Chapter 7 Impulse and Momentum

Velocity of the Center of Mass

If the total linear momentum of a system of particles remains constant during an interaction such as a collision, the velocity of the center of mass also remains constant.

Conservation of Linear Momentum + Equation

m(1)v(f1) + m(2)v(f2) = m(1)v(01) + m(2)v(02) Which is final total linear momentum = initial total linear momentum m(1) and m(2) are the masses, v(f1) and v(f2) are the final velocities, and v(01) and v(02) are the initial velocities of the objects.

Linear Momentum (equation)

p = mv p = linear momentum m = mass v = velocity

Misconceptions

Momentum is a VECTOR and DIRECTION matter (+) going right vs (-) going left.

Impulse-momentum theorem (equation)

(Net) F (change in) t = mv(force) - mv(first)

Elastic Collision

A collision between two or more objects in which both momentum and kinetic energy are conserved, such as in the collision between two steel balls. The total kinetic energy of the system before the collision is the same as after the collision.

Inelastic Collision

A collision between two or more objects in which momentum is conserved but kinetic energy is not conserved, such as two railroad cars which collide and lock together. The total kinetic energy of the system is not the same as after the collision.

Misconceptions #9

If; KE(total initial) = KE(total final) then the collision is elastic and if it is not then a collision is inelastic.

Misconceptions #6

In a perfectly elastic collision, the objects must bounce off of each other and KE must be conserved; ((v(1) - v(2))initial = -((v(1) - v(2))final

Misconceptions #7

In an inelastic collision, the KE is not conserved as it turns into thermal energy, etc.

Impulse (equation)

J = F(change in) t = (change in)p = mv(f) - mv(o) t = time J = impulse F = force m = mass

Misconceptions #4

The equation (net)F = (change in)p / (change in) t Allows for the change in momentum to forced as it is also (net) F = ma

Internal Forces

The forces which act between the objects of a system.

External Forces

The forces which act on the object of a system from outside the system, that is, by an agent which is not a part of the system of objects which are bring studied.

Impulse-momentum theorem

The impulse-momentum theorem states that when a net force F acts on an object, the impulse of the net force is equal to the change in momentum of the object.

Location of the Center of Mass + Equation

The location of the center of mass of two particles lying on the x axis is given by Xcm = ((m(1)x(1) + m(2)x(2)) / ((m(1) + m(2)) Where m(1) and m(2) are the masses of the particles and x(1) and x(2) are their positions relative to the coordinate origin. If the particles move with velocities v(1) and v(2), the velocity v(cm) of the center of the mass is; Vcm = ((m(1)v(1) + m(2)v(2)) / ((m(1) + m(2))

Misconceptions #8

The misconception is in an inelastic collision the objects will always stick together. In an inelastic collision, the objects can both stick together (perfectly inelastic) or can bounce off of each other.

Misconceptions #3

The misconception is momentum is lost in inelastic collisions. Momentum is always conserved no matter if it's an inelastic or elastic collision.

Momentum

The momentum of an object is the product of its mass and velocity, to change the momentum of an object you must apply an Impulse, which is the product of force and the time in which force acts. With no external forces acting on a system of objects, momentum is said to be conserved; if the total momentum before the event is equal to the total momentum after the event.

Center of mass

The point at which the total mass of a system of masses can be considered to be concentrated.

Conservation of Linear Momentum

The principle of conservation of linear momentum states that the total linear momentum of an isolated system remains constant. For a two-body collision, the conservation of momentum can be written as: (see next card). When the total linear momentum is conserved in a two dimensional collision, x and y components of the total linear momentum are conserved seperatly

Linear Momentum

The product of a mass of an object and it's velocity. Momentum is a vector quantity, and thus the total linear momentum of a system of objects is the vector sum of individual momenta of the objects in the system. Linear momentum is a vector that points in the same direction as velocity.

Impulse

The product of the average force acting on an object and the time during which it acts. Impulse is a vector quantity, and can also be calculated by finding the area under a force versus time curve. Points in the same direction as the average force.

Misconceptions cont #2

There is no momentum if two objects are moving towards each other with the same mass and velocity.

Misconceptions #5

To find impulse when given a F vs time graph, impulse is the area under the graph.