Central Force with Origin on Circle
المؤلف:
Sidney B. Cahn And Boris E. Nadgorny
المصدر:
A GUIDE TO PHYSICS PROBLEMS
الجزء والصفحة:
part 1 , p 10
25-7-2016
1754
Central Force with Origin on Circle
A particle of mass m moves in a circular orbit of radius R under the influence of a central force F(r). The center of force C lies at a point on the circle (see Figure 1.1). What is the force law?
Figure 1.1
SOLUTION
The differential equation of the orbit comes to the rescue here. From Figure 1.2, we see that the orbit equation is
Figure 1.2
(1)
so
(2)
and
(3)
Applying the differential equation of the orbit and substituting (2) and (3) into it, we obtain
(4)
We are required to find
(5)
so
(6)
and finally
(7)
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