Five objects, each of mass M, are equally spaced on the arc of a semicircle of r

Question

Five objects, each of mass M, are equally spaced on the arc of a semicircle of radius R as shown in the figure below. An object of mass m is located at the center of curvature of the arc.

(a) If M is 2.7 kg, m is 1.8 kg, and R is 10.0 cm, what is the gravitational force on the particle of mass m due to the five objects? Choose right to be the +x direction and up to be the +y direction.
x component = 0N
y component =

(b) If the object whose mass is m is removed, what is the gravitational field at the center of curvature of the arc? Again, choose right to be the +x direction and up to be the +y direction.
x component = 0N
y component =

Explanation / Answer

M = 2.7 kg m = 1.8 kg R = 10 cm = 0.1 m A) For the net gravitational force on m due to five M's is given by: The horizontal component of the force get cancelled due to symmetry Fx = 0 The vertical component of the force is given by: Fy = GMm/R2 (sin0 + sin45 + sin90 + sin 135 + sin180) Fy = GMm/R2 (2sin45 + 1) Fy = (6.67*10^-11 Nm2/kg2)(2.7 kg)(1.80 kg)/0.01 m^2 (v2 + 1) Fy =7.825 * 10^-8 N N B) The gravitational field at the center of curvature of the arc is given by g = F/m The X component is zero gx = 0 The Y component is gy = 7.825*10-8 N/ 1.8 kg gy = 4.347*10-8 m/s2

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