In deep space, sphere a of mass 94 kg is located at the origin of an x axis and sphere b of mass 100 kg is located on the axis at x = 1.8 m. sphere b is released from rest while sphere a is held at the origin. (a) what is the gravitational potential energy of the two-sphere system just as b is released? (b) what is the kinetic energy of b when it has moved 0.60 m toward a?

(a)

The gravitational potential energy of the two-sphere system is given by

(1)

where

G is the gravitational constant

is the mass of sphere A

is the mass of sphere B

r = 1.8 m is the distance between the two spheres

Substitutign data in the formula, we find

and the sign is negative since gravity is an attractive force.

(b)

According to the law of conservation of energy, the kinetic energy gained by sphere B will be equal to the change in gravitational potential energy of the system:

(2)

where

is the initial potential energy

The final potential energy can be found by substituting

r = 1.80 m -0.60 m=1.20 m

inside the equation (1):

U=-\frac{(6.67\cdot 10^{-11})(94 kg)(100 kg)}{1.2 m}=-5.22\cdot 10^{-7} J

So now we can use eq.(2) to find the kinetic energy of sphere B:

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