the person holding the crutch. Let's say P1 is the pressure if NO rubber tip was attached and P2 is the pressure after rubber tip is attached. And let A1, A2 be the corresponding areas of contact with the floor.
then,
P1 x A1 = P2 x A2
A1= pi x 1.2 x 1.2 => area = pi x R^2
A2= pi x 2.8 x 2.8
then,
P1 x pi x 1.2 x 1.2 = P2 x pi x 2.8 x 2.8
=> P1 x 1.44 = P2 x 7.84
hence, P1/P2 = 49/9