| Linear momentum is defined as mass•velocity and has units of kg•m/s. Mathematically it is |
| expressed as, p = mv, and is a vector quantity. The bold font is used to call your attention to the |
| fact that momentum and velocity are vector quantities. If the net force acting on an object is zero, |
| its momentum is conserved in a collision and can be expressed as pi = pf, where i and f stand for |
| initial and final. This conservation law implies that the total momentum of the universe is constant. |
| |
| When discussing the conservation of momentum, one must distinguish between internal and |
| external forces. Internal forces consist of a action-reaction pair of forces according to Newton’s |
| third law. External forces are forces that exist due to outside influences, i.e. gravity or friction. A |
| conservative force such as gravity does not “drain” the system of any energy. However, a force such as friction or air resistance is a nonconservative |
| force, which converts some of the mechanical energy into heat. An ideal situation exists when the net force sums to zero and there are no net external |
| forces. This situation gives the following result: Δp = 0, pi = pf when the momentum of the system is constant. Keeping simple what is simple, we will |
| only consider a collision of two objects. This leads to: |
| Δp = 0 |
| pi = pf |
| m1v1 + m2v2 = m1v1‘ + m2v2‘ |
| Because there are only two objects involved in this collision, there are only two terms representing the initial momentum and two terms representing the |
| final momentum. |
| |
| A second important consideration involving collisions is that of energy. For simplicity, we will consider two objects traveling on a horizontal surface |
| without friction. There are three categories of collisions: completely elastic, completely inelastic, or somewhere in the middle. Given that the ΣFnet = 0, |
| momentum will be conserved but this is not necessarily true about kinetic energy, KE. Remembering that energy can take many forms i.e. heat, light, and |
| sound, a perfectly elastic collision only exists when ΔKE = 0. If the kinetic energy of the system equals zero after a collision the collision is said to be |
| completely inelastic. Through an unfortunate choice of words, it sometimes sounds like energy is “lost”. Energy is not lost but rather converted into |
| undesirable forms which decrease the kinetic energy of a system. Keeping simple what is simple, we will only consider a collision of two objects. For an |
| inelastic collision, the following is true: |
| ΔKE ≠ 0 |
| KEi ≠ KEf |
| 1/2m1v12 + 1/2m2v22 ≠ 1/2m1v1‘2 + 1/2m2v2‘2 |
|
| and for an elastic collision, the following is true: |
|
| ΔKE = 0 |
| KEi = KEf |
| 1/2m1v12 + 1/2m2v22 = 1/2m1v1‘2 + 1/2m2v2‘2 |
|
| Another must to remember is that energy is a scalar quantity. Unlike momentum which is a vector that you resolve vector components, energy is a scalar |
| and a negative sign simply represents a decrease in energy. |
| |
| These concepts will become clearer as you use the simulator and work through some of the problems. |
| |
| |
