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MOMENTUM Forces – “Time of Action” Forces in physics cover a wide range of timescales: “Steady Forces” “Impact Forces” “Periodic Forces” F F F t Examples: t Examples: t Examples: ● Earth-Moon gravity ● Sound waves ● Collisions ● Lift force on a plane ● Elastic forces (springs) ● Explosions Forces and Time – “The Big Picture” ● ● ● What determines the overall effect of forces on a physical system? The strength and direction of Fnet F net a= m – Newton's Second Law: – We can calculate instantaneous acceleration Also, the amount of time Fnet acts for – – A weak force acting for a short time has little effect A strong force acting for a long time has large effect Impulse ● To emphasize the importance of “time of action”, physicists invented the concept of “impulse” – Describes the overall effect of the force F avg =average force exerted Impulse = F avg t ● Example: Impact Force t =time of action F Favg t Impact Forces and Damage ● Consider two different impact forces: F F Fpeak Fpeak t ● These two forces produce the same impulse – ● t But the peak force is different in the two cases! The peak force determines the damage to objects – Strong, quick forces are more damaging than weak, slow ones Impact Forces – Examples Water Balloon Toss Golf club hits ball ● ● Large force acting for short time ● Amount of force at any time can be estimated by deformation of ball ● Balloon breaks if force gets too large To stop balloon without breaking it, must exert weak force for long time Impulse and Mass ● For a given impulse: – – ● A system with small mass will feel a large effect A system with large mass will feel a small effect Example: Swinging a baseball bat Has a large effect on a baseball Has a small effect on a dump truck Momentum ● An impulse produces a change in velocity ( Δv ) – ● The size of Δv depends on the mass of the system To emphasize the importance of mass, physicists invented the concept of “momentum” Momentum = m v ● m = mass v = velocity An impulse changes the momentum of a system F t = m v Momentum vs. Impulse in Physical Systems What Systems “Have” ● Mass ( m ) ● Position ( x ) ● Velocity ( v ) ● Acceleration ( a ) ● Momentum ( mv ) x m v a What Systems “Exchange” ● Force ( F ) ● Impulse ( F t ) F The “Force-Momentum Chain” Force Impulse Change in Momentum Time ● Newton's Third Law: The force exerted by the system is equal in strength to the force exerted on the system ● If a system's momentum is changing in a certain direction: – ● Another system's momentum changes in the opposite direction Systems can exchange momentum, but never create it Conservation of Momentum ● If the external Fnet on a system is zero: – – The momentum of that system will stay constant Internal forces do not change the system's momentum The total momentum of the Earth-Moon system is constant (The Earth and Moon exchange momentum) ● If the external Fnet on a system is not zero: – – The system exchanges momentum with another system One gets more positive, the other gets more negative Collisions ● Consider a two-object collision – ● Let the system be made up of both objects The impact force is an internal force to the system – – – The external force is zero The total momentum stays constant Rightward momentum is transferred to second object Collisions of Unequal Mass ● General rule – The larger the mass, the smaller the Δv The truck has a small change in speed, but the car takes off The truck picks up a small speed, but the car has a large change in velocity Elastic vs. Inelastic Collisions ● Elastic collisions – ● The objects bounce off each other with little deformation Inelastic collisions – – – As a result of the collision, the objects: Change shape Stick together Impulse and “Bounce-Backs” ● Consider a small object colliding with a very large one – – The large object gets a very small Δv (ignore it) Let's focus on the small object “Perfectly Inelastic” Collision “Perfectly Elastic” Collision The small object sticks to the big one Small object bounces off big one The impulse is just enough to stop the small object The impulse stops the small object AND pushes it back ( 2x as much ) Explosions ● System includes an exploding object – – Any forces exerted by the explosion will be internal The total momentum of the system will be conserved m1v1 ● m2v2 Total momentum is zero before and after explosion! – After explosion: left momentum + right momentum = 0 Summary ● When an external force acts for a certain amount of time, it delivers an impulse to the system ( F t ) ● The impulse changes the momentum of the system ● If we choose our system so there is no external force: – – ● The total momentum of the system remains constant This is true even if there are internal forces acting We can use this “conservation of momentum” to predict the effects of collisions and explosions