Linear Momentum and Collisions

Momentum and Impulse m F m A block of mass (m) is acted upon by a force (F) After a time (D) the block acquires a velocity vf Momentum is conserved Momentum is a vector

Momentum and Impulse Newton’s 2nd Law p Using Calculus: Newton’s form of his 2nd law

v1 u1 Fm = - FM M m FM Fm M m v = u FmDt = - FMDt M m v2 u2 Dpm = - DpM m(u2 - u1) = -M(v2 - v1) Conservation of Momentum: Blocks have the same speed (v) at closest approach. mu2 - m u1 = - Mv2 + Mv1 Conservation of Momentum Mv1 + m u1 = Mv2 + mu2 p(before) = p(after)

before vo after M m v = ? M m Using the conservation of momentum to find the final speed when two blocks stick together.

after before v vo M m Find the speed of the bullet and block after impact.

Collisions Elastic Collisions Inelastic Collisions Momentum and Kinetic Energy are both conserved Inelastic Collisions Elastic and Inelastic collisions A perfectly inelastic collision losses as much kinetic energy as possible Only Momentum is conserved

Perfectly Inelastic Collision before v1 v2 after m1 m2 vf m1 m2 Find the final speed after a Perfectly Inelastic Collision Linear Momentum and Collisions.ppt

Elastic Collision (General Equations) v1i v2i m1 m2 m2 m1 v1f v2f General Equations for an elastic collision. Velocity is a vector - use + and - to indicate directions.

Elastic Collision (v2i = 0) m2 m1 v1i m2 m1 v1f v2f Special Case: Elastic collision with m2 initially at rest.

Elastic Collision (v2i = 0 and m1= m2) V2f = V1i Special Case: Elastic collision with equal masses and with m2 initially at rest.

Ballistic Pendulum vo M h m v Ballistic Pendulum Cons. Energy Cons. Momentum vo M m v Ballistic Pendulum Use conservation of momentum and energy.

Ballistic Pendulum Find the speed of the bullet vo M h m v Cons. Momentum vo M m v

Ballistic Pendulum h Cons. Energy M v

Collisions in two dimensions p1f p1i m1 m1 m2 p2f Linear Momentum and Collisions.ppt

Collisions in two dimensions y p1i = m1v1i p1f = m1v1f p2f = m2v2f q f P1i = P1f + P2f x m1v1f cos(q) + m2v2f cos(f) = m1v1i m1v1f sin(q) + m2v2f sin(f) = 0

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