Objectives:

• Predict the change in momentum from the average force exerted on an object and the time interval during which it acts.

• Develop an expression to solve for a final or initial velocity of an object undergoing a change in momentum.

• Analyze data, graphs, and visual representations of objects undergoing a change in momentum.

​Momentum

• ​Mass in Motion

• ​2 variables

  • ​how much stuff is moving and how fast the stuff is moving

​Equations

• ​Momentum

  • ​p=mv Mass x Velocity

  • ​objects tendency to remain in motion

​Laws of Conservation (isolated system)

• a principle that the momentum before a collision is equal to the momentum after the collision

• ​What goes in must come out

​Equations

• Impulse

  • ​change in momentum

  • ​p_f - p_i = Δp (change)

    • ​p_f is the final momentum

    • ​p_i is the initial momentum

    • ​J is given to represent a change in impulse

      • ​J=Δp

• ​ F=J/Δt

• ​Δp=m(v_f-v_i)

​Velocity Time Graph

• ​Case A

  • ​initial velocity 5 m/s

  • ​final velocity -3m/s

• ​Case B

  • ​initial velocity 3 m/s

  • ​final velocity -1 m/s

F vs. t graphs

Because impulse is the product of the sum of the forces and time interval, impulse is the area under a F vs. t graph.

​Elastic Collision (rebound)

• ​collision involving a change in direction and speed of motion and kinetic energy is conserved

​Inelastic Collision

• ​A collision involving a change speed but not direction of motion

  • ​momentum is conserved but Kinetic energy is transferred

​How we define the system matters...

​Consider two carts (A and B), both with a mass of 1 kg. Cart A is moving to the right at 2 m/s and Cart B is stationary. They collide; Cart A comes to rest, and Cart B moves to the right at 2 m/s.

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​Inertia Versus Momentum

• ​Inertia

  • ​the resistance of an object to move

• ​momentum

  • ​mass in motion