chap9 - M O MENTUM Momentum Impulse Conservation of...

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Unformatted text preview: M O MENTUM! Momentum Impulse Conservation of Momentum in 1 Dimension Conservation of Momentum in 2 Dimensions Angular Momentum Torque Moment of Inertia Momentum Defined p = m v p = momentum vector m = mass v = velocity vector Momentum Facts • p = m v • Momentum is a vector quantity! • Velocity and momentum vectors point in the same direction. • SI unit for momentum: kg · m /s (no special name). • Momentum is a conserved quantity (this will be proven later). • A net force is required to change a body’s momentum. • Momentum is directly proportional to both mass and speed. • Something big and slow could have the same momentum as something small and fast. Momentum Examples 10 kg 3 m /s 10 kg 30 kg · m /s Note: The momentum vector does not have to be drawn 10 times longer than the velocity vector, since only vectors of the same quantity can be compared in this way. 5 g 9 k m / s p = 45 kg · m /s at 26º N of E 26º Equivalent Momenta Bus: m = 9000 kg; v = 16 m /s p = 1.44 ·10 5 kg · m /s Train: m = 3.6 ·10 4 kg; v = 4 m /s p = 1.44 ·10 5 kg · m /s Car: m = 1800 kg; v = 80 m /s p = 1.44 ·10 5 kg · m /s continued on next slide Equivalent Momenta (cont.) The train, bus, and car all have different masses and speeds, but their momenta are the same in magnitude. The massive train has a slow speed; the low-mass car has a great speed; and the bus has moderate mass and speed. Note: We can only say that the magnitudes of their momenta are equal since they’re aren’t moving in the same direction. The difficulty in bringing each vehicle to rest--in terms of a combination of the force and time required--would be the same, since they each have the same momentum. Impulse Defined Impulse is defined as the product force acting on an object and the time during which the force acts. The symbol for impulse is J . So, by definition: J = F t Example: A 50 N force is applied to a 100 kg boulder for 3 s. The impulse of this force is J = (50 N) (3 s) = 150 N · s. Note that we didn’t need to know the mass of the object in the above example. Impulse Units J = F t shows why the SI unit for impulse is the Newton · second. There is no special name for this unit, but it is equivalent to a kg · m /s. proof: 1 N · s = 1 (kg · m /s 2 ) (s) = 1 kg · m /s { F net = m a shows this is equivalent to a newton. Therefore, impulse and momentum have the same units, which leads to a useful theorem. Impulse - Momentum Theorem The impulse due to all forces acting on an object (the net force) is equal to the change in momentum of the object: F net t = ∆ p We know the units on both sides of the equation are the same (last slide), but let’s prove the theorem formally: F net t = m a t = m ( ∆ v / t) t = m ∆ v = ∆ p Imagine a car hitting a wall and coming to rest. The force on the car due to the wall is large (big F ), but that force only acts for a small amount of time (little t ). Now imagine the same car moving at the same speed but...
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This note was uploaded on 11/17/2011 for the course PHYS 121 taught by Professor Burgeson during the Fall '11 term at BYU.

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chap9 - M O MENTUM Momentum Impulse Conservation of...

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