Chapter 7, Problem 7.34P

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)

A block of mass M, capable of sliding with negligible friction over a horizontal air rail, is attached to one end of the rail by a spring of negligible mass and elastic constant k, initially relaxed. A projectile with mass m and horizontal velocity v, hits the block at t=0, as shown in the figure below; the projectile is attached to the block. The expression of the system's displacement X for t > 0 is:

The following figure shows two particles of masses m1 and m2, with velocities before the collision of magnitude v1 and v2. If the collision is perfectly elastic, find the magnitude of the velocities v1' and v2' after the collision and the angle of incidence θ (theta), as a function of the masses and velocities before the collision.

A smooth sphere A of mass 2m  moving with velocity (3i+4j)ms-1 impinges obliquely on another smooth sphere B of same radius but  of mass 3m and which is moving with velocity (2i-j)ms-1 ,At the instant of collision ,The line joining the centers of A and B is parrallel to the vector i .Given that the coefficient of restitution between A and B is 2/3 I)Find the speed of A after collision With detailed steps please

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.

Consider a head-on, elastic collision between twobodies whose masses are m and M, with Itis well known that if m has speed and M is initiallyat rest, m will bounce straight back with its speedunchanged, while M will remain at rest (to anexcellent approximation). Use this fact to predict thefinal velocities if M approaches with speed and mis initially at rest.

show complete solution and free body diagrams

Use the additivity of moments to find the COM of an ice cream cone consisting of a semicircle of density ρρ on top of an equilateral triangle of side 6 and density 5ρ5ρ.

Find the magnitude of the initia acceleration of a uniform sphere with mass .010kg if released from rest at point P and acted on only by forces of gravitational attraction of the spheres at A and B.