Linear momentum formula

Conservation of Momentum using Control Volumes Conservation of Momentum using Control Volumes Conservation of Linear Momentum Recall the conservation of linear momentum law for a system: In order to convert this for use in a control volume, use RTT with B = m V, beta = V we get: NOTE: Recall that at any instant of time t, the system & CV occupy the SAME physical space. So, the forces of the system are the same at the forces of the control volume at a given instant. • For a fixed control volume we have the following equation: This is a vector equation so it has three components. • First, let us consider the component in the X-direction. We will drop the cv subscript since it is understood. The conservation of linear momentum equation becomes: Notice that the V dot n term is a scalar, not a vector. • Next, let us consider the component in the Y-direction. The conservation of linear momentum applied to the y-direction becomes: • Similarly, the conservation of momentum could be applied to the Z-direction. • It is now time for a few simplifications for the right hand side of the CLM equation. • First, let us assume that we have one dimensional inlets and outlets. This implies that our velocity vector V is parallel to our normal to the surface vector n. We also assume that the velocity is constant across the inlet or outlet surface. Assuming density is constant, we can rewrite the last term in our CLM equation: This holds true because V dot n = V for outlets and -V for inlets. W...

• Physics • Mechanics and Materials • Momentum Momentum We hear the word momentum a lot, especially in sports. When a team, for instance, is playing well and winning games consistently, we say that team has momentum. While we may not use this word in a quantitative sense in everyday life, momentum is actually related to mathematics when it comes to physics.Any object with mass that is moving has momentum. In… Momentum • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • We hear the word ...

Term (symbol) Meaning Linear momentum ( p p p p ) Product of an object's mass and velocity. Also called “momentum” for short. Momentum is conserved when no external forces act on a system. Vector quantity with SI units of kg ⋅ m s \dfrac s kg ⋅ m ​ start fraction, start text, k, g, end text, dot, start text, m, end text, divided by, start text, s, end text, end fraction . Equation Symbols Meaning in words p = m v p = mv p = m v p, equals, m, v p p p p is momentum, m m m m is mass, and v v v v is velocity Momentum is mass times velocity. Δ p = F net Δ t \Delta p = F_\text F net ​ F, start subscript, start text, n, e, t, end text, end subscript is the net external force, Δ p \Delta p Δ p delta, p is change in momentum, and Δ t \Delta t Δ t delta, t is the time over which a net force acts Change in momentum is proportional to the net external force and the time over which a net force acts. A bigger net force over the same time period means a larger change in momentum. For example, a heavy truck coming to a stop will have a much larger change in momentum than a light car in the same amount of time. A larger change in momentum means a larger external force is needed to slow it down, so the truck brakes have to work much harder! • Some people think momentum and kinetic energy are the same. They are both related to an object’s velocity (or speed) and mass, but momentum is a vector quantity that describes the amount of mass in motion. Kinetic energy is a measure of an object’s en...

Momentum (P) is equal to mass (M) times velocity (v). But there are other ways to think about momentum! Force (F) is equal to the change in momentum (ΔP) over the change in time (Δt). And the change in momentum (ΔP) is also equal to the impulse (J). Impulse has the same units as momentum (kg*m/s or N*s). Created by Sal Khan. When doing momentum problems to obtain the combined velocity, why is it that we do not use the concept of kinetic energy? We can use mv^2/2 to obtain this value, so why would it not work if when we assume v is a constant value after collision and that m is the sum of the two masses, we solve for a different value of v compared to solved with the momentum method? The main reason one cant apply "Work Energy Theorem (Kinetic Energy Conservation, as in this case)" on this problem, because some Kinetic Energy is stored as Potential Energy (Which is due to deformation caused by the collision at the surface of impact) thus the final Kinetic Energy is not equal to initial KE. NOTE: If this question proclaimed an elastic collision between the objects. Then KE(initial)=KE(final), because elastic collision means that the surfaces of the bodies AFTER (NOT DURING) the impact will reform fully to their original shapes, thus no extra PE is stored AFTER the collision. Acceleration = (v-u)/t where v: Final Velocity u: Initial Velocity t: Time elapsed The numerator is change in velocity (v-u), but the whole expression tells you the amount the velocity changes per unit t...

There are many conserved quantities in physics. They are often remarkably useful for making predictions in what would otherwise be very complicated situations. In mechanics, there are three fundamental quantities which are conserved. These are momentum, energy, and angular momentum. Conservation of momentum is mostly used for describing collisions between objects. Just as with the other conservation principles, there is a catch: conservation of momentum applies only to an isolated system of objects. In this case an isolated system is one that is not acted on by force external to the system—i.e., there is no external impulse. What this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system. p 1 i + p 2 i + … = p 1 f + p 2 f + … \mathbf + \ldots p 1 i ​ + p 2 i ​ + … = p 1 f ​ + p 2 f ​ + … p, start subscript, 1, i, end subscript, plus, p, start subscript, 2, i, end subscript, plus, dots, equals, p, start subscript, 1, f, end subscript, plus, p, start subscript, 2, f, end subscript, plus, dots Consider a collision between two objects, object A and object B. When the two objects collide, there is a force on A due to B— F A B F_\mathrm F B A ​ F, start subscript, B, A, end subscript . The forces act between the objects when they are in contact. The length of time for which the objects are in contact— t A B t_\mathrm t B A ​ t, sta...

Fluids eBook: Linear Momentum Equation Ch 4. Fundamental Laws (Integral Anal.) Multimedia Engineering Fluids Mass Momentum Momentum Energy Fluids Linear Momentum Equation New eBook website Chapter 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Appendix eBooks Author(s): Chean Chin Ngo Kurt Gramoll ©Kurt Gramoll FLUID MECHANICS - THEORY The linear momentum equation will be presented in this section. The details of the derivation are omitted, with attention focused on proper use of the equation. Linear Momentum Equation Linear momentum equation for fluids can be developed using Newton's 2nd Law which states that sum of all forces must equal the time rate of change of the momentum, Σ F = d(m V)/dt. This easy to apply in particle mechanics, but for fluids, it gets more complex due to the Unit Normal Vector where V is the velocity vector, n is the outward unit normal vector, and Σ F represents the sum of all forces (body and surface forces) applied to the control volume. The actual derivation of this equation is omitted but can be easily done using Reynolds Transport Theorem. This is similar to the conservation of mass equation, but it has an added velocity term in each integral. Also, the sum is not zero, but equal to all the applied forces. Physically, the linear momentum equation states that the sum of all forces applied on the control volume is equal to the sum of the rate of change of momentum inside the control volume and the net flux of momentum through the control surface. For steady f...

https://phys.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FUniversity_Physics%2FBook%253A_University_Physics_(OpenStax)%2FBook%253A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)%2F09%253A_Linear_Momentum_and_Collisions%2F9.S%253A_Linear_Momentum_and_Collisions_(Summary) Expand/collapse global hierarchy • Home • Bookshelves • University Physics • Book: University Physics (OpenStax) • University Physics I - Mechanics, Sound, Oscillations, and Waves (OpenStax) • 9: Linear Momentum and Collisions • 9.S: Linear Momentum and Collisions (Summary) Expand/collapse global location \( \newcommand\) • • • • • • • • • • Key Terms center of mass weighted average position of the mass closed system system for which the mass is constant and the net external force on the system is zero elastic collision that conserves kinetic energy explosion single object breaks up into multiple objects; kinetic energy is not conserved in explosions external force force applied to an extended object that changes the momentum of the extended object as a whole impulse effect of applying a force on a system for a time interval; this time interval is usually small, but does not have to be impulse-momentum theorem change of momentum of a system is equal to the impulse applied to the system inelastic collision that does not conserve kinetic energy internal force force that the simple particles that make up an extended object exert on each o...