Momentum - Lecture Slides - Basic Concepts of Physics, Slides of Physics

Download Momentum - Lecture Slides - Basic Concepts of Physics and more Slides Physics in PDF only on Docsity! Chapter 6: Momentum docsity.com Momentum = “inertia in motion” Specifically, momentum = mass x velocity = m v Eg. Just as a truck and a roller skate have different inertia, when they are moving, they (generally) have different momenta. Question: (i) Does the truck always have more inertia than the roller skate? (ii) What about momentum? (i) Yes (mass larger) (ii) No – e.g. a roller skate rolling has more momentum than stationary truck. Momentum depends on speed as well as mass . docsity.com Impulse cont. • The “effectiveness” of the force in causing a change in momentum is called the impulse: Impulse = force x time-interval = F t How exactly is the momentum changed? Use N’s 2nd law, a = F/m, or, F =ma. So, impulse = ma t = m (change in velocity/time) time = m (change in velocity) i.e. impulse = change in momentum Ft =(mv) docsity.com Using the impulse-momentum relation Increasing momentum • As highlighted by the broken-down car example, need to apply large force for a large time. • E.g. The longer the barrel of a cannon, the greater the speed of the emerging cannonball because the forces on it from the expanding gasses have more time to act. • E.g. Why does an archer pull his arrow all the way back before releasing it? To give more time for the (time-varying) elastic force of the bow to act, so imparting greater momentum. docsity.com Decreasing momentum over a long time Often you want to reduce the momentum of an object to zero but with minimal impact force (or injury). try to maximize the time of the interaction (recall Ft =(momentum)) Eg. Riding with the punch, when boxing, rather than moving into it… Here, by moving away, the time of contact is extended, so force is less than if he hadn’t moved. Here, by moving into the glove, he is lessening the time of contact, leading to a greater force, a bigger ouch! docsity.com Questions a) Is the impulse to stop a 10 kg bowling ball moving at 6 m/s less, greater or the same, if it is done in 1s rather than 2s? Same, since impulse = change in momentum is the same whatever the time it takes. b) Is the force you must exert to stop it less, greater, or the same, if done in 1s or 2s? Twice as great force if you do it in 1s than if you do it in 2s, because change in momentum = impulse = Ft. (so half t means twice F) c) In a general situation, when does impulse equal momentum? If the object’s initial momentum is zero, then impulse = momentum change = final mom. – initial mom. = final mom. Likewise, if object is brought to rest, then impulse = - initial momentum. 0 docsity.com Decreasing momentum over a short time On the other hand, sometimes you want to obtain large forces when decreasing momentum. Want short impact times. Eg. This is how in karate (tae kwon do), an expert can break a stack of bricks with a blow of a hand: Bring in arm with tremendous speed, i.e. large momentum, that is quickly reduced on impact with the bricks. The shorter the time, the larger the force on the bricks. docsity.com Bouncing Why is it that if the expert makes her hand bounce back upon impact, she can increase the force on the bricks? Because, bouncing means reversing of momentum, so even greater momentum change. Eg. Say a 1-kg object at 1-m/s comes to rest. Then (mom) = 0 -1 kg m/s = -1 kg m/s Say instead it bounces back at 1 m/s. The change in momentum is then -1-(1) =-2kg m/s (Don’t be fazed by the – signs, they just indicate direction – the point is that the size of the change is larger in the bouncing case) docsity.com Whenever an interaction occurs in a system, forces occur in equal and opposite pairs. Which of the following do not always occur in equal and opposite pairs? 1. Impulses. 2. Accelerations. 3. Momentum changes. 4. All of these occur in equal and opposite pairs. 5. None of these do. docsity.com 1. Impulses. 2. Accelerations. 3. Momentum changes. 4. All of these occur in equal and opposite pairs. 5. None of these do. Whenever an interaction occurs in a system, forces occur in equal and opposite pairs. Which of the following do not always occur in equal and opposite pairs? Answer: 2 Because time for each interaction part is the same, impulses and momentum changes also occur in equal and opposite pairs. But not necessarily accelerations, because the masses of the interaction may differ. Consider equal and opposite forces acting on masses of different magnitude. F m  a F m a docsity.com Collisions • Momentum is conserved during a collision, because all forces acting in collision are internal to the system of colliding objects: Net momentum before collision = net momentum after collision Momentum is redistributed among the participants of the collision. Example: Two equal-mass balls colliding: a) The moving ball comes to rest, the other moves off with the speed of the colliding ball. b) Head-on collision – each ball reverses its momentum pi = p1 pf = p2 = pi pi = p–p = 0 pi = -p+p = 0 of system of colliding objects docsity.com Clicker Question A garbage truck and a mini car have a head-on collision. Which vehicle experiences the greater force of impact? A) Both same B) The garbage truck C) The mini-car D) Impossible to say without more information Answer: A From Newton’s 3rd Law of action-reaction. Again, distinguish force from effect of force! docsity.com More Questions In the head-on collision between the garbage truck and a mini car: a) Which experiences the greater impulse? Both same (same force over same time interval) b) Which experiences the greater momentum change? Both same (momentum of system conserved, so momentum change of truck is equal and opposite to the momentum change of the car) c) Which experiences the greater acceleration? The car (smaller mass) docsity.com Questions continued d) Say the garbage truck weighs 15 000-kg, and the mini car weighs 1000 kg. Let’s say the truck is initially moving at 30 km/h and the car is at 60 km/h. If the two stick together after the collision, then what is their speed after the head-on collision? Momentum conservation means: mom. of truck before + mom. of car before = mom of (car+truck) after i.e. mt vt - mc vc = (mt+mc) v (- on left because opp dir) (15000)(30) - (1000)(60) = (16000) v So, v = 24.375 km/h Note that they do eventually come to rest because of friction on the road – an external force. Since the impact time is relatively short, we can ignore this external force during the collision since it is much smaller than the collisional impact force. Hence we assume momentum is conserved in the collision. docsity.com Eg. Firecracker exploding as it is falling, (or a radioactive nucleus breaking up..) Momenta of final fragments add to give net momentum equal to the initial. Eg. Billiard balls – ball A strikes B which was initially at rest. Parallelogram with A’ and B gives original momentum of A. docsity.com Clicker Question If all people, animals, trains and trucks all over the world began to walk or run towards the east, then the A) earth would spin a bit faster B) earth would spin a bit slower C) earth’s spin would not be affected at all Answer: B The total momentum of people etc + earth must remain the same because there is no change in the external force – the running to the east is an internal force to the people + earth system. Since the people gain momentum to the east, then the earth must lose momentum in the east direction, therefore it spins a bit slower. (Note that the earth spins towards the east) docsity.com Clicker Question If while floating in outer space you take your shoe off and throw it away, you and the shoe will A) move away from each other, but at different speeds B) move away from each other at the same speed C) move a short distance and then slow down D) move a short distance and then go faster Answer: A The total momentum of you + shoe is conserved, so your change in momentum is equal and opposite to the change in momentum of the shoe. Since the shoe weighs less, its speed is higher. docsity.com