Two 26 kg spheres are fixed in place on a y-axis, one at y = 0.50 m and the othe

Question

Two 26 kg spheres are fixed in place on a y-axis, one at y = 0.50 m and the other at y = -0.50 m. A 10 kg ball is then released from rest at a point on the x-axis that is at a great distance (effectively infinite) from the spheres. The only forces acting on the ball are the gravitational forces from the spheres.
(a) When the ball reaches the (x, y) point (0.30 m, 0), what is its kinetic energy?
__ J

(b) When the ball reaches the (x, y) point (0.30 m, 0), what is the net force acting on it from the spheres, in unit-vector notation?
( __ + ___ ) N

Explanation / Answer

KE = d(GPE) Since the 2 spheres act equally on the ball d(GPE) = 2*G*M*m/R where R = v[x²+y²]. a) KE = 2*6.67E-11*26*10/v[.50²+.30²] = 59.48E-9 J b) Fx = 2*G*M*m*x/[(x²+y²)^1.5] = 38.94E-9 N in the -x direction

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