Linear Momentum AP B CHAPTER 7 Momentum Linear

Linear Momentum AP B CHAPTER 7

Momentum Linear Momentum of a body is defined as the product of its mass and its velocity. Momentum symbol, ρ (rho), = mv. Since velocity is a vector, momentum is also a vector with its direction being that of the object’s velocity. Units of momentum are derived: kg*m/s A fast moving car has more momentum than a slower moving car of the same mass and a heavy truck has more momentum than a light car at the same speed.

Enter Force A force is required to change the momentum of an object. Forces can increase, decrease, or change direction of an object’s momentum. ΣF=Δρ/Δt. The rate of change of momentum is equal to the net force applied. ΣF= the net force on the object. Δρ is the change in Momentum and Δt is the Time interval for the change.

Deriving force changing momentum Recall from Newton’s second law: ΣF=ma, and =m a Because a = Δv/Δt we arrive at F=ma. We have dealt with changes in velocity, but it is important to note that sometimes MASS can change, such as a rocket in takeoff burning fuel!

Conservation of Momentum Under certain circumstances, momenta is a conserved quantity. Consider certain types of collisions…

Changes in momenta Although the momenta of each ball changes as a result of the collision, the total momenta of the system remains constant. This is found by the sum of the individual momenta. m 1 v 1 + m 2 v 2= m 1 v 1’ + m 2 v 2’ Momentum before = momentum after This is a general Law of Conservation of Momentum and applies for the SYSTEM involved.

Collisions and Impulse From Newton’s 2 nd law: Fnet = rate of change in momentum (Δρ/Δt) therefore, in a collision a force exerted over a period of time (Impulse) changes the momentum of an object (Δmv). FΔt = Δρ Impulse = change in momentum In a collision, the force between objects is generally NOT constant. It is often sufficient to approximate the average force over that time interval. This impulse is the area under the curve of a F vs. t graph.

Conservation of Energy and Momentum in collisions When objects collide, we can compare energy before and after collisions. If no damage is done and no heat is produced, the collision is considered elastic and the total KE is conserved as well as the total momentum. At the atomic level, this is common. On the “macro” level, elastic collisions are rare as thermal energy, sound, & other forms are produced.

Energy conservation of collisions The total energy in a collision is ALWAYS conserved, even when Kinetic energy is not. Collisions where KE is NOT conserved are considered inelastic collisions. These tend to convert KE to other forms of energy (often thermal) so we write: