Momentum and Impulse

Let’s start with everyday language What do you say when a sports team is on a roll? They may not have the lead but they may have ___________ MOMENTUM A team that has momentum is hard to stop.

Momentum Momentum can be defined as "mass in motion." All objects have mass; so if an object is moving, then it has momentum Momentum depends upon the variables mass and velocity Momentum = mass * velocity p = m * v where m = mass and v=velocity

Momentum is a vector quantity To fully describe the momentum of a 5-kg bowling ball moving westward at 2 m/s, you must include information about both the magnitude and the direction of the bowling ball p = m * v p = 5 kg * 2 m/s west p = 10 kg m/s west

So What’s Momentum ? Momentum = mass x velocity This can be abbreviated to : . p = mv Or, if direction is not an important factor : . . momentum = mass x speed So, A really slow moving truck and an extremely fast roller skate can have the same momentum.

Question : 1 kg 10 m/sec 1000 kg .01 m/sec Under what circumstances would the roller skate and the truck have the same momentum ? If the roller skate was moving incredibly fast, or, if the truck was moving incredibly slow! A 1000 kg truck moving at 0.01 m/sec has the same momentum as a 1 kg skate moving at 10 m/sec. Both have a momentum of 10 kg m/sec. ( 1000 x .01 = 1 x 10 = 10 )

Let’s practice A 1200 kg car drives west at 25 m/s. What is the car’s momentum? Identify the variables: 1200 kg = mass 25m/s, west = velocity P = mv = 1200 x 25 = 30000 kg m/s, west

Types of Collisions Elastic: objects hit each other, then bounce apart Inelastic: objects hit each other and stick together (making one object of mass equal to the sum of the two original objects) Explosions: one object breaks aparts into two or more objects

Identify this Collision Elastic, they all bounced apart. Their momenta are all different because they all have different speeds

Identify this Collision Inelastic, the skater’s momentum collides with the skateboard’s momentum (zero), they become one total mass traveling at one speed

Identify these TWO Collisions Inelastic as rocket sled hits car, which leads to an explosion of car particles!

Conservation of Momentum Since energy is conserved, or, never lost only transferred – we also say that momentum of a “system” is also conserved, it is transferred to various objects in the system A system is just a way of saying “a set of objects that we are paying attention to”.

Momentum of a System A collision yields a change in momentum, so, there is an initial momentum p And a final momentum p’ (pronounced p-prime) In a collision, the initial and final momenta must be equal. Momentum = mv p(initial) = p(final), or simply p = p’ mv(initial) = mv(final), or simply mv= mv’

Momentum of objects of a System Most systems have multiple “parts” or objects Example: A skater runs to the right and jumps onto a stationary skateboard, what are the parts of the initial system? p(skater) + p(board) = ps+ pb The skater lands on the skateboard and they both roll away together to the right p’(sb)

Collision Math and Predictions Mathematically collisions look complicated, but that’s just because each part has a label. We’ll say ms stands for “mass of skater” And mb stands for “mass of board” We’ll say vs stands for “initial velocity of skater”, vb stands for “initial velocity of board” Remember, velocity has a direction, this could change your + or – sign in the math!!

Collision Math con’t. Remember, momentum is conserved p(system) = p’(system) msvs + mbvb = msv’s + mbv’b Simplified: msvs + mbvb = msbv’sb Keep in mind, after collision, the skater and the board are together (their masses add together) and travel at the same speed!

Give it a shot! Skater’s mass is 50kg, the board’s mass is 3kg. The skater runs with a speed of 2 m/s The board is not moving initially, it’s at rest. What is the final velocity of the skater+board system? Remember, p(system) = p’(system) msvs + mbvb = msbv’sb (50kg)(2m/s)+(3kg)(0m/s) = (50kg+3kg)v’sb 100kg*m/s = (53kg)v’sb 1.89 m/s = v’sb This makes sense because additional mass (the board) would decrease the total speed after the collision.

Collision Equation Examples A 2kg green billiard ball rolling at 5m/s to the right collides with the red ball of the same mass rolling to the left at 3m/s. After the collision, the green ball rolls to the left at a speed of 0.5m/s. Calculate the speed and direction of the red ball after the collision. m(g)vi(g) + m(r)-vi(r) = m(g)-vf(g) + m(r)?vf(r) 2.5 m/s to the right And this makes sense; green ball transferred nearly all its initial speed to the red ball, shooting both in the opposite direction