Slide 1 / 90 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 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. Click to go to website: www.njctl.org Slide 2 / 90 Momentum www.njctl.org Slide 3 / 90 Momentum Click on the topic to go to that section · Momentum · Momentum Change and Impulse · The Momentum of a System of Objects · Conservation of Momentum · Conservation of Momentum in Collisions and Explosions · Collisions in Two and Three Dimensions
Slide 4 / 90 Momentum Return to Table of Contents Slide 5 / 90 Momentum Defined Newton’s First Law tells us that – objects remain in motion with a constant velocity unless acted upon by a force. In our experience: · When objects of different masses travel with the same velocity, the one with most mass is hardest to stop. · When objects of equal mass travel with different velocities, the fastest one is hardest to stop. Slide 6 / 90 Momentum Defined · 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!
Slide 7 / 90 Momentum is a Vector Quantity Since: · mass is a scalar quantity · velocity is a vector quantity and: · momentum = mass × velocity Momentum is a vector quantity Slide 8 / 90 SI Unit for Momentum There no specially named units for momentum. We just use the product of the units of mass and velocity... mass x velocity kg ⋅ m/s Slide 9 / 90 1 Which has more momentum? A A large truck moving at 30 m/s B A small car moving at 30 m/s C Both have the same momentum. Answer
Slide 9 (Answer) / 90 1 Which has more momentum? 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] Slide 10 / 90 2 What is the momentum of a 20 kg object moving to the right with a velocity of 5.0 m/s? Answer Slide 10 (Answer) / 90 2 What is the momentum of a 20 kg object moving to the right with a velocity of 5.0 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]
Slide 11 / 90 3 What is the momentum of a 20 kg object with a velocity of 5.0 m/s to the left? Answer Slide 11 (Answer) / 90 3 What is the momentum of a 20 kg object with a velocity of 5.0 m/s to the left? 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] Slide 12 / 90 4 What is the velocity of a 5.0kg object whose momentum is −15.0 kg # m/s? Answer
Slide 12 (Answer) / 90 4 What is the velocity of a 5.0kg object whose momentum is −15.0 kg # m/s? m = 5 kg ⋅ m/s p = −15 kg Answer p = mv divide both sides by m ⋅ m/s)/(5 kg) v = p/m = (−15 kg = − 3 m/s [This object is a pull tab] Slide 13 / 90 5 What is the mass of an object whose momentum is 35 kg ⋅ m/s when its velocity is 7.0 m/s? Answer Slide 13 (Answer) / 90 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 ⋅ 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]
Slide 14 / 90 Momentum Change & Impulse Return to Table of Contents Slide 15 / 90 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 · to p f - the final momentum (just after the event) The equation for momentum change is: Slide 16 / 90 Momentum Change = Impulse Momentum change equation: Newton's First Law tells us that the velocity (and so the momentum) of an object won't change unless the object is affected by an external force. 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 17 / 90 SI Unit for Impulse There no specially named unit for impulse. We just use the product of the units of force and time... force x time N ⋅ s Recall that N=kg ⋅m/s 2 , so N ⋅ s=kg ⋅m/s 2 x s = kg ⋅ m/s - the same as momentum! Slide 18 / 90 Effect of Collision Time on Force Impulse = F (∆t) = F (∆t) Changing the duration ∆t of an impulse by a small F (newtons) amount can greatly change the force exerted on an object! ∆t (seconds) Slide 19 / 90 Real World Applications Impulse = F (∆t) = F (∆t) · Car Design / Accidents · airbags · collisions head-on vs walls · crush zones · Jumping / Landing · Boxing / Martial Arts · Hitting Balls - Golf, Baseball... · Catching Balls
Slide 20 / 90 6 An external force of 25 N acts on a system for 10 s. How big is the impulse delivered to the system? Answer Slide 20 (Answer) / 90 6 An external force of 25 N acts on a system for 10 s. How big is the impulse delivered to the system? F = 25 N Δt = 10 s Answer I = F Δt = (25N) (10 s) = 250 N•s [This object is a pull tab] Slide 21 / 90 7 In the previous problem, an external force of 25 N acted on a system for 10 s. We found that the impulse delivered was 250 N-s. What was the change in momentum of the system? Answer
Slide 21 (Answer) / 90 7 In the previous problem, an external force of 25 N acted on a system for 10 s. We found that the impulse delivered was 250 N-s. What was the change in momentum of the system? I = 250 N•s Answer I = Δp Δp = 250 N•s [This object is a pull tab] Slide 22 / 90 8 The momentum change of an object is equal to the ______. A force acting on it B impulse acting on it C velocity change of the object D object's mass times the force acting on it Answer Slide 22 (Answer) / 90 8 The momentum change of an object is equal to the ______. A force acting on it B impulse acting on it C velocity change of the object D object's mass times the force acting on it Answer B [This object is a pull tab]
Slide 23 / 90 9 Air bags are use in cars because they: A increase the force with which a passenger hits the dashboard B increase the duration (time) of the passenger's impact C decrease the momentum of a collision D decrease the impulse in a collision Answer B Slide 23 (Answer) / 90 9 Air bags are use in cars because they: A increase the force with which a passenger hits the dashboard B increase the duration (time) of the passenger's impact C decrease the momentum of a collision D decrease the impulse in a collision B Answer By increasing the amount of time during the collision, the force required to reduce the passenger's momentum is reduced. This in B turn reduces or prevents injury. [This object is a pull tab] Slide 24 / 90 10 One car crashes into a concrete barrier. Another car crashes into a collapsible barrier at the same speed. What is the difference between the 2 crashes? A change in momentum B force on the car C impact time D both B & C Answer
Slide 24 (Answer) / 90 10 One car crashes into a concrete barrier. Another car crashes into a collapsible barrier at the same speed. What is the difference between the 2 crashes? A change in momentum B force on the car C impact time D both B & C C Answer Whether the wall is padded or not, the car 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] Slide 25 / 90 11 In order to increase the final momentum of a golf ball: maintain the speed of the golf club after the collision A (called "following through") B increase the force hitting the ball increase the time of contact between the club and ball C any or all of the above D Answer Slide 25 (Answer) / 90 11 In order to increase the final momentum of a golf ball: maintain the speed of the golf club after the collision A (called "following through") increase the force hitting the ball B increase the time of contact between the club and ball C D D any or all of the above 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]
Slide 26 / 90 12 An external force acts on an object for 0.0020 s. During that time the object's momentum increases by 400 kg-m/s. What was the magnitude of the force? Answer Slide 26 (Answer) / 90 12 An external force acts on an object for 0.0020 s. During that time the object's momentum increases by 400 kg-m/s. What was the magnitude of the force? Δt = 0.002 s Δp = 400 kg•m/s Answer I = FΔt = Δp F = Δp/Δt = (400 kg•m/s)/(0.002 s) = 200,000 N [This object is a pull tab] Slide 27 / 90 * 13 A 50,000 N force acts for 0.030 s on a 2.5 kg object that was initially at rest. What is its final velocity? Answer
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