Interactions between cells and viruses depend on multiple factors, such as adhesion forces, specific binding, long-range forces such as electrostatics, entropic forces due to crowding (we'll encounter those in the second part of the course) and electric screening due to the presence of charged ions in the solution. In an attempt to describe the interactions between a cell and a virus, modelers have come up with the following potential energy as a function of their distance r 2. U(r) = er/a (1) The constants a, b and c are all positive real numbers. (a) Find the dimensions of the numbers a, b, and c. (b) In terms of a, b, and c, find the force between the cell and the virus at r = 0. Is this force attractive or repulsive? (c) Find the equilibrium point(s) of this potential energy and determine whether they are stable or unstable.
Interactions between cells and viruses depend on multiple factors, such as adhesion forces, specific binding, long-range forces such as electrostatics, entropic forces due to crowding (we'll encounter those in the second part of the course) and electric screening due to the presence of charged ions in the solution. In an attempt to describe the interactions between a cell and a virus, modelers have come up with the following potential energy as a function of their distance r 2. U(r) = er/a (1) The constants a, b and c are all positive real numbers. (a) Find the dimensions of the numbers a, b, and c. (b) In terms of a, b, and c, find the force between the cell and the virus at r = 0. Is this force attractive or repulsive? (c) Find the equilibrium point(s) of this potential energy and determine whether they are stable or unstable.
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Transcribed Image Text:Interactions between cells and viruses depend on multiple factors, such as adhesion forces,
specific binding, long-range forces such as electrostatics, entropic forces due to crowding
(we'll encounter those in the second part of the course) and electric screening due to
the presence of charged ions in the solution. In an attempt to describe the interactions
between a cell and a virus, modelers have come up with the following potential energy as
a function of their distance r
U(r) = er/a
(1)
The constants a, b and c are all positive real numbers.
(a) Find the dimensions of the numbers a, b, and c.
(b) In terms of a, b, and c, find the force between the cell and the virus at r = 0. Is this
force attractive or repulsive?
(c) Find the equilibrium point(s) of this potential energy and determine whether they
are stable or unstable.
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