Linear impulse

Physics> Linear momentum

Linear momentum is a derivative of the mass and velocity of an object, which is preserved in elastic and inelastic collisions.

Learning challenge

• Determine the momentum of two colliding objects.

Key points

• Linear impulse reflects a vector concept characterized by direction and magnitude.
• Momentum is important because it acts as a stored quantity.
• The momentum of a system of particles is the sum of their momenta. If the masses of two particles m_one and m₂, and the velocities v_one and v₂, then the total impulse: p = p_one + p_{2 =} m_onev_one + m₂v_2…

Terms

• Elastic collision is an impact between two bodies, where the total kinetic energy after the collision is equal to the exponent before it. Elastic ones appear in cases where there is no pure transformation of kinetic energy into other forms.
• Inelastic collision – kinetic energy is not conserved.
• Conservation is a measurable property of an isolated physical system not to change as it evolves.

Within the limits of classical mechanics, a linear impulse acts as the derivative of the mass and velocity of an object: p = mv (p and v are vectors). It is a vector concept with direction and magnitude. The linear momentum is important because it is a conservative value, that is, in a closed system it will remain stable.

Impulse has a direction, so it can be applied in predicting the resulting direction of objects after impact between them and the speed. The momentum remains stable under inelastic and elastic collisions. If the collision happened on a plane with friction or air resistance, then their impulses will need to be taken into account.

Let’s follow this with an example. The momentum of the systems of two particles is equal to the sum of their momenta. If their masses m_one and m₂, and the velocities v_one and v₂, then the total impulse: p = p_one + p_{2 =} m_onev_one + m₂v_2…

Don’t forget that momentum and velocity are vector quantities. If the particles are displaced in one direction, then v_one and v₂ possess one sign.

We choose a plane for the movement of x and y and write the total impulse as:

p_x = p_1x + p_{2x =} m_onev_1x + m₂v_2x…

P_y = p_1y + p_{2y =} m_onev_1y + m₂v_2y…

In the case of two-dimensionality, the impulse is decomposed into two components, and the equation for each will repeat the above.

Momentum is important because it has the ability to persist.

The total momentum of the system is conserved (we neglect the loss of friction)

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