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# Mechanics: Collision, momentum, energy, spring, projectile.

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1. A rifle bullet with mass .010 kg strikes and embeds itself with a block of mass .990kg which rests on a frictionless horizontal surface and is attached to a coil spring 10.cm. Calibration of the spring shows that a force of 1.5 N is required to compress a spring 1.0 cm
a. find the magnitude of the velocity of the block just after impact
b. what was the initial speed of the bullet

2. A Neutron collides with mass (m) elastically with a nucleus of mass (M), which is initially at rest show that if the neutron's initial Kinetic Energy is K sub o the maximum kinetic energy that it can lose during the collision is 4mMKo/(M+m)^2

3. A neutron with a mass 1.67*10^-27kg, moving with speed of 4.5*10^4m/s, makes a head on collision with a boron nucleus with mass 17.0*10^-27
a. If the collision is completely inelastic so the neutron and boron nucleus stick together, what is the final kinetic energy of the system expressed as a fraction of the original kinetic energy K sub 0
b. If the collision is perfectly elastic what fraction of the neutrons original kinetic energy is transferred to the borons nucleus

4. Fission the process that supplies energy in nuclear power plants occur when heavy nucleus is spit into two medium size nuclei. one such reaction would occur if a neutron colliding with a U nucleus split that nucleus into a Ba and Kr nucleus. In this reaction tow neutrons would be split off from the original U. Before the collusion the neutron is on the x-axis and ager the Ba is moving in the positive z direction and Kr in the negative z direction. The three neutrons are in the xy plane. If they incoming neutron has an initial velocity with the magnitude of 4.0*10^6m/s and final velocity with magnitude of 2.0*10^6m/s in the directions, what are the speeds of the other two neutrons, what can you say of the speeds of Ba and Kr. (the mass of Ba nucleus is 2.3^10^-25kg and Kr is about 1.5*10^-25kg

5. A frame with mass .2kg when suspended from a certain coil spring is found to stretch the spring .1m. A lump of putty with a mass of .4kg is dropped from rest onto the frame from height .3 m and sticks to it. Find maximum distance the frame moves downward.

6. A 20 kg projectile is fired at an angle of 60 degrees above the horizontal with a muzzle velocity of magnitude 160m/s. At the highest point of its trajectory the projectile explodes into two fragments with equal mass one falls vertically with zero initial speed.
a. how far from the point of firing does the other fragment strike if the terrain is level
b. how much energy was released during the explosion