Calculators/Physics/Momentum and collisions

Momentum and collisions

Momentum p = m·v · inelastic collision

Momentum and collisions — illustration
Momentum p
10 kg·m/s

Momentum p = m·v is the body’s “quantity of motion” — a vector pointing along the velocity. Unit: kg·m/s.

Momentum is the product of mass and velocity — a body's "quantity of motion":

p=m⋅vp=m\cdot v

It is a vector quantity (its direction matches the velocity). In an isolated system the conservation of momentum holds: the total momentum before an interaction equals the total momentum after it.

For an inelastic collision (the bodies stick together and move as one) the common velocity is:

v=m1v1+m2v2m1+m2v=\frac{m_1 v_1+m_2 v_2}{m_1+m_2}

Velocities are signed — a negative value means motion in the opposite direction. Note: in an inelastic collision momentum is conserved, but kinetic energy decreases (part of it turns into heat).

Examples

m = 2 kg, v = 5 m/s
→ p = 10 kg·m/s
Collision: 2 kg (3 m/s) + 1 kg (−1 m/s)
→ v = (6−1)/3 ≈ 1.67 m/s

Frequently asked questions

Is energy conserved in a collision?+

Momentum always is (in an isolated system). Kinetic energy only in an elastic collision; in an inelastic one part of it turns into heat and deformation.

What does a negative velocity mean?+

Motion in the opposite direction. When adding momenta you must account for the signs — two bodies moving towards each other have momenta of opposite sign.

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