Momentum
- Definition - The strength or force that something has when it is moving.
- Momentum is always conserved when there is no external apply to the system.
- Momentum is a vector.
- SI units: - kg*m/s
Isolated System:
An isolated system is one in which the objects interact only with each other and not with the environment, or the sum of external exforces exerted on it is zero.
An isolated system is one in which the objects interact only with each other and not with the environment, or the sum of external exforces exerted on it is zero.
Mass is a conserved quantity:
It is constant in an isolated system. If the shystem is not isolated and its mass changes, we can always find the system in which the mass is constant.
Related Equation:
momentum initial + change in momentum = momentum final
It is constant in an isolated system. If the shystem is not isolated and its mass changes, we can always find the system in which the mass is constant.
Related Equation:
momentum initial + change in momentum = momentum final
Linear Momentum
p is a vector quantity that is the product of an object's mass m and velocity v. The total momentum of the system is the sum of the momenta of all objects in the system.
Impulse
J is the product of the average external force Favg exerted on an object during a time interval (change in time) and that time interval.
Related Equations:
p is a vector quantity that is the product of an object's mass m and velocity v. The total momentum of the system is the sum of the momenta of all objects in the system.
Impulse
J is the product of the average external force Favg exerted on an object during a time interval (change in time) and that time interval.
Related Equations:
- p = mv
- p (system) = p1 +p2 +...
- J = Favg * (time f - time i)
Generalized impulse-momentum principle:
The change in momentum of a system is equal to the net external impulse exerted on it. If the net impulse is zero, then the momentum of the system is constant. If the objects outside the system exerted forces on it and change its momentum, we can always redefine the system by including all interacting objects to keep the momentum of this new system constant. Therefore, momentum is conserved quantity.
Related Equations (According to the graph below):
The change in momentum of a system is equal to the net external impulse exerted on it. If the net impulse is zero, then the momentum of the system is constant. If the objects outside the system exerted forces on it and change its momentum, we can always redefine the system by including all interacting objects to keep the momentum of this new system constant. Therefore, momentum is conserved quantity.
Related Equations (According to the graph below):
- ( m1v1i + m2v2i + ... ) + Net Force on system * change in time = ( m1v1f + m2v2f +... )
- x- and y-component forms:
- m1v1ix + m2v2ix + Net Force on system x * change in time = m1v1fx + m2v2fx
- m1v1iy + m2v2iy + Net Force on system y * change in time = m1v1fy + m2v2fy
Collision
- In an isolated sysyem ---> no external forces
- Elastic collision:
- An elastic collision is a collision in which there is no net loss in kinetic energy in the system as a result of the collision. Both momentum and kinetic energy are conserved quantities in elastic collisions.
- Momentum initial = Momentum final
- Energy initial = Energy final
- Ineslastic collision:
- An inelastic collision, in contrast to an elastic collision, is a collision in which kinetic energy is not conserved due to the action of internal friction. In collisions of macroscopic bodies, some kinetic energy is turned into vibrational energy of the atoms, causing a heating effect, and the bodies are deformed.
- Momentum initial = Momentum final
Collision in Two Dimensions:
- For a collision where objects will be moving in 2 dimensions (e.g. x and y), the momentum will be conserved in each direction independently (as long as there's no external impulse in that direction). In other words, the total momentum in the x direction will be the same before and after the collision.
Center of Mass:
- The center of mass is a position defined relative to an object or system of objects. It is the average position of all the parts of the system, weighted according to their masses.
- One quick technique which lets us avoid the use of vector arithmetic is finding the center of mass separately for components along each axis. I.e:
For object positions along the x axis:- x cm = (m1x1 + m2x2 + ... + mnxn) / (m1 + m2 + ... + mn)
- y cm = (m1y1 + m2y2 + ... + mnyn) / (m1 + m2 + ... + mn)
- Newton's second Law of center of mass:
- F net = Macm
- Newton's second Law of center of mass:
Force V.S. Time Graph
- The area under a force-time graph is force multiplied by time, which is a quantity called impulse. Impulse is equal to the change in momentum of an object.
https://www.google.com/imgres?imgurl=https%3A%2F%2Fi.ytimg.com%2Fvi%2Fv_ce18NkWK8%2Fmaxresdefault.jpg&imgrefurl=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3Dv_ce18NkWK8&docid=XxwExudhtM4JdM&tbnid=LH1yJ_V9dl_ceM%3A&vet=10ahUKEwj_ruCSoZbnAhWriOAKHVJiAEgQMwhOKAkwCQ..i&w=1280&h=720&bih=646&biw=1260&q=force%20time%20graph%20impulse&ved=0ahUKEwj_ruCSoZbnAhWriOAKHVJiAEgQMwhOKAkwCQ&iact=mrc&uact=8
Momentum Bar Chart:
- One tool which can be utilized to express an understanding of the momentum-impulse model is to draw a bar chart.
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