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Momentum and Impulse Physics 11, Unit 3 This section: see pages 195 to 205 in text Momentum and Impulse http://www.youtube.com/watch?v=yUpi V2I_IRI Why are buses safer than other vehicles??? Up to 13 minutes (we will watch the rest later!) What is momentum? Sports: A team that has the momentum is on the move and is going to take some effort to stop. Physics: It refers to the quantity of motion that an object has. If an object is in motion then it has momentum. The amount of force over a given time. Momentum - Summary Momentum (p): The quantity of motion that an object has. Formula If an object is in motion then it has momentum. Vector (direction of velocity) p = mv Units kg m/s (don’t use P! P=Power!) An example to think about… Think of two cars of equal mass. If one car is moving faster, it will take more force to stop the faster car in the same time interval. If you have a car and a truck, the truck has more mass so has more momentum – it will take longer for it to stop than the car. Example A cement truck full of cement has a mass of 42000kg. It travels north at 18 m/s. A) Calculate the truck's momentum. B) How fast must a 750 kg Honda Civic travel in order to have the same momentum? Example A cyclist is travelling at 32km/h and the bike and rider have a mass of 85kg. What is their momentum? p mv p 85kg(8.89m / s ) p 760kgm / s Try this: Page 197, question 29 Relating this to Force According to Newton's first law, if no net force acts on an object, its velocity is constant. Its mass will not change. Therefore, if no force acts on an object, momentum is constant. Momentum is conserved. Newton's second law describes how the velocity of a body changes if a net force acts on it. (Acceleration occurs if a net force acts on it). We have looked at motion and forces already…However… When an object is accelerated, typically the force will only be applied for a given time This holds true for things like: Explosions Collisions Recoil So instead of considering Newton’s Second Law (F = ma) as we have previously discussed, we will rearrange the equation so we can look at momentum and impulse Momentum – derivation of formula Momentum can also be defined starting from Newton’s Second Law The rate of change of momentum can also be used to determine the force F ma mv F t mv f mvi F t p mv Impluse - Derivation Using the definition of acceleration (change in velocity divided by change in time) we can rewrite Newton’s Second Law Rearranging gives impulse F ma mv F t j Ft mv Impulse - Summary Impulse (j): Force applied over a given time Also known as change in momentum Vector (same direction as the force) Formula: j = F∆t Units: Ns ***(but Ns = same unit as kg m/s) How are impulse and momentum related? (Copy) Same units Impulse is like momentum except we use it for sudden changes in momentum, like for collisions, explosions, and recoil Impulse is the change in momentum (not just the momentum) so you need vi and vf Example A tennis ball is struck by a racquet with a force of 750N; if the time of contact was 0.023s, what impulse was delivered to the ball? j Ft mv j 750 N (0.023s) j 17 Ns Try these… Page 200, questions 30, 31, 32 How does impulse/momentum affect sports? Why does your coach tell you to “follow through” when you shoot a puck in hockey or hit a ball in baseball? http://www.youtube.com/watch?v=OrLcZNG 0N0I (first part is “mathy” but second part is about the follow through so keep watching ) Impulse-Momentum Connection Collisions and explosions happen so quickly that it is often impossible to calculate anything more than an average force. This is because the force changes so quickly. By examining the momentum before and after the interaction between 2 objects, we can determine impulse. Impulse-Momentum Theorem (copy) Impulse is the difference between the final momentum and initial momentum of an object involved in an interaction. Problem A baseball of mass 0.145kg is pitched toward a batter with an initial velocity of 35m/s. If the batter hits the ball in the opposite direction at 45m/s, determine the force that is applied by the bat on the ball if the contact time was 0.013s. HINT: Remember that impulse is equal to the change in momentum… Did you get an answer of 890 N [away from the batter] More Practice http://www.physicsclassroom.com/class/mo mentum/u4l2e.cfm (for you to check out if needed) Think of a dump truck and a car. If they are stopped in the same time interval, it will take ______ (more or less) force to stop the truck than the car. Why? Think of two cars of equal mass. If one car is moving faster, it will take _____ (more or less) force to stop the faster car in the same time interval. A golf club strikes a golf ball. The club and ball remain in contact for 0.60 ms. The 45 g ball leaves the club with a speed of 70. m/s. Calculate the average force of the club on the ball. Answer: 5250 = 5300 N [away from club] Try These Page 203 33-35 Page 209 37-46