Two 10 kg spheres are fixed in place on a y axis, one at y = 0.20 m and the othe
ID: 1378872 • Letter: T
Question
Two 10 kg spheres are fixed in place on a y axis, one at y = 0.20 m and the other at y = ?0.20 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?
(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? (Express your answer in vector form.)
Explanation / Answer
a) Apply Enrgy conservation
initial mechanical enrgy = final mechanical enrgy
k1+ u1 = k2 + u2
0 + 0 = k2 - 2*G*m^2/r
k2 = 2*G*m^2/r
= 2*6.67*10^-11*10^2/sqrt(0.3^2 + 0.2^2)
= 3.7*10^-8 J <<<<<<-------Answer
b) let F1 and F2 are the forces exerted by the fixed bodies on third body.
F1 = F2 = G*m^2/r^2
= 6.67*10^-11*10^2/(0.2^2 + 0.3^2)
= 5.13*10^-8 N
theta = tan^-1(0.2/0.3)
= 33.7 degrees
Fnet = 2*F1*cos(theta)
= 2*5.13*10^-8*cos(33.7)
= 8.54*10^-8 N
so, Fnet = -8.54*10^-8 i N + 0 j + 0k <<<<<<-------Answer
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