Unit 9 Momentum Impulse 1 Momentum Define momentum

Unit 9: Momentum & Impulse

• • • • • 1. Momentum Define momentum and distinguish between momentum and velocity. momentum = (mass)(velocity) 2. Impulse Define impulse; distinguish between impulse and force. Determine the impulse acting on an object via a F vs t graph given the change in momentum. Determine the force acting on an object, given its change in momentum. 3. Conservation of Momentum Show that the system momentum before a collision is equal to the system momentum after the collision. system momentum = constant Show that the total system momentum after an explosion remains zero. Distinguish between elastic and inelastic collisions (∆Ek 1 ≠ ∆Ek 2) Use conservation principles to solve momentum problems involving elastic and inelastic collisions for initial velocity, final velocity or mass, given the other values.

Momentum & Impulse The final unit in our study of classical physics mechanics brings together many models from previous units. In this unit we will connect: • Constant velocity model • Uniform acceleration model • Newton’s 1 st, 2 nd, & 3 rd Laws of Motion • Conservation of energy model

Momentum & Impulse Our previous work examined the relationship of the motion of an object and the energy it stores in motion. This relationship was described by: • the mass of the object • the velocity of the object Energy kinetic: Ek= ½ mv 2

Momentum & Impulse Therefore, two objects with the same mass could store different amounts of energy if the velocities were different. Likewise, two objects with the same velocity could store different amounts of energy if the masses were different. As we consider our new model, we will further examine the relationship of mass and velocity in connection with Newton’s Laws.

Momentum & Impulse Newton’s 1 st Law holds that an object in motion will continue moving in the same manner (no velocity change) unless acted on by an unbalanced force. (Fnet=0 N : constant velocity or Fnet≠ 0 N : uniform acceleration) Newton’s 2 nd Law describes this change in motion by quantifying the relationship between net force (Fnet) and the mass of the object. (acceleration= Fnet/mass) Newton’s 3 rd Law holds that two objects interacting with each other must exert equal magnitude, but opposite direction forces on each other. (FA B=-FB A)

Momentum & Impulse Rearranging Newton’s 2 nd Law we get: Fnet= m(a) Using the definition of acceleration (Δv/Δt) we get: Fnet= m (Δv/Δt) Multiplying both sides by Δt simplifies to Fnet(Δt) = m (Δv) This simplification allows the motion allows a comparison of the mass and velocity of two objects that are interacting with each other according to Newton’s 3 rd Law

Momentum & Impulse Fnet A B(Δt) = m. A (Δv. A) Fnet B A(Δt) = m. B (Δv. B) According to Newton’s 3 rd Law, FA B=-FB A. Therefore, adding the first two relationships results in the following: Fnet A B(Δt) = m. A (Δv. A) +Fnet B A(Δt) = m. B (Δv. B) 0 = m. A (Δv. A) + m. B (Δv. B)

0 = m. A (Δv. A) + m. B (Δv. B) 0 = m. A (vf. A- vi. A ) + m. B (vf. B- vi. B) 0 = m. Avf. A- m. Avi. A + m. Bvf. B- m. Bvi. B m. Avi. A + m. Bvi. B = m. Avf. A+ m. Bvf. B This new relationship holds that the sum of the products of two objects mass and velocities before interaction must equal the sum of the products after the interaction.

Model Summary Conservation of momentum relationship m. Avi. A + m. Bvi. B = m. Avf. A+ m. Bvf. B Impulse – Change in Momentum relationship (impulse) = (change in momentum) Fnet(Δt) = m (Δv)

Model Summary Conservation of momentum relationship m. Avi. A + m. Bvi. B = m. Avf. A+ m. Bvf. B The conservation of momentum is unlike the conservation of energy in that momentum is directional. This allows a system with no initial momentum to change into a system with momentum provided the sum of the momenta is zero.

Model Summary Impulse – Change in Momentum relationship (impulse) = Fnet(Δt) = (change in momentum) m (Δv) Using the Impulse-Momentum relationship, it is possible to analyze a system to determine what factor could be modified to either increase of decrease force acting on an object. A common application of this concept is found in safety features engineered into automobiles.

Model Summary Impulse – Change in Momentum relationship (impulse) = (change in momentum) Fnet(Δt) = m (Δv) One representation used to compare changes to a system is the force versus time graph. The graph below compares two scenarios where change in momentum is the same; however maximum force is changed by increasing the time interval for the event. The areas under the curves represent the impulse and for both situations, the areas would be equal. If the time interval is extended, then the same change in momentum can occur using a smaller average force. Force Time

Resources • Honors Text – pages 198 -216 • CP Text – pages 58 -64