Newton's Law Of Gravitation

The force of interaction between any two particles having masses m1 and m2 separated by a distance r is attractive and acts along the line joining the particles. The magnitude of the force is given by

F = (11.1)

where G is a universal constant having the same value for all pairs of particles. Its numerical value is 6.67 × 10 ^-11 Nm2/kg2.

1. Similarly , the second particle exerts a force on the first particle that is directed towards the second particle along the line joining the two. These forces are equal in magnitude but oppositely directed.
2. In the vector form, equation (11.1) may be written as
3. (11.2)
4. where one must remember that has its origin at the source of the force.

To compute the force between them requires integral calculus. However, for the special case of a uniform spherical mass distribution, r may be taken as the distance to the center. Also, when the separation between two objects is very much larger than their sizes, they may be approximated as point masses and then, equation (11.1) may be used.

(11.3)

Problem Solving Strategy:

1. 1.Set up a convenient coordinate system
2. Indicate the directions of the forces acting on the particle under consideration.
3. Calculate the (scalar) magnitudes of the forces.
4. Find the net force by using the component method.

Solution

1. The first two steps have already been done in the figure. The magnitudes of forces are
2. F ₂₁ = Gm2m1/L2 = 1.33 × 10 ^-10 N
3. F ₂₃ = Gm2m3/L2 = 1.01 × 10 ^-10 N
4. The net force on m ₂ is
5. 
6. Its components are
7. F _2x = -F ₂₁ cos60 ^o + F ²³ cos60 ^o = -1.6 × 10 ^-11 N
8. F _2y = -F21sin60 ^o – F ²³ sin60 ^o = -2.03 × 10 ^-10 N
9. Thus,

F ₂ = -(1.6 + 20.3 ) × 10 ^-11 N