Linear Momentum Momentum Linear Momentum of a body is defined as the product of its mass and its velocity. Momentum symbol, (rho), = mv.rho), = mv. Since velocity is a vector, momentum is also a vector with its direction being that of the objects 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 objects momentum. F=/t. The rate of change of momentum F=/t. The rate of change of momentum is equal to the net force applied. F=/t. The rate of change of momentum F= the net force on the object. is the change in
Momentum and t is the Time interval for the change. Deriving force changing momentum Recall from Newtons second law: F=/t. The rate of change of momentum F=ma, and mv mv 0 v F
m =ma t t t Because a = v/t 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. m1v1 + m2v2= m1v1 + m2v2 Momentum before = momentum after This is a general Law of Conservation of Momentum and applies for the SYSTEM involved. Collisions and Impulse From Newtons 2nd law: Fnet = rate of change in momentum (rho), = mv./t) therefore, in a collision a force exerted over a period of time (rho), = mv.Impulse) changes
the momentum of an object (rho), = mv.mv). Ft = 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. Ft 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. ( 1 2 ) before ( 1 2 ) after 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 (rho), = mv.often thermal) so we write: ' 1 KE1 KE2 KE KE ' 2
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