11. Momentum & Impulse

A neutron is an electrically neutral subatomic particle with a mass just slightly greater than that of a proton. A free neutron is radioactive and decays after a few minutes into other subatomic particles. In one experiment, a neutron at rest was observed to decay into a proton (mass 1.67×10^-27 kg) and an electron (mass 9.11×10^-31 kg) . The proton and electron were shot out back-to-back. The proton speed was measured to be 1.0 ×10⁵ m/s, and the electron speed was 3.0×10⁷ m/s. No other decay products were detected. How much momentum did this neutrino 'carry away' with it?

The nucleus of the polonium isotope ²¹⁴Po (mass 214 u) is radioactive and decays by emitting an alpha particle (a helium nucleus with mass 4 u). Laboratory experiments measure the speed of the alpha particle to be 1.92×10⁷ m/s . Assuming the polonium nucleus was initially at rest, what is the recoil speed of the nucleus that remains after the decay?

An object at rest on a flat, horizontal surface explodes into two fragments, one seven times as massive as the other. The heavier fragment slides 8.2 m before stopping. How far does the lighter fragment slide? Assume that both fragments have the same coefficient of kinetic friction.

A 195-kg projectile, fired with a speed of 116 m/s at a 60.0° angle, breaks into three pieces of equal mass at the highest point of its arc (where its velocity is horizontal). Two of the fragments move with the same speed right after the explosion as the entire projectile had just before the explosion; one of these moves vertically downward and the other horizontally. Determine the velocity of the third fragment immediately after the explosion.

(II) An atomic nucleus initially moving at 320 m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 280 m/s. If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?

An atomic nucleus of mass m traveling with speed v collides elastically with a target particle of mass 2m (initially at rest) and is scattered at 90°. At what angle does the target particle move after the collision?

An atomic nucleus of mass m traveling with speed v collides elastically with a target particle of mass 2m (initially at rest) and is scattered at 90°. What are the final speeds of the two particles?

(II) An atomic nucleus of mass m traveling with speed v collides elastically with a target particle of mass 2m (initially at rest) and is scattered at 90°. What fraction of the initial kinetic energy is transferred to the target particle?

A 3.0-kg block slides along a frictionless tabletop at 8.0 m/s toward a second block (at rest) of mass 4.5 kg. A coil spring, which obeys Hooke’s law and has spring constant k = 850 N/m, is attached to the second block in such a way that it will be compressed when struck by the moving block, Fig. 9–43. Is the collision elastic? Ignore the mass of the spring.

INT Two hydrogen atoms collide head-on. The collision brings both atoms to a halt. Immediately after the collision, both atoms emit a 121.6 nm photon. What was the speed of each atom just before the collision?