From http://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/u4l1b.html- by Tom Henderson
The Impulse-Momentum Change Theorem
Momentum and Impulse Connection
Momentum is a commonly used term in sports. <![if !vml]>
<![endif]>When asports announcer says that a team has the momentum they mean that the team is reallyon the move and is going to be hard to stop. An object with momentumis going to be hard to stop. To stop such an object, it is necessary to apply aforceagainst its motion for a given period of time. The more momentum whichan object has, the harder that it is to stop. Thus, it would require a greateramount of force or a longer amount of time (or both) to bring an object withmore momentum to a halt. As the force acts upon the object for a given amountof time, the object's velocity is changed; and hence, the object's momentum ischanged.
The concepts in the above paragraph should not seem likeabstract information to you. You have observed this a number of times if youhave watched the sport of football. In football, the defensive players apply aforce for a given amount of time to stop the momentum of the offensive playerwho has the ball. You have also experienced this a multitude of times whiledriving. As you bring your car to a halt when approaching a stop sign orstoplight, the brakes serve to apply a force to the car for a given amount oftime to stop the car's momentum. An object with momentum can be stopped if aforce is applied against it for a given amount of time.
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A force acting for a given amount of time will change anobject's momentum. Put another way, anunbalanced force always accelerates an object - either speeding it up orslowing it down. If the force acts opposite the object's motion, it slowsthe object down. If a force acts in the same direction as the object's motion,then the force speeds the object up. Either way, a force will change thevelocity of an object. And if the velocity of the object is changed, then themomentum of the object is changed.
These concepts are merely an outgrowth of Newton'ssecond law as discussed in an earlier unit.
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If both sides of the above equation are multiplied by the quantity t, a newequation results.
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This equation is one of two primaryequations to be used in this unit. To truly understand the equation, it isimportant to understand its meaning in words. In words, it could be said thatthe force times the time equals the mass times the change in velocity. Inphysics, the quantity Force*time is known as the impulse. And since thequantity m*v is the momentum, the quantity m*"Delta "v must be thechange in momentum. The equation really says that the
Impulse =Change in momentum
One focus ofthis unit is to understand the physics of collisions. The physics of collisionsare governed by the laws of momentum; and the first law which we discuss inthis unit is expressed in the above equation. The equation is known as the impulse-momentum change equation. The law can be expressed this way:
In a collision, an objectexperiences a force for a specific amount of time which results in a change inmomentum (the object's mass either speeds up or slows down). The impulseexperienced by the object equals the change in momentum of the object. Inequation form, F * t = m * Delta v.
from http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/SHM/HookesLaw.html
Hookes Law - Spring Force
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| Fs | = Force exerted by the spring. SI: N |
| k | = Spring Constant. SI: N/m <![if !vml]> |
| x | = Displacement from equilibrium position. SI: m |
<![endif]>* The negative sign indicates that the spring force is a restoringforce, i.e., the force Fs always acts in the oppositedirection from the direction in which the system is displaced. Here we assumethat the positive direction for values of x are the same as the positivevalues of the force.
* The origin has to be placed at the position where the spring systemwould be in static equilibrium for the equation Fs = -k xto be valid. This is the location were the net force on the object to which thespring is attached is equal to zero. If not, then Fs = -k(x- xo) where xo is equilibrium positionrelative to the origin.
* Springs are normally assumed to be massless so their inertia can beneglected. This also means that the force exerted by both ends of the springare the same but in opposite directions.
