Momentum (P) is mass in motion. It's a vector value, calculated by P = mass*velocity, hence its description. It's also a measurement of how hard it is to stop a certain object. Momentum is conserved in an isolated system, where there is no external force or impulse. Impulse is force acting over time, or the change in momentum.
Collisions
A collision occurs when two objects contact each other, exerting a force onto each other. There are two categories of collisions, with two types in each category: Elastic and Inelastic...
Elastic Collisions
Perfectly Elastic
In a perfectly elastic collision, kinetic energy is conserved and the objects involved are not deformed or changed in any way. The objects bounce apart, in a way. Momentum is conserved. |
Superelastic/Explosion
In an explosion, kinetic energy increases and a release of potential energy also occurs. |
Inelastic Collisions
Perfectly Inelastic
In a perfectly inelastic collision, kinetic energy is lost, and the objects will stick together and become one object; they don't "bounce" apart. |
Inelastic
In inelastic collisions, kinetic energy is lost, and the objects involved will deform and crash, but not stick together or bounce apart. |
Impulse
Impulse is a force acting over some time, and accounts for a change in momentum. When there is impulse in a collision, momentum is not conserved.
Equation of Impulse (J): J = F * Δt = ΔP P(initial) + J = P(final) https://stickmanphysics.com/stickman-physics-home/momentum-impulse-and-conservation-of-momentum/ |
Momentum Representations
Momentum can be represented using bar charts, in a similar way to energy. These 3-part charts are called LIL charts and look how they are spelled:
The graphs on the outside (L) are where the momentum bar charts are drawn. The bar in the middle (I) shows the impulse, which would result in some sort of change in momentum if there is impulse, or an outside force.
In the LIL chart for the system of the woman, we see that there is a change in momentum (nothing to something), and therefore, we see some volume in the impulse bar. In comparison, the system including both the woman and her son has no impulse because the system includes the forces which increased the momentum (AKA the woman on the son and vice versa). This is an example of an isolated system. |
Conservation of Momentum
Momentum is conserved in an isolated system; this means that as long as there is no external net force (impulse), total momentum in the system is constant throughout the collision.
Momentum is conserved in an object's center of mass. An object's center of mass can be visualized as the point at which the object is able to be balanced.
Momentum is conserved in an object's center of mass. An object's center of mass can be visualized as the point at which the object is able to be balanced.
For example, a hot air balloon of mass M is at rest in the sky. There is a man of mass m climbing a ladder up the balloon. As the man moves higher in position in relation to the earth at constant velocity v, the balloon's height will decrease. The balloon's velocity will be V. As the man's mass m moves higher, the balloon M must move lower to conserve momentum and the position of the center of mass.
mv = MV The balloon-man system is an isolated system, and thus has no external forces acting on it. Therefore, the total momentum must be constant throughout. Seeing as the balloon begins at rest, the initial momentum is 0. If the man begins to move at velocity v upwards, the center of mass is also moving upwards. Thus, to conserve momentum. the balloon must move down at a velocity (V) which its mass multiplied by that will be equivalent to the mass of the man m multiplied by his velocity, thus keeping the momentum of the center of mass 0. |
The Relationship Between Momentum, Energy, Forces, and Kinematics
In problem solving, such as the example below from mastering physics, equations and representations of different subjects of physics are related and used. Aspects of different types of equations can be found using other equations in other topics in physics. As seen below, a critical part of finding the mass of the block was time in the air. Without using kinematic equations, the time in the air, used to find the velocity of the block-clay system would not have been able to be solved for. Additionally, finding a mass required knowledge of momentum and also kinematics.