Important Concepts:
The Law of Conservation of Momentum states that the sum total of the momentum of a system of bodies before interaction equals the sum total of the momentum of the system of bodies after interaction.
The Law of Conservation of Energy states that the sum total of the energy possessed by a system remains constant, although it may be converted from one form into another.
An elastic collision is one in which the total kinetic energy of a system of bodies before collision equals the total kinetic energy of the system of bodies after collision. The total kinetic energy of a system of bodies experiencing elastic collision is conserved.
An inelastic collision is one in which the total kinetic energy of a system of bodies before collision does not equal the total kinetic energy of the system of bodies after collision. The total kinetic energy of a system of bodies experiencing inelastic collision is not conserved.
Momentum is a vector quantity.
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Useful Equations:
Pbefore = Pafter
Pbefore - Pafter = 0P = mvFt = m(vbefore-vafter)
Pbefore - Pafter = 0P = mvFt = m(vbefore-vafter)KEmechanical = mvexp2/2 PEgravitational = mgh PEelastic = kxexp2/2
PEgravitational = mgh PEelastic = kxexp2/2KEbefore = KEafter KEbefore - KEafter = 0(for elastic collisions)
KEbefore - KEafter = 0(for elastic collisions) ____________________________________________________________
Answer the following questions on a separate sheet of paper. Remember to employ proper problem-solving techniques and to show all work.
1. A 10,000-kg railroad car traveling at a speed of 24.0 m/s strikes an identical car at rest. If the cars lock together as a result of the collision, what is their common speed afterward?
2. Calculate the recoil velocity of a 5.0-kg rifle that shoots a 0.050-kg bullet at a speed of 120 m/s.
3. A billiard ball of mass m moving with a speed v collides head-on with a second ball of equal mass at rest (v2 = 0). Calculate are the speeds of the two balls after the collision, assuming it to be elastic.
4. A billiard ball of mass 1.0 kg and traveling with a velocity of 1.7 m/s due East collides head-on (linearly) with a ball of identical mass traveling at 3.4 m/s due West. Calculate the respective velocities of the balls after collision, assuming it to be elastic.
5. A proton of mass 1.01 u (unified atomic mass unit) traveling with a speed of 3.60 x 10exp4 m/s has an elastic head-on collision with a helium nucleus
(mHe nucleus = 4.00 u) initially at rest. What are the velocities of the proton and helium nucleus after the collision? (Note: 1.00 u = 1.66 x 10exp-27 kg)
6. Based on your solution of problem 1 above, calculate the how much of the initial kinetic energy is transformed into thermal or other forms of energy.
7. A billiard ball moving with speed v1 = 3.0 m/s in the +x direction strikes an equal mass ball initially at rest. The two balls are observed to move off at 45 degrees with respect to the +x axis, ball 1 above the x axis and ball 2 below the x axis. Calculate the speeds of the two balls. (Think!)
