Momentum Another way to look at motion Momentum = mass x velocity p = m· v kg· m/s = kg· m/s Momentum is a vector. Direction matters!

What is momentum? Synonyms: Impetus, Forward Progress, Oomph You recognize it when you see it: Big truck travelling fast – lots of momentum Skate board travelling fast – not so much momentum Housefly moving slow – hardly any momentum Large momentum—hard to stop

Calculating momentum What is the momentum of a 100 kg football player moving east at 8 m/s? m = 100 kg v = 8 m/s east p = m · v p = 100 x 8 = 800 kg·m/s east

Momentum vs Kinetic Energy KE also involves mass and velocity. Let’s compare: Momentum Kinetic Energy m∙v ½ m·v2 kg·m/s J or kg·m2/s2 Vector, +/- shows direction Scalar, always + Conserved in collisions Usually not conserved in collisions Changed by impulse, F∙t Changed by work, F·d

Momentum vs Kinetic Energy example That v2 term in KE = ½ m·v2 is important! Consider a glacier. Mass = 1012 kg Velocity = 10-5 m/s Momentum, m∙v, is big, 107 kg·m/s. You wouldn’t easily stop a glacier! But the KE, ½ m·v2, is only about 50 J, as much energy as you would get dropping your physics book on your foot. That low v affects KE much more than it does momentum! And a large momentum doesn’t always mean a large KE!

Changing momentum Momentum is most interesting when it changes or is conserved (as in collisions). How do we change the momentum of an object? Requires a force, and what matters is the time over which the force is applied. Force x time is Impulse. Symbol is sometimes J Impulse J = F ∙ t Unit is N·s Impulse is also the change in momentum, so J = ∆p = m·∆v = F ∙ t (so N·s = kg·m/s) Impulse is a vector, too, so direction matters.

Impulse example #1 What is the change in momentum of a 2000 kg truck initially travelling 30 m/s north when a braking force of 600 N is applied for 90 seconds? m = 2000 kg vi = +40 m/s F = -600 N t = 90 s ∆p = ? ∆p = F∙t = -600 · 90 = -54000 N·s  

Impulse example #1 continued What is the final velocity of the truck? ∆p = -54000 N·s m = 2000 kg vi = +40 m/s vf = ? ∆p = m∆v = m(vf - vi) -54000 = 2000 (vf – 40) -27 = vf – 40 vf = 13 m/s North Truck slows from 40 m/s to 13 m/s over the 90 s period. You can see, applying more force or applying it for a longer time would both slow the truck even more.

Impulse example #2 Compare the force required to stop a 1000 kg car moving 50 m/s by a) applying the brakes for 10 s, or b) hitting a tree and stopping in 0.2 s. ∆p is the same either way! ∆p = m∆v = m(vf – vi) = 1000 (0 – 50) = -50000 kg·m/s a) t = 10 s, ∆p = -50000 kg·m/s F·t = ∆p F = ∆p/t = -50000/10 = -5000 N   b) t = 0.2 s, ∆p = -50000 kg·m/s F = ∆p/t = -50000/0.2 = -250,000 N If you were the driver, which would you rather experience, -5000 N or – 250,000 N?

Impulse summary Impulse changes momentum. Both F and time matter. Long time with a small force = Short time with a big force.   Why do baseball players or golfers like to “follow through” when hitting the ball? Follow through increases the contact time which increases the impulse which increases the change in momentum. Why do bungee jumpers use stretchy bungees instead of steel cables? Impulse and change in momentum are the same, but stopping more slowly as the bungee stretches requires less force. Steel cables stop you faster, requiring much more force.

Next time, momentum in collisions. Sure to be a big hit!