Physics 30 Lesson 3 Impulse and Change in Momentum

Transcription

1 Phyic 30 Leon 3 Ipule and Change in Moentu I. Ipule and change in oentu According to Newton nd Law of Motion (Phyic Principle 1 on the Data Sheet), to change the otion (i.e. oentu) of an object an unbalanced force ut be applied. If, for exaple, we want to change the otion of a car we have to apply a force for a given tie. urther, one could apply a large force for a hort tie or a aller force for a longer tie to effect the ae change in velocity. Beginning with Newton nd Law we can derive a ueful equation that decribe the relationhip between force ( ), tie ( t ), a () and change in velocity ( v ). Thi equation i on your forula heet. a Recall that ean the change in v velocity t t v The product of a and change in velocity i the change in oentu ( p v ). The product of force and tie ( t) i called the ipule. The ipule that act on an object reult in a change in the object oentu. Since ipule i a cobination of force and tie, one can apply a large force for a hort tie or a all force for a long tie or a ediu force for a ediu tie to achieve the ae change in oentu. or exaple, iagine a peron juping off a three tory building. If the peron landed on the ground on her back he would experience a very large force over a hort topping tie. The force would be large enough to caue ignificant daage to the body. However, if he landed on a large piece of foa like they ue for pole vault her topping tie would be longer and the force acting on her would be far aller. Thi i the ae idea behind the ue of elatic rope for wall cliber, air bag in car, and other afety device. Exaple 1 An average force of 17.0 N act on an object for 0.0. What i the change in oentu? p t p 17N(0.0) p 0.4 N or 0.4 Do not itake the change in velocity for the final velocity kg Note that the unit N i equivalent to kg /. Why? Ipule (t N ) i equal to change in oentu ( v ). kg Dr. Ron Licht 3 1

2 Exaple A.00 kg puck lide to the right at 10.0 / on a frictionle urface and collide with a tationary.00 kg puck. The.00 kg puck rebound with a peed of.0 /. A. What i the final velocity of the.00 kg puck? Before After v 10.0 v 0 p p v v v v v v v v.00kg( 10.0 ) 0.00kg(.0 ) v.00kg v 7.1 or 7.1 eat v.0 v? B. What i the change in oentu of each puck? p v (v v ) f i p.00kg(.0 ( 10.0 )) p 6. kg Note that the change in oentu are the ae value, but for one object it i poitive and the other i negative. Thi i a conequence of the conervation of oentu i.e. the total change in oentu i zero: p v (v v ) f i p.00kg( 7.1 0) p 6. C. If the interaction lated for 3.0, what average force acted on each a? t v t v v t.00kg(+7.1 0) kg p p p kg p ( 6. ) ( 6. ) p0 v t.00kg(.0 ( 10.0 )) kg 033N 033N Note that the force are equal and oppoite i.e. Newton 3 rd Law of Motion. Dr. Ron Licht 3

3 Refer to Pearon page 44 to 467 for a dicuion about ipule and change in oentu. II. Analyi of Interaction Involving Ipule In the real world, the change in oentu of an object i rarely due to a contant force that doe not change over tie. or exaple, conider a golf ball bouncing off of a floor. When the ball trike the floor the force build up over tie and reache a axiu when the ball i at it greatet copreion. A the ball rebound fro the floor, the force decreae to zero over tie. Exaple Golf ball bouncing off floor t = t = t = 0.00 t = t=0.004 A force-tie diagra howing the ipule acting on the ball will look oething like the following: orce Area equal the ipule orce area = t area = ipule Tie Tie orce-tie Graph for Golf Ball orce-tie for Contant orce (for coparion) The ipule ay be found by calculating the area under the force tie graph. Dr. Ron Licht 3 3

4 Exaple 3 (N) orce on a Ball a a unction of Tie t () Calculate the net ipule delivered to the ball fro t = 0.0 to t = 7.0. The net ipule can be calculated a the area of the force-tie graph (N) t () Ipule = (+)+(+16)+(+4)+(-4)+(-) = +16 N Refer to Pearon page 49 to 46 for a dicuion about ipule and force-tie graph. Dr. Ron Licht 3 4

5 III. Practice proble 1. A.0 kg object i initially oving north at.00 /. If it i brought to a top in 0.7 : A. What i the ipule? B. What i the force required?. A 7 kg peron fall fro a height of.0. If the peron land on a bed, what i the change in oentu? What i the ipule? If the topping tie wa 0.7 what average force did the bed apply on the peron? IV. Hand-in Aignent 1. What quantitie are ued to calculate ipule? State the unit of ipule.. Uing the concept of ipule, explain how a karate expert can break a board. 3. ro the graph to the right, what i the agnitude of the ipule provided to a 4 g tenni ball that i erved due outh? What i the velocity of the ball when the racquet and ball eparate? (.0 N [S], / [S]) 4. Whiplah occur when a car i rear-ended and either there i no headret or the headret i not properly adjuted. The toro of the otorit i accelerated by the eat, but the head i jerked forward only by the neck, cauing injury to the joint and oft tiue. What i the average net force on a otorit' neck if the toro i accelerated fro 0 to 14.0 / [W] in 0.13? Aue that the force acting on the head ( =.40 kg) i the ae agnitude a the force on the toro. (.60 x10 N [W]) Dr. Ron Licht 3

6 . Uing the principle of ipule and change in oentu, explain how the ue of eat belt and headret ave live and prevent injurie. 6. Two en puhing a talled car generate a net force of +40 N for.0. What i the final oentu of the car? (+4. x 10 3 kg /) 7. A woan drive a golf ball off the tee to a peed of /. The a of the ball i 4 g and the tie of contact wa 6.0. A. What i the change in oentu of the ball? (+1.3 kg /) B. What i the ipule? (+1.3 N) C. What wa the average force exerted by the club on the ball? (+10 N) D. If the angle of flight wa initially 0 o fro the horizontal, how far would the ball go before it landed? (1 ). A child hit a ball with a force of 10 N. If the ball and bat are in contact for 0.1, what ipule doe the ball receive? What i it change in oentu? If the a of the ball i 70 g and the ball wa initially oving toward the boy at 1. /, what i it final velocity? (+1 N, +1 kg /,+11. /) 9. A 300 g ball i truck by a bat with an ipact that lat If the ball ove through the air toward the bat at 0 / and leave at 100 / in the oppoite direction, calculate the average force exerted by the bat on the ball? (.3 x 10 3 N) 10. An.0 g bullet travelling at 400 / goe through a tationary block of wood in 4.0 x 10-4, eerging at 100 /. A. What average force did the wood exert on the bullet? ( 6.0 x 10 3 N) B. How thick i the wood? (1.0 x 10-1 ) 11. A trea of water trike a tationary turbine blade (ee drawing). The incident water trea ha a velocity of +1.0 / and the exiting trea ha a velocity of 1.0 /. The water trike the blade at a rate of.0 kg/. ind the net force acting on the water and on the blade. ( 900 N,+900 N) Dr. Ron Licht 3 6