Sphere A with mass 70 kg is located at the origin of an xy coordinate system; sphere B with mass 73 kg is located at coordinates ( 0.23 m, 0); sphere C with mass 0.55 kg is located at coordinates ( 0.15 m, 0.14 m). In unit-vector notation, what is the gravitational force on C due to A and B?

Chapter 13, Problem 011 In the figure, two spheres of mass m = 9.24 kg. and a third sphere of mass M form an equilateral triangle, and a fourth sphere of mass mą is at the center of the triangle. The net gravitational force on that central sphere from the three other spheres is zero. (a) What is the value of mass M? (b) If we double the value of m4, what then is the magnitude of the net gravitational force on the central sphere? M (a) Number Units (b) Number Units Click if you would like to Show Work for this question: Open Show Work Question Attempts: 0 of 10 used SUBMIT ANSWER SAVE FOR LATER

In the figure, three 9.74 kg spheres are located at distances d₁ = 0.953 m, and d₂ = 0.215 m. What are the (a) magnitude and (b) direction (relative to the positive direction of the x axis) of the net gravitational force on sphere B due to spheres A and C? (a) Number i (b) Number i dr B Units Units î ✪

One dimension. In the figure, two point particles are fixed on an x axis separated by distance d. Particle A has mass ma and particle B has mass 4.00 ma. A third particle C, of mass 73.0 ma, is to be placed on the x axis and near particles A and B. In terms of distance d, at what x coordinate should C be placed so that the net gravitational force on particle A from particles B and Cis zero? Number Units

Problem 2:  An object with mass m1 = 42 kg is located at the origin. Another object with mass m2 = 86 kg is located at l2 = 0.105 m. Consider position la = 0.035 m between the two objects and along the axis connecting them. Refer to the diagram. The gravitational field of m1 is denoted by g1. Enter an expression for the gravitational field g1 at position la in terms of m1, la, and the gravitational constant G.  The gravitational field of m2 is denoted by g2. Enter an expression for the gravitational field of m2 at la in terms of m2, m1, la, l2 and the gravitational constant G.  Enter and expression for the total gravitational field at position la, g, in terms of the quantities defined in the problem.

A planet of mass 5 ⨯ 1024 kg is at location <4 ⨯ 1011, −4 ⨯ 1011, 0> m.  A star of mass 4 ⨯ 1030 kg is at location <−6 ⨯ 1011, 4 ⨯ 1011, 0> m. (a) What is the relative position vector pointing from the planet to the star? (b) What is the distance between the planet and the star? (c) What is the unit vector in the direction of r? (d) What is the magnitude of the force exerted on the planet by the star?(e) What is the magnitude of the force exerted on the star by the planet? (f) What is the force (vector) exerted on the planet by the star? (g) What is the force (vector) exerted on the star by the planet? (Note the change in units.)

In the figure below, three point particles are fixed in place in an xy plane. Particle A has mass mA, particle B has mass 2.35mA, and particle C has mass 3.45mA. A fourth particle D, with mass 4.40mA, is to be placed near the other three particles. In terms of distance d, at what coordinates should particle D be placed so that the net gravitational force on particle A from particles B, C, and D is zero? (a) C 1.5d x coordinate d (b) y coordinate Bo A d x

Three lead balls of mass m₁ = 14 kg, m₂ = 27 kg, and m3 = 9.7 kg are arranged as shown in the figure below. Find the total gravitational force exerted by balls 1 and 2 on ball 3. Be sure to give the magnitude and the direction of this force. N magnitude direction ° counterclockwise from the +x-axis y (m) 4 m1 3 L- 2+ m₂ 1 0 2 3. 4 5 M3 -x-(m)

Four uniform spheres, with masses ma 65 kg, MB = 10 kg, mc 190 kg, and mp notation, what is the net gravitational force on sphere B due to the other spheres? - = 45 kg, have (x, y) coordinates of (0, 50 cm), (0, 0), (−80 cm, 0), and (40 cm, 0), respectively. In unit-vector

A ring of radius 5 m lies in the x,y plane, centered on the origin. The portions of the ring in the first and third quadrants have a mass density of 11.9 kg/m, while the portions of the ring in the second and fourth quadrants have a mass denisty of 10.3 kg/m. Find the z-component of the gravitational field due to the ring at a point P on the z-axis at a distance 7 m from the origin. Use G = 6.673e-11 N*m^2/kg^2