Two particles and B have the same momenta. Particle A is 3.0 times as massive as particle B (i.e. M. =3.0M). What is the ratio of their kinetic energy? Answer: K: Ka =

Two masses, m, and m, move on the xy plane towards each other as shown in the figure. The first mass m,=1.1kg is moving with a speed v,=6.7m/s while m,-4.3kg is moving with a speed v,=10.6m/s . As a result of the collision m, comes to rest. What is the final speed of m,? Express your answer using two decimal places. Before the collision

Two particles of masses m and 2m move along the x axis with equal by magnitude but oppositely directed velocities, as shown in the figure below. V (2m) m What is the total linear momentum of the system? Px = mv O Px = -my O py = 3mv O Px = mv?

A radioactive nucleus with an atomic mass of 238 atomic mass units (AMU) is at rest and suddenly emits an alpha particle of atomic mass 4 AMU and velocity 1 × 106 m/s.  What will be the velocity of the remaining (‘daughter’) nucleus of atomic mass 234 AMU?

Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (ªHe) from gold-197 nuclei (197 Au). The energy of the incoming helium nucleus was 7.28 × 10-13 J, and the masses of the helium and gold nuclei were 6.68 × 10-27 kg and 3.29 × 10-25 kg, respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the collision.) (a) If a helium nucleus scatters to an angle of 136° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus. 4He speed 197 Au velocity t 197 Au direction 14500000 0.0140 -17 m/s X m/s ° counterclockwise from the +x-axis (b) What is the final kinetic energy (in J) of the helium nucleus? 7.02e-13 J

A radioactive nucleus at rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momenta of Pe=9.67x10-23 kg. m/s and p = 5.99×10-23 kg. m/s. respectively. (Figure 1) Figure Pnuc nuc +y 0 Onuc Py Pe 1 of 1 +X Part A Determine the magnitude of the momentum of the second (recoiling) nucleus. Express your answer to three significant figures and include the appropriate units. Pnuc= Submit Part B Onuc = Submit μA 4 Provide Feedback Value Request Answer Determine the angle between the momentum of the electron and the momentum of the second (rec Express your answer using three significant figures. [VE| ΑΣΦ 1 → C Request Answer Units 1 ? ?

Consider the ballistic pendulum setup: A bullet of mass m with speed vo hits a pendulum bob of mass M, suspended by a massless rope of length L. The bullet gets stuck inside, making the pendulum swing up to some height. What is the maximum height the pendulum can reach? L m M Solution: At the start, the bullet has a momentum mvn. When they collide and the bullet gets inside, the speed of the combined masses can be obtained using conservation of linear momentum. mvo = (m + M)v, where v is the speed of the combined masses. Therefore, we get m V = т+ M At the instant the masses move, they initially have purely kinetic energy given by 1 т? T = -(т + M)u? 2 т+ M This kinetic energy becomes potential energy at the maximum height. We get m2 1 (m + M)v² 1 = (m + M)gh. 2 т + M Finally, we have h = m2 v02 1 2 (m+M)2 Question 2a Show that the angle from the figure is given by 0 = cos™ ,-1 1 2g L(m+M)² m²V02

Nuclear Fusion Reaction In a human-scale model of a nuclear fusion reaction, two "deuterons" smash together head-on. Each has a mass of 2.0147kg and is moving at speed vd. The result is a "Helium-3 nucleus" (mass 3.0160kg) and a separate "neutron" (mass 1.0090kg). Amazingly, this reaction produces a positive Wnc of 3.96 × 10 14 J -- by converting mass into kinetic energy as predicted by Einstein's E mc² = The "neutron" moves with a speed of un after the reaction. E 4 ☑ Vd 1.57×107 m (no answer) Correct Answer: 3.64 S Un ×107 m S + + D D 3Не N. Proton Neutron http://fusion.srubar.net

A radioactive nucleus at rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momenta of pe = 8.95×10-23 kg-m/s and Py = 6.18x10-23 kg. m/s, respectively. (Figure 1) Figure Pnuc (nuc) +y 0 Onuc Pv Pe Part A Determine the magnitude of the momentum of the second (recoiling) nucleus. Express your answer to three significant figures and include the appropriate units. Pnuc = Submit Part B ■ μÅ Value Request Answer Pearson Units Review | Constan ?

There are two relativistic particles of identical mass m that move towards each other along the same axis. The magnitudes of their momenta are the same. They collide head-on to form a new particle of mass 8m. What were the magnitudes of momenta of the initial particles?