Chapter 9, Problem 9.15P

Problem 05, part B

Let two particles of equal mass m collide. Particle 1 has initial velocity v, directed to the right, and particle 2 is initially stationary.  Now assume that the mass of particle 1 is 2m, while the mass of particle 2 remains m. If the collision is elastic, what are the final velocities v1 and v2 of particles 1 and 2? Express the velocities in terms of v.

Set up the integrals to find the ycoordinate of the center of mass for a region of density (x;y)inside the circle x^2 + y^2 = 4 and below y = sqrt (2)

Find the center of mass and the moments of inertia about the coordinate axes of a thin plate bounded by the line y = x and the parabola y = x2 in the xy-plane if the density is d(x, y) = x + 1.

The Moon is 60 Earth radii (i.e. 60 rEarth) from the center of the Earth and has a mass of 0.012 Earth masses (i.e. 0.012 mEarth) a. How many Earth radii is the center of mass (the “barycenter”) of the Earth-Moon system from the center of the Earth? b. Is the center of mass inside the Earth or outside the Earth? c. What point along the line from the center of the Earth to the center of the Moon orbits the barycenter of the Solar System in a (nearly) circular orbit (e.g. the center of the Earth, the barycenter of the Earth-Moon system, the midpoint, the center of the Moon)?

For the distribution of particles appearing in the plane of the figure, all particles have the same mass m. Determine: a) The coordinates of the center of mass of the systemb) The coordinates in which a fourth particle of mass 2m must be placed so that the center of mass of the new system moves to the origin of coordinates.

Find the center of mass of a cone of uniform density that has a radius R at the base, height h, and mass M. Let the origin be at the center of the base of the cone and have +z going through the cone vertex.

A prjectile of mass m is launched with initial velocity v0 at angle (theta) from the +x direction. From the origin, the projectile is connected to massless spring with force constant k, as shown. A. Set up the equations of motion of the projectile, both in the horizontal and vertical directions

Three metallic balls, each of mass 2 kg, are placed at the vertices of an equilateral triangle of side length 2 m. (a) Find the CM of the system. (b) Express the position vector from origin to the CM in terms of unit vectors. (c) Find the direction of the position vector with respect to the +x axis.