Slide 1 / 63 Slide 2 / 63 New Jersey Center for Teaching and Learning Progressive Science Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and teachers. These materials may not be used for any commercial purpose without the written Momentum permission of the owners. NJCTL maintains its website for the convenience of teachers who wish to make their work available to other teachers, participate in a virtual professional learning community, and/or provide access to course materials to parents, students and others. www.njctl.org Click to go to website: www.njctl.org Slide 3 / 63 Slide 4 / 63 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 Return to Table of · Elastic Collisions Contents http:/ / njc.tl/ ko http:/ / njc.tl/ kp Slide 5 / 63 Slide 6 / 63 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 click here for a introductory video on momentum from Bill Nye! http:/ / njc.tl/ kp http:/ / njc.tl/ kp
Slide 7 / 63 Slide 8 / 63 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 Answer http:/ / njc.tl/ kp http:/ / njc.tl/ kq Slide 9 / 63 Slide 10 / 63 2 3 What is the momentum of a 20 kg object with a velocity of What is the momentum of a 20kg object with a velocity of +5.0 m/s? −5.0m/s? Answer Answer http:/ / njc.tl/ kr http:/ / njc.tl/ ks Slide 11 / 63 Slide 12 / 63 5 4 What is the mass of an object whose momentum is 35 kg ⋅ m/s What is the velocity of a 5.0kg object whose momentum is −15.0 kg # m/s? when its velocity is 7.0 m/s? Answer Answer http:/ / njc.tl/ kt http:/ / njc.tl/ ku
Slide 13 / 63 Slide 14 / 63 Change in Momentum Suppose that there is an event that changes an object's momentum. from p 0 - the initial momentum (just before the event) · by Δp - the change in momentum · Momentum Change & Impulse to p f - the final momentum (just after the event) · The equation for momentum change is: Return to Table of Contents http:/ / njc.tl/ kv http:/ / njc.tl/ kv Slide 15 / 63 Slide 16 / 63 Momentum Change = Impulse SI Unit for Impulse Momentum change equation: There no specially named unit for impulse. We just use the product of the units of force and time... Newton's First Law tells us that the force x time velocity (and so the momentum) of an object won't change unless the object is N ⋅ s affected by an external force. Recall that N=kg ⋅m/s 2 , so 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 : N ⋅ s=kg ⋅m/s 2 x s = kg ⋅ m/s Where the impulse is: - the same as momentum! http:/ / njc.tl/ kv http:/ / njc.tl/ kv Slide 17 / 63 Slide 18 / 63 Effect of Collision Time on Force Real World Applications Impulse = F t = F t change in momentum Impulse = F t = F t change in momentum · Car Design / Accidents > airbags force (newtons) > collisions head-on vs walls > crush zones · Jumping / Landing time (seconds) · Boxing / Martial Arts Changing the duration (t) of an impulse by a small · Hitting Balls - Golf, Baseball... amount can greatly reduce the force on an object http:/ / njc.tl/ kv · Catching Balls http:/ / njc.tl/ kv
Slide 19 / 63 Slide 20 / 63 6 An external force of 25N acts on a system for 10s. How big is the 7 In the previous problem, an external force of 25N acted on a impulse delivered to the system? 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? Answer Answer http:/ / njc.tl/ kw http:/ / njc.tl/ kx Slide 21 / 63 Slide 22 / 63 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 Answer B http:/ / njc.tl/ ky http:/ / njc.tl/ kz Slide 23 / 63 Slide 24 / 63 11 In order to increase the final momentum of a golf ball, we could: 10 One car crashes into a concrete barrier. Another car crashes into a collapsible barrier at the same speed. What is the difference not change the speed of the golf club after the collision between the 2 crashes? A B increase the force acting on it A change in momentum B force on the car increase the time of contact between the club and ball C C impact time all of the above D D both B & C are true Answer Answer http:/ / njc.tl/ l0 http:/ / njc.tl/ l1
Slide 25 / 63 Slide 26 / 63 * 12 An external force acts on an object for 0.0020 s. During that time 13 A 50,000 N force acts for 0.030 s on a 2.5 kg object that was the object's momentum increases by 400 kg-m/s. What was the initially at rest. What is its final velocity? magnitude of the force? Answer Answer http:/ / njc.tl/ l2 http:/ / njc.tl/ ls Slide 27 / 63 Slide 28 / 63 The Momentum of a System of Objects If a system contains more than one object, it's total momentum is the vector sum of the momenta of those objects. The Momentum of p system = ∑ p a System of Objects p system = p 1 + p 2 + p 3 +... p system = m 1 v 1 + m 2 v 2 + m 3 v 3 +... Return to Table of It's critically important to note that Contents momenta add as vectors, not as scalars. http:/ / njc.tl/ l3 http:/ / njc.tl/ l3 Slide 29 / 63 Slide 30 / 63 The Momentum of a System of Objects Example Determine the momentum of a system of two objects: m 1, has a mass p system = m 1 v 1 + m 2 v 2 + m 3 v 3 +... of 6 kg and a velocity of 13 m/s towards the east and m 2 , has a mass of 14 kg and a velocity of 7 m/s towards the west. In order to determine the total momentum of a system, First: (Choose east as positive) + Determine a direction to be · considered positive m 1 = 6 kg v 1 = 13 m/s Assign positive values to · Answer momenta in that direction m 2 = 14 kg Assign negative values to - · v 2 = −7 m/s momenta in the opposite direction p system = p 1 + p 2 Then: Add the momenta to get a total. p system = m 1 v 1 + m 2 v 2 http:/ / njc.tl/ l3 http:/ / njc.tl/ l3
Slide 31 / 63 Slide 32 / 63 14 Determine the magnitude of the momentum of a system of two 15 Determine the momentum of a system of two objects: the first has objects: m 1 , has a mass of 6.0kg and a velocity of 20m/s north a mass of 8 kg and a velocity of 8 m/s to the east while the and m 2 , has a mass of 3kg and a velocity 20m/s south. second has a mass of 5 kg and a velocity of 15 m/s to the west. Answer Answer http:/ / njc.tl/ l4 http:/ / njc.tl/ l5 Slide 33 / 63 Slide 34 / 63 16 Determine the momentum of a system of 3 objects: The first has a mass of 7.0 kg and a velocity of 23 m/s north; the second has a mass of 9.0 kg and a velocity of 7 m/s north; and the third has a mass of 5.0 kg and a velocity of 42 m/s south. Conservation of Momentum Answer Return to Table of Contents http:/ / njc.tl/ l6 http:/ / njc.tl/ l7 Slide 35 / 63 Slide 36 / 63 Conservation Laws Momentum is Conserved Some of the most powerful concepts in science are called In the last unit we learned that energy is conserved. "conservation laws". Conservation laws: Like energy, momentum is a conserved property of nature. It is apply to closed systems - where the objects only interact with not created or destroyed; · each other and nothing else. enable us to solve problems without worrying about the · So in a closed system we will always have the same amount of details of an event. momentum. The only way the momentum of a system can change is if momentum is added or taken away by an outside force. http:/ / njc.tl/ l7 http:/ / njc.tl/ l7
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