Slide 1 / 65 Slide 2 / 65 Algebra Based Physics Momentum 2015-12-02 www.njctl.org Slide 3 / 65 Slide 4 / 65 Momentum Click on the topic to go to that section · Momentum Impulse · Momentum Momentum of a System of Objects · · Conservation of Momentum · Inelastic Collisions and Explosions · Elastic Collisions Return to Table of Contents https://www.njctl.org/video/?v=vCZuOPzzPb0 https://www.njctl.org/video/?v=ImQuL1LkzQs Slide 5 / 65 Slide 6 / 65 Momentum is a Vector Quantity Momentum Defined Newton’s First Law tells us that – objects remain in motion with Recall that: a constant velocity unless acted upon by a force. mass is a scalar quantity In our experience: and velocity is a vector quantity When two objects of different masses travel with the same · velocity, the one with more mass is harder to stop. Since: momentum = mass × velocity When objects of the equal masses travel with different · speeds, the faster one is harder to stop. momentum must be a vector quantity Define a new quantity, momentum ( p ), that takes these · observations into account: momentum = mass × velocity p =mv View a video about momentum, from Bill Nye the Science Guy! https://www.njctl.org/video/?v=y2Gb4NIv0Xg
Slide 7 / 65 Slide 8 / 65 SI Unit for Momentum 1 Which has more momentum? A A large truck moving at 30 m/s There no specially named unit for momentum. We just use the product of the units of mass and velocity... B A small car moving at 30 m/s mass x velocity C Both have the same momentum. kg ⋅ m/s https://www.njctl.org/video/?v=TEgJZPNKrF8 Slide 8 (Answer) / 65 Slide 9 / 65 2 What is the momentum of a 20 kg object with a 1 Which has more momentum? velocity of +5.0 m/s? A A large truck moving at 30 m/s B A small car moving at 30 m/s C Both have the same momentum. A Answer Both have the same speed, but the truck has the larger mass [This object is a pull tab] https://www.njctl.org/video/?v=TEgJZPNKrF8 https://www.njctl.org/video/?v=5K5szGWdTS8 Slide 9 (Answer) / 65 Slide 10 / 65 What is the momentum of a 20 kg object with a 2 3 What is the momentum of a 20kg object with a velocity of +5.0 m/s? velocity of −5.0m/s? m= 20 kg Answer v = 5 m/s p = mv = (20 kg)(5 m/s) ⋅ m/s = 100 kg [This object is a pull tab] https://www.njctl.org/video/?v=5K5szGWdTS8 https://www.njctl.org/video/?v=tJJNPix769s
Slide 10 (Answer) / 65 Slide 11 / 65 3 What is the momentum of a 20kg object with a 4 What is the velocity of a 5.0kg object whose velocity of −5.0m/s? momentum is −15.0 kg ⋅ m/s? m= 20 kg Answer v = −5 m/s p = mv = (20 kg)(−5 m/s) ⋅ m/s = −100 kg [This object is a pull tab] https://www.njctl.org/video/?v=zSNVlfYxlKY https://www.njctl.org/video/?v=tJJNPix769s Slide 11 (Answer) / 65 Slide 12 / 65 What is the velocity of a 5.0kg object whose 5 4 What is the mass of an object whose momentum is 35 momentum is −15.0 kg ⋅ m/s? kg ⋅ m/s when its velocity is 7.0 m/s? m = 5 kg p = −15 kg ⋅ m/s Answer p = mv divide both sides by m v = p/m = (−15 kg ⋅ m/s)/(5 kg) = − 3 m/s [This object is a pull tab] https://www.njctl.org/video/?v=zSNVlfYxlKY https://www.njctl.org/video/?v=y1143dHjhl8 Slide 12 (Answer) / 65 Slide 13 / 65 5 What is the mass of an object whose momentum is 35 kg ⋅ m/s when its velocity is 7.0 m/s? v = 7 m/s Momentum Change & Impulse ⋅ m/s p = 35 kg Answer p = mv divide both sides by v ⋅ m/s)/(7 m/s m = p/v = (35 kg ) = 5 kg [This object is a pull tab] Return to Table of Contents https://www.njctl.org/video/?v=y1143dHjhl8 https://www.njctl.org/video/?v=pCAvyCCA3L0
Slide 14 / 65 Slide 15 / 65 Momentum Change = Impulse Change in Momentum Momentum change equation: Suppose that there is an event that changes an object's momentum. from p 0 - the initial momentum (just before the event) · Newton's First Law tells us that the by Δp - the change in momentum · velocity (and so the momentum) of an to p f - the final momentum (just after the event) · object won't change unless the object is affected by an external force. The equation for momentum change is: When an outside force F acts on the object for a time Δt , it delivers an impulse I to the object that changes its momentum : Where the impulse is: Slide 16 / 65 Slide 17 / 65 Effect of Collision Time on Force SI Unit for Impulse Impulse = F t = F t change in momentum There no specially named unit for impulse. We just use the product of the units of force and time... force x time N ⋅ s force (newtons) Recall that N=kg ⋅ m/s 2 , so N ⋅ s=kg ⋅ m/s 2 x s time (seconds) = kg ⋅ m/s Changing the duration (t) of an impulse by a small amount can greatly reduce the force on an object - the same as momentum! Slide 18 / 65 Slide 19 / 65 Real World Applications 6 An external force of 25N acts on a system for 10s. How big is the impulse delivered to the system? Impulse = F t = F t change in momentum Car Design / Accidents · airbags · collisions head-on vs walls · crush zones · Jumping / Landing · Boxing / Martial Arts · Hitting Balls - Golf, Baseball... · https://www.njctl.org/video/?v=_819N8wiu_o Catching Balls ·
Slide 19 (Answer) / 65 Slide 20 / 65 6 An external force of 25N acts on a system for 10s. How 7 In the previous problem, an external force of 25N acted big is the impulse delivered to the system? on a system for 10s. We found that the impulse delivered was 250 N-s. What is the magnitude of the change in momentum of the system? F = 25 N Δt = 10 s Answer I = F Δt = (25N) (10 s) = 250 N•s [This object is a pull tab] https://www.njctl.org/video/?v=_819N8wiu_o https://www.njctl.org/video/?v=3rkbZoAdxVk Slide 20 (Answer) / 65 Slide 21 / 65 7 In the previous problem, an external force of 25N acted 8 The momentum change of an object is equal to the ______. on a system for 10s. We found that the impulse A force acting on it delivered was 250 N-s. What is the magnitude of the B impulse acting on it change in momentum of the system? C velocity change of the object D object's mass times the force acting on it I = 250 N•s Answer I = Δp Δp = 250 N•s [This object is a pull tab] https://www.njctl.org/video/?v=3rkbZoAdxVk https://www.njctl.org/video/?v=b_ZkShN9sjU Slide 21 (Answer) / 65 Slide 22 / 65 8 The momentum change of an object is equal to the 9 Air bags are use in cars because they: ______. A increase the force with which you hit the dashboard A force acting on it B increase the duration (time) of impact in a collision B impulse acting on it C decrease the momentum of a collision C velocity change of the object D decrease the impulse in a collision D object's mass times the force acting on it Answer B B [This object is a pull tab] https://www.njctl.org/video/?v=b_ZkShN9sjU https://www.njctl.org/video/?v=sihCqAZaMMQ
Slide 22 (Answer) / 65 Slide 23 / 65 9 Air bags are use in cars because they: 10 One car crashes into a concrete barrier. Another car crashes into a collapsible barrier at the same speed. A increase the force with which you hit the dashboard What is the difference between the 2 crashes? B increase the duration (time) of impact in a collision A change in momentum C decrease the momentum of a collision B force on the car D decrease the impulse in a collision C impact time B Answer D both B & C are true By increasing the amount of time during the collision, the force required to reduce the passenger's momentum is reduced. This in turn reduces or prevents injury. B [This object is a pull tab] https://www.njctl.org/video/?v=ZZoM42bQb-I https://www.njctl.org/video/?v=sihCqAZaMMQ Slide 23 (Answer) / 65 Slide 24 / 65 11 In order to increase the final momentum of a golf ball, 10 One car crashes into a concrete barrier. Another car we could: crashes into a collapsible barrier at the same speed. not change the speed of the golf club after the collision A What is the difference between the 2 crashes? increase the force acting on it B A change in momentum B force on the car increase the time of contact between the club and ball C C impact time D D all of the above D both B & C are true Whether the wall is padded or not, the car Answer experiences the same change in momentum, and so the same impulse. The only difference is that the impact time has increased (which in turn reduces the force experienced by the car). [This object is a pull tab] https://www.njctl.org/video/?v=ZZoM42bQb-I https://www.njctl.org/video/?v=7hgSkFwqQPo Slide 24 (Answer) / 65 Slide 25 / 65 11 In order to increase the final momentum of a golf ball, 12 An external force acts on an object for 0.0020 s. During we could: that time the object's momentum increases by 400 kg- not change the speed of the golf club after the collision A m/s. What was the magnitude of the force? B increase the force acting on it increase the time of contact between the club and ball C all of the above D D Following through, hitting the golf ball harder, Answer and/or increasing the impact time will all result in an increase in the final momentum of the golf ball. [This object is a pull tab] https://www.njctl.org/video/?v=7hgSkFwqQPo https://www.njctl.org/video/?v=c5OVsX3cpcg
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