the potential energy of a system of two particle separated by a distance r is given by u(r) = A/r , where A is constant . find the radial force Fr that each particle exerts on the other
dU = work done=potential change
or
force dr = dU
U = A/r
dU/dr = F = -A/r^2
Sign of A depends on attractive or repulsive.
To find the radial force (Fr) that each particle exerts on the other in a system with potential energy u(r) = A/r, we can use the concept of force being the negative gradient of potential energy.
The force between the two particles is given by:
Fr = -d(u(r))/dr
To find the derivative (-d(u(r))/dr), we need to differentiate the potential energy expression u(r) with respect to r.
First, rewrite the expression for potential energy:
u(r) = A/r
Differentiating u(r) with respect to r involves applying the chain rule. Let's break it down step by step:
1. Rewrite u(r) as A * r^(-1):
u(r) = A * r^(-1)
2. Apply the power rule to differentiate each term:
d(u(r))/dr = d(A * r^(-1))/dr
Applying the power rule, we get:
d(u(r))/dr = -A * r^(-2)
Therefore, the radial force (Fr) is given by:
Fr = -d(u(r))/dr = -(-A * r^(-2)) = A * r^(-2)
So, the radial force that each particle exerts on the other is given by Fr = A * r^(-2).