Notes

• Please turn in Exam Regrades• Brian Greene “Fabric of the Cosmos” on Public

Television tonight, 9pm• Today’s Colloquium: “Adventures in Underground

Space”

Review: Center of Mass

Find the position of the center of mass of a regular cone of mass density r, with height R and radius R.

R

R

Center of Mass Reference Frame

Back to Elastic Collisions

Special Cases

Two titanium spheres approach each other head-on with the same speed, then collide elastically. After the collision, one of the spheres, with mass 300g, is at rest. What is the mass of the other sphere?sphere?

In World War I, the most awesome weapons of war were huge cannons mounted on railcars. The figure shows such a cannon, mounted so that it will project a shell at an angle of 30°. With the car initially at rest the cannon fires a 200kg projectile at 125 m/scar initially at rest, the cannon fires a 200kg projectile at 125 m/s. Now, consider a system composed of the cannon, shell, and railcar, all rolling on a track without friction losses., g(a) Will the total vector momentum of the system be conserved before and after the shell is fired?(b) If the mass of the railcar and cannon is 5000 kg, what will be the recoil velocity of the car along the track?

30°

A pendulum consists of a 0.4 kg bob attached to a string of length 1.6m. A block of mass m rests on a horizontal frictionless surface. The pendulum is released from rest at an angle of 53°with the vertical and the bob collides elastically with the blockwith the vertical and the bob collides elastically with the block.

a) Find the velocity of the pendulum h b f i iat the bottom of its swing.

b) Following the collision, the block slides a a and the pend l mslides away, and the pendulum swings back up to a maximum angle of 5.73° from the vertical.angle of 5.73 from the vertical. Find the velocity of the pendulum immediately after the collision.

c) Find the velocity of the block after the collision.

d) Determine the mass m.