Find the potential energy of the gravitational interation of a point mass of mass m and a thin uniform rod of mass M and length l, if they are located along a straight line such that the point mass is at a distance 'a' from one end. Also find the force of their interaction.
Answers
Answered by
0
Explanation:
Choose the location of the point mass as the origin. Then the potential energy dU of an element of mass dM=
l
M
dx of the rod in the field of the point mass is
dU=−γm
l
M
dx
x
1
where x is the distance between the element and the point. (Note that the rod and the point mass are on a straight line.) If then a is the distance of the nearer end of the rod from the point mass.
U=−γ
l
mM
∫
a
a+l
x
dx
=−γm
l
M
ln(1+
a
l
)
The force of interaction is
F=
∂a
∂U
=γ
l
mM
×
1+
a
l
1
(−
a
2
l
)=−
a(a+l)
γmM
Similar questions