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MOMENTUM AND IMPULSE • Momentum is a vector. • An object with momentum is MOVING. • Impulse is a change is momentum. • When two (or more) objects collide, the momentum of the objects before the collision is the same as the momentum after the collision I. Definition of LINEAR MOMENTUM p = mv Units: kg m/s • Momentum, p, is a vector. It is the product of an object’s mass and velocity. • An object at rest has a momentum of 0. • This helps distinguish momentum from inertia. An object must be in MOTION to have momentum. • An object with a SMALL mass can have a LARGE momentum if it has a LARGE v. • An object with a LARGE mass can have a SMALL momentum if it is at rest or moving slowly. 1 II. IMPULSE A. Definition of IMPUSLE IMPULSE is a CHANGE in MOMENTUM. Well, you won’t likely change an object’s momentum by changing its mass. Momentum changes when an unbalanced force causes a CHANGE IN ACCELRATION. In other words, a change in velocity is accompanied by a change in momentum. If the word “impulse” makes you think about time, your intuition is correct. Impulse has to do with changing momentum with a force applied over a given time. Here’s the math: F = ma Δv F=m t Ft = mΔv Impulse = force x time force x time equals a change in momentum 2 B. Examining the IMPULSE equation Ft = mΔv Let’s set the right hand side of the equation, change in momentum, equal to a constant. It doesn’t change. Now, what happens if we change force and time on the left hand side? for a given value of momentum change… A LARGE FORCE is required for a SMALL (short) contact time of the force. A SMALL FORCE is required for a LARGE (long) contact time of the force. Basically, the shorter the contact time, the larger the force for a given momentum. If you run into a brick wall with momentum x, the contact time is short and the force large (ouch!) If you run into a wall of pillows with momentum x, the contact time is long and force small (pain is minimized) 3 III. CONSERVATION OF MOMENTUM For a collision occurring between object 1 and object 2 in an ISOLATED system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. That is, the momentum lost by object 1 is equal to the momentum gained by object 2. The cue ball, when it strikes the yellow motionless ball, transfers its momentum to the yellow ball. The cue ball has a final momentum of 0. The word ISOLATED means that external forces do not act on the colliding objects 4 conservation of momentum, continued By Newton’s 3rd law, we know that during a collision, the force exerted by each object is equal in magnitude and opposite in direction F2 F 1 = −F 2 m1 m2 F1 If m1 > m2 but their velocities are the same when they collide, in which direction will the balls move? since the contact time is the same, the impulse is the same (but in opposite directions) F 1t = −F 2t m1Δv1 = −m2 Δv2 all the - signs are doing is indicating DIRECTION 5 conservation of momentum, continued For momentum to be conserved, the sum of the momentum of each colliding body before and after the collision must equal 0. (m1v1 + m2 v2 )before + (m1v1 + m2 v2 )after = 0 Newton’s cradle. This toy shows how the momentum of one sphere is transferred to a sphere on the other end of the row. 6