Unit 1: Momentum & Impulse

Transcription

1 Imulse and Change in Momentum Unit 1: Momentum & Imulse Momentum is a vector quantity. It is the roduct o a body s mass and its velocity. mv Units: kgm/s Imulse is a vector quantity. It is deined as the alication o a net orce on an object over a eriod o time. Imulse = t Units: Ns F net This imulse-momentum equation states that an imulse on an object causes a change in its momentum (i.e. m v) : Imulse = F t m v or F t The imulse-momentum equation well exlains the concet o cushioning. Based on F, we see that t F 1 t (inverse relationshi) A cushion will change an object s momentum over a longer eriod o time, and thus, this will decrease the orce on the object. Note: Imulse (change in momentum) remains constant and unaected. Ex. A 16.0 kg object hits the ground with a downward velocity o 6.64 km/h. I it exeriences an imulse rom the ground o 500 Ns uwards, determine its inal momentum. 3

2 1. A ball is thrown at 10 m/s towards various barriers. In which case does the ball exerience the greatest imulse? A. The ball hits a wall and rebounds at.0 m/s. B. The ball hits a wall and rebounds at 7.0 m/s. C. The ball hits a wall, sticks to it and stos moving. D. The ball breaks a window and continues moving at 10 m/s in the original direction.. A rock climber alls and is saved rom injuries by a climbing roe that is slightly elastic. The imortance o the elasticity o the climbing roe can be understood in terms o imulse because elasticity results in A. decreased orce during an increased time interval B. increased orce during an increased time interval C. decreased orce during a decreased time interval D. increased orce during a decreased time interval Imulse or a Changing Net Force I the net orce on an object is changing (usually shown on a F - t grah), then: Imulse = Area between the line and the t-axis This grah shows the relationshi between the orce on a kg ootball and the time a kicker s oot is in contact with the ball. As a result o the kick, the ootball, which was initially at rest, has a inal seed o 8.5 m/s. Force as a unction o time NR. 3 The magnitude o the maximum orce, Fmax, exerted on the ball during the kicking rocess, exressed in scientiic notation, is a.b 10 c N. The values o a, b, and c are,, and. 4

3 Law o Conservation o Momentum Momentum is conserved or collisions and exlosions only i the system is isolated. All objects involved in the collision / exlosion must be included. There is no net external orce (Fnet = 0) on the entire system throughout the motion So, when you consider the entire system, all orces must cancel! Conservation o momentum states that the total momentum o a system remains constant. i.e. Ti T There are three interactions you should be amiliar with: #1. Collision: Hit and bounce 1 i i 1 v m v m v m v m1 1i i 1 1 #. Collision: Objects stick to each other 1 i i 1 m v m v m m v 1 1 i i 1 #3. Exlosion (Recoil): An object (initially at rest) exlodes into two ieces v m v m1 1 Ex. Determine the initial velocity o the 800 g ball. 5

4 Elastic Collisions Elastic collisions are those where both momentum and kinetic energy are conserved. Ti T and EkTi EkT Note: A collision is considered inelastic when momentum is conserved, but kinetic energy is not conserved (energy is lost due to heat / sound). Use the ollowing inormation to answer the next question. A 4.0 kg toy car, moving East at 3.0 m/s, collides with an 8.0 kg toy truck that is initially at rest. Ater the collision, the car is moving West at 1.0 m/s, while the truck is moving East at.0 m/s. 7. Which o the ollowing is true? A. Momentum is not conserved, and the collision is not elastic. B. Momentum is conserved, and the collision is not elastic. C. Momentum is not conserved, and the collision is elastic. D. Momentum is conserved, and the collision is elastic. Two-Dimensional Interactions The Law o Conservation o Momentum also alies to two dimensional interactions. Since momentum is a vector quantity that is conserved during interactions, we use a vector diagram to solve two dimensional roblems. There are two situations you need to be amiliar with: 1. Tail-to-Ti (Grahical) Analysis 1 Conservation o momentum Ti T Stick! 1 7 1

5 . Comonents Analysis 1 x 1 1 x 1 y y Boom! x x 1 y y Conservation o Tx momentum (x) Tx 1x x 1x x Conservation o Ty momentum (y) Ty 1y y 1y y Ex. Sketch the vector triangle that would determine their velocity ater the collision. Comonents Analysis Ex. For the collision shown, determine the magnitude o. 8

6 Curve-Straightening and Grahical Analysis Examle. In a circular motion exeriment, the eriod o rotation (T) is varied and the resulting centrietal acceleration (ac) is measured. All other variables are held constant. a c T 4 r where r is the radius o the circle. Sketch the straightened curve. Exlain how to determine the radius using the signiicance o the sloe. 8. A.0 kg uck traveling due east at.5 m/s collides with a 1.0 kg uck traveling due south at 3.0 m/s. They stick together on imact. The resultant direction o the combined ucks is A. 31º S o E B. 40º S o E C. 50º S o E D. 59º S o E 9

7 9. A glass ornament o mass 575 g sitting on a table is subjected to a resonant requency o 440 Hz. The ornament breaks into three ieces that travel horizontally across the rictionless tableto. Fragment A has a mass o 168 g and ragment B has a mass o 1 g. The magnitude o the momentum o the third iece o glass, ragment C, is A kg m/s B kg m/s C..8 kg m/s D kg m/s m B = 1 g v B = 9.00 m/s B = 1.91 kg m/s m A = 168 g v A = 15.0 m/s A =.5 kg m/s 10. In a circular motion exeriment, a mass is swung in a circle with a constant radius r. The eriod o rotation (T) is varied and the resulting orbital seed (v) is measured. The known equation relating the variables would be vt r. For the straightened relationshi, which o the ollowing determines the radius rom the signiicance o the sloe? A. r sloe B. 1 r sloe C. r D. sloe sloe r 10

8 Unit : Forces and Fields The Fundamental Law o Electric Charges states that: There are two tyes o charges: ositive (deicit o e-) and negative (excess o e-) Like charges reel each other Oosite charges attract each other Law o Conservation o Charges: Electric charge can neither be created nor destroyed but may be transerred. Induced Searation o Charge (Charged object attracting a neutral object) When a net negative object (or examle) is brought near (without touching) the neutral object, the electrons are reelled (due to like charges). This induces a searation o charge within the neutral object. Since an oosite charge is induced in the closest region, they attract. e- reelled Net Net + Net Matter can become electrically charged through three dierent rocesses: 1. Charging by riction (gain equal but oosite charges) When two objects (tyically insulators) are rubbed together, riction creates heat energy. The material with a stronger hold on electrons will stri electrons o the other material. This gives the objects equal but oosite charges.. Charging by conduction (gains same charge) When a negatively charged rod (or examle) is touched to a neutral conducting object, some o the excess electrons on the rod (reelled by neighbouring electrons), move over to the object. Thus, both objects gain a negative charge. Note: I the two metal objects are identical (in mass and volume), then they will gain equal charges. 3. Charging by induction (gains oosite charge) When a net negative rod (or examle) is brought near (without touching) a grounded electroscoe, electrons are reelled (due to like charges) and travel into the ground. I the ground is then removed (while the negative rod is still close), then the scoe gains a ositive charge Net Rod Neutral scoe e- Ground 11

9 RTD Exam Pre Physics 30 Practice Questions Physics 30 Practice Questions

10 RTD Exam Pre Physics 30 Practice Questions NR. 1 In a vehicle saety test, a kg truck travelling at 60.0 km/h collides with a concrete barrier and comes to a comlete sto in 0.10 s. The magnitude o the change in the momentum o the truck, exressed in scientiic notation, is 10 w kg m/s. (Record your three-digit answer in the numerical-resonse section on the answer sheet.). A small rubber ball moving at high seed strikes a stationary cart. As a result o the collision, the rubber ball rebounds and the cart rolls orward. Which object exerienced the greater magnitude o imulse? A. The cart B. The rubber ball C. Both exerienced the same magnitude o imulse D. It deends on whether the collision was elastic or inelastic 3. The risk o a motorist becoming atally injured in a vehicle collision is reduced when an airbag or a seatbelt is used because the airbag or seatbelt i change in momentum by ii the stoing orce the motorist exeriences. The statement above is comleted by the inormation in row Row i ii A. achieves the same decreasing B. achieves the same increasing C. decreases the decreasing D. increases the increasing NR. 4 A kg vehicle moving westward at 15.0 m/s is subjected to a N s imulse to the north. The magnitude o the inal momentum o the vehicle, exressed in scientiic notation is a.bc 10 d kg m/s. The values o a, b, c, and d are,,, and. NR. 5 A kg ball moving at 40.0 m/s is struck by a bat. The bat reverses the ball s direction and gives it a seed o 50.0 m/s. The average orce the bat alies to the ball i they are in contact or 6.00 ms, exressed in scientiic notation is a.bc 10 d N. The values o a, b, c, and d are,,, and

11 RTD Exam Pre Physics 30 Practice Questions SOLUTIONS mv = m v v i = 1580 kg ( m/s) = kgm/s. C Based on Newton s 3 rd Law, the orces (and thus, imulses) are equal but oosite. 3. A An airbag has no eect on imulse (change in momentum). Instead, it increases the time o collision, thus decreasing the orce (inverse relationshi between F and t ) I i I 10,000 15,000 = kgm/s (Re: Away rom bat +) F t mv = mv v i mv vi kg50m / s 40m / s F = = N t s Ft 8.0 N 1.0 s 6. C Since orce is constant, F t mv v m 5.0 kg v v v i v v vi = 1.6 m/s m/s = 4.6 m/s i = 1.6 m/s 7. A I = total area = (8.0 N) (1.0 s) (8.0 N) (0.5 s) = 8 Ns + Ns = 10 Ns (East +, West ) Cons o Momentum T T (1.) (40) = (1.) (5) + 6 v v = 13 m/s East (U +, Down ) Cons o Momentum T T 0 = (0.00) (841) v v = m/s m1v1 m1v1 mv 0 m1v1 mv Cons o Momentum T T m 1v1 m1 m v ( ) () = ( ) v v = m/s 11. A In a collision, momentum is conserved. Since this collision will deinitely create heat and sound, it is not elastic (i.e. total kinetic energy is not conserved) Beore the collision: car = 9,400 kgm/s x = 9,400 kgm/s ; y = 0 Ater: x 1 = 0,000 cos 0 = 18,794 kgm/s ; y 1 = 0,000 sin0 = 6840 kgm/s Tx Tx 9,400 = 18,794 + x x = 10,606 kgm/s Ty Ty 0 = y y = 6840 kgm/s = 1,61 kgm/s ; v = 8.41 m/s m A Cons o Momentum T T 0 m1v1 mv 0 = (3) (15) + ( ) v v = 0.35 m/s 14. C Beore the collision, the y-comonent o the momentum is zero. Ater: 1 = (18.8) (0.14) =.63 kgm/s ; y 1 =.63 sin 67 =.48 kgm/s The total momentum ater the collision must also be zero, so the y-comonents are equal but oosite. Thus, y =.48 kgm/s I = 10,000 Ns i = 15,000 kgm/s