Assignment:
Problem 1
In the figure, a square of edge length 24.0 cm is formed by four spheres of masses m1 = 5.30 g, m2 = 2.50 g, m3 = 0.500 g, and m4 = 5.30 g. In unit-vector notation, what is the net gravitational force from them on a central sphere with mass m5 = 2.10 g?
Problem 2
Two dimensions. In the figure, three point particles are fixed in place in anxy plane. Particle A has mass mA = 5 g, particle B has mass 2.00mA, and particle C has mass 3.00mA. A fourth particle D, with mass 4.00mA, is to be placed near the other three particles. What (a) x coordinate and (b) y coordinate should particle D be placed so that the net gravitational force on particle A from particles B, C, and D is zero (d = 18 cm)?
Problem 3
Three point particles are fixed in position in an xy plane. Two of them, particle A of mass 5 g and particle B of mass 11 g, are shown in the figure with a separation of dAB = 0.466 m at angle Θ = 30°. Particle C, with mass 8 g, is not shown. The net gravitational force acting on particle A due to particles B and C is 2.26 x 10-14 N at an angle of -163.8°. from the positive x axis. What are (a) the x coordinate and (b) the y coordinate of particle C?
Problem 4
Certain neutron stars (extremely dense stars) are believed to be rotating at about 0.93 rev/s. If such a star has a radius of 43 km, what must be its minimum mass so that material on its surface remains in place during the rapid rotation?
Problem 5
Two concentric spherical shells with uniformly distributed masses M1 and M2 are situated as shown in the figure. Find the magnitude of the net gravitational force on a particle of mass m, due to the shells, when the particle is located at each of the radial distances shown in the figure: (a) a, outside both shells, (b) b, between the two shells and (c) c, inside both shells. State your answers in terms of the given variables, using G when applicable.
