M OMENTUM Momentum Impulse Momentum Defined p momentum

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M OMENTUM! Momentum Impulse

M OMENTUM! Momentum Impulse

Momentum Defined = p = momentum vector m = mass v = velocity vector

Momentum Defined = p = momentum vector m = mass v = velocity vector

Momentum Facts • p = mv • • Velocity and momentum vectors point in

Momentum Facts • p = mv • • Velocity and momentum vectors point in the same direction. • SI unit for momentum: - (no special name). • Momentum is a conserved quantity (this will be proven later). • • 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

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. /s m k 9 26º 5 g p = 45 kg · m /s at 26º N of E

Equivalent Momenta Car: m = -- kg; v = -- m /s p =

Equivalent Momenta Car: m = -- kg; v = -- m /s p = 1. 44 · 105 kg · m /s Bus: m = -- kg; v = -- m /s p = 1. 44 · 105 kg · m /s Train: m = 3. 6 · 104 kg; v = 4 m /s p = 1. 44 · 105 kg · m /s continued on next slide

Equivalent Momenta (cont. ) The train, bus, and car all have different masses and

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. --

Impulse Defined Impulse is defined as the product force acting on an object and

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: = 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

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 Fnet = m a shows this is equivalent to a newton. --

Impulse - Momentum Theorem The impulse due to all forces acting on an object

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: net t =

Stopping Time Ft = Ft Imagine a car hitting a wall and coming to

Stopping Time Ft = Ft 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 this time hitting a giant haystack and coming to rest. The force on the car is much smaller now (little F ), but it acts for a much longer time (big t ). In each case the impulse involved is the same since the change in momentum of the car is the same. Any net force, no matter how small, can bring an object to rest if it has enough time. A pole vaulter can fall from a great height without getting hurt because the mat applies a smaller force over a longer period of time than the ground alone would.