Exercise 2.3.3-5 Knife in a jar of peanut butter You all will have had an experience similar to

• finding that a kitchen knife could be supported vertically in a jar of peanut butter

without the knife touching the bottom of the jar or

• finding that a screwdriver could be supported vertically in a can of grease without the

screwdriver touching the bottom of the can.

To better understand such observations, consider a knife that is allowed to slip slowly into

a Bingham plastic, until it comes to rest without being in contact with any of the bounding

surfaces of the system. Relate the depth H to which the knife is submerged and the total

weight of the knife to the properties of the Bingham plastic. You may assume that you know

both the mass density p(w)

of the metal and the mass density p

{1) of the fluid, you may

neglect end effects at the intersection of the knife with the fluid-fluid interface, and you may

approximate the knife as parallel planes ignoring its edges.

Hint: Make the same assumption about the pressure that you did in solving Exercise 2.2.3-1.