Two identical particles, each of mass m, are located on the x axis at x=+x0 and...

Two identical particles, each of mass m, are located on the x axis at x=+x0 and x=-x0

a.

Determine a formula for the gravitational field due to these two particles for points on the y axis; that is, write g⃗ g→ as a function of y, m, x0, and so on.

Express your answers in terms of the variables y, m, x0, and appropriate constants. Enter your answers separated by a comma.

b.

At what point (or points) on the y axis is the magnitude of g⃗ g→ a maximum value, and what is its value there? [Hint: Take the derivative dg⃗ /dy.]

Express your answer(s) in terms of the variables y, m, x0, and appropriate constants. If there is more than one point, enter each point separated by a comma.

c.

What is the maximum value of the magnitude of g⃗ g→?

Express your answers in terms of the variables y, m, x0, and appropriate constants.

Expert Solution

genius_generous answered 2 years ago

Two 8.00 µC charged particles are located on the x axis. One isat x =...

Two 8.00 µC charged particles are located on the x axis. One is at x = 1.00 m, and the other is at x = -1.00 m.(a) Determine the electric field on the y axis at y = 0.800 m.N/C i + N/C j(b) Calculate the electric force on a -3.00 µC charge placed on the y axis at y = 0.800 m.N i + N j

Two particles are fixed on an x axis. Particle 1 of charge 49.0 μC is located...

Two particles are fixed on an x axis. Particle 1 of charge 49.0 μC is located at x = -34.5 cm; particle 2 of charge Q is located at x = 33.6 cm. Particle 3 of charge magnitude 43.9 μC is released from rest on the y axis at y = 34.5 cm. What is the value of Q if the initial acceleration of particle 3 is in the positive direction of (a) the x axis and (b) the y...

Two particles are fixed on an x axis. Particle 1 of charge 57.8 μC is located...

Two particles are fixed on an x axis. Particle 1 of charge 57.8 μC is located at x = -12.7 cm; particle 2 of charge Q is located at x = 16.3 cm. Particle 3 of charge magnitude 40.6 μC is released from rest on the y axis at y = 12.7 cm. What is the value of Q if the initial acceleration of particle 3 is in the positive direction of (a) the x axis and (b) the y...

Two particles are fixed on an x axis. Particle 1 of charge 51.4 μC is located...

Two particles are fixed on an x axis. Particle 1 of charge 51.4 μC is located at x = -22.8 cm; particle 2 of charge Q is located at x = 10.8 cm. Particle 3 of charge magnitude 20.8 μC is released from rest on the y axis at y = 22.8 cm. What is the value of Q if the initial acceleration of particle 3 is in the positive direction of (a) the x axis and (b) the y...

Four identical particles of mass 0.50 kg each are placed at vertices of a 2.0 m...

Four identical particles of mass 0.50 kg each are placed at vertices of a 2.0 m * 2.0 m square and held there by four massless rods, which form the sides of the square. What is the rotational ineria of this rigid body about aubout an axis that (a) passes through the midpoints of opposite sides and lies in the plane of the square, (b) passes through the midpoint of one of the sides and is perpendicular to the plane...

In the figure, two particles, each with mass m = 0.77 kg, are fastened to each...

In the figure, two particles, each with mass m = 0.77 kg, are fastened to each other, and to a rotation axis at O, by two thin rods, each with length d = 5.2 cm and mass M = 1.0 kg. The combination rotates around the rotation axis with angular speed ? = 0.32 rad/s. Measured about O, what is the combination's (a) rotational inertia and (b) kinetic energy?

At one instant, the center of mass of a system of two particles is located on...

At one instant, the center of mass of a system of two particles is located on the x-axis at x=2.0m and has a velocity of (5.0m/s). One of the particles is at the origin. The other particle has a mass of 0.10kg and is at rest on the x-axis at x= 8.0m. 1.What is the mass of the particle at the origin? 2. Calculate the total momentum of this system. 3. What is the velocity of the particle at the...

Two identical blocks of mass M = 2.60 kg each are initially at rest on a...

Two identical blocks of mass M = 2.60 kg each are initially at rest on a smooth, horizontal table. A bullet of very small mass m = 20 g (m << M) is fired at a high speed v. = 120 m/s towards the first block. It quickly exits the first block at a reduced speed of 0.40 v, then strikes the second block, quickly getting embedded inside of it. All the motion happens on the x-axis. (a) find the...

Four identical particles of mass 0.738 kg each are placed at the vertices of a 4.28...

Four identical particles of mass 0.738 kg each are placed at the vertices of a 4.28 m x 4.28 m square and held there by four massless rods, which form the sides of the square. What is the rotational inertia of this rigid body about an axis that (a)passes through the midpoints of opposite sides and lies in the plane of the square,(b)passes through the midpoint of one of the sides and is perpendicular to the plane of the square,...

a.) Two identical particles of charge 3 μμC and mass 6 μμg are initially at rest...

a.) Two identical particles of charge 3 μμC and mass 6 μμg are initially at rest and held 3 cm apart. How fast will the particles move when they are allowed to repel and separate to very large (essentially infinite) distance? b) Now suppose that the two particles have the same charges from the previous problem, but their masses are different. One particle has mass 6 μμg as before, but the other one is heavier, with a mass of 48...

Question