AP Physics. Chapter 9 Review. Momentum et. al.

Transcription

1 AP Physics Chapter 9 Review Moentu et. al.

2 1. A 2000-kg truck traveling at a speed of 3.0 akes a 90 turn in a tie of 4.0 onds and eerges fro this turn with a speed of 4.0. What is the agnitude of the average resultant force on the truck during this turn? Δv = v f v i ( ) ( 3ˆ i + 0 ˆ j ) Δv = 0ˆ i + 4 ˆ j ( ) Δv = 3ˆ i + 4 ˆ j Δv = i ˆ 2 + ˆ j 2 = 5 2

3 #1.2 FΔt = Δv F = Δv Δt ( ) 5 F = 2000kg 4 F = 2500N ( ) 3

4 2. A 1.5-kg object oving with a speed of 4.0 collides perpendicularly with a wall and eerges with a speed of 6.0 in the opposite direction. If the object is in contact with the wall for 5.0, what is the agnitude of the average force on the object by the wall? FΔt = Δv F = Δv Δt ( ) 6 F = 1.5kg F = 3000N ( ( ))

5 3. A 1.5-kg playground ball is oving with a velocity of 3.0 directed 30 below the horizontal just before it strikes a horizontal surface. The ball leaves this surface 0.50 s later with a velocity of 4.0 directed 60 above the horizontal. What is the agnitude of the average resultant force on the ball? ( ) v i = 2.6ˆ i 1.5 ˆ j ( ) v f = 2ˆ i ˆ j Δv = v f v i ( ) ( 2.6ˆ i 1.5 ˆ j ) Δv = 2ˆ i ˆ j Δv = 0.6ˆ i ˆ j Δv = ( ) i ˆ 2 + ˆ j 2 = 5 5

6 #3.2 FΔt = Δv F = Δv Δt ( ) 5 F = 1.5kg 0.5 F =15N ( ) 6

7 16 F(N) t ( ) 4. The only force acting on a 2.0-kg object oving along the x axis is shown. If the velocity v x is +2.0 at t = 0, what is the velocity at t = 4.0? 7

8 16 F(N) t ( ) [( 8) + [ 1 ( 1 )( 8N) ] + [ 1 ( 2 )( 16N) ] ]N Δp = 20N 9

9 16 F(N) t ( ) Δp = ( v f v ) i Δp = v f v i Δp + v i = v f Δp + v i v f = 20 Kg v f = 12 = v f ( ) 2 + ( ) #4.4 10

10 5. A 3.0-kg ball with an initial velocity of (4i + 3j) collides with a wall and rebounds with a velocity of (-4i + 3j). What is the ipulse exerted on the ball by the wall? Δp = p f p i Δp = 3Kg( 4i + 3j) 3Kg( 4i + 3 j) Δp = 12i + 9 j 12i 9 j Δp = 24i N 11

11 6. A 0.15-kg baseball is thrown with a speed of 40. It is hit straight back at the pitcher with a speed of 80. What is the agnitude of the ipulse exerted on the ball by the bat. Δp = p f p i Δp = 0.15Kg( 80) Δp = 18 N ( ) Kg ( ) 12

12 7. A 12-g bullet is fired into a 3.0-kg ballistic pendulu initially at rest and becoes ebedded in it. The pendulu subsequently rises a vertical distance of 12 c. What was the initial speed of the bullet? E Botto = E Top v o K B = U Top 1 v 2 2 B = gh v B = 2gh v B = 2g 0.12 ( ) v B =

13 #7.2 p i = p f v o = ( + M) v v o = + M v v o = v o = 384 ( ) 14

14 8. A 10-g bullet oving 1000 strikes and passes through a 2.0-kg block initially at rest, as shown. The bullet eerges fro the block with a speed of 400. To what axiu height will the block rise above its initial position? p i = p f v p b = p b + p B 15

15 p i = p f p b = p b + p B b v o = b v b + M v B ( b v o v ) b M v B = 3 ( ) 600 = v B = 0.01kg #8.2 ( ) This is the velocity of the Block, by itself, after the collision! 16

16 #8.3 Fro conservation of Energy! h = ( v ) 2 B 2g ( h = 3 ) 2 2g h =

17 9. A 12-g bullet oving horizontally strikes and reains in a 3.0-kg block initially at rest on the edge of a table. The block, which is initially 78.4 c above the floor, strikes the floor a horizontal distance of 100 c fro its initial position. What was the initial speed of the bullet? v o t = 2y g = c v x = x t = =

18 v o t h u d v = 2.5 p i = p f b v o = ( b + M) v B ( )( ) v o = b + M b v o = v B ( ) 2.5 = ( ) 19

19 10. A 6.0-kg object oving 5.0 collides with and sticks to a 2.0-kg object. After the collision the coposite object is oving 2.0 in a direction opposite to the initial direction of otion of the 6.0-kg object. Deterine the speed of the 2.0-kg object before the collision. 6kg 5.0 h v 2 o u t d 6kg 20

20 6kg 5.0 p 1i + p 2i = p 1 v 1i + 2 v 2i = ( 1 + ) 2 v 2 v 2i = ( 1 + ) 2 v 1 v 1i ( ) v 2i = v 2i = 8kg 2 ( ) 2 v 2i = 23 v o v 1 v 1i ( ) 6kg t h u d 2 6kg ( ) ( ) 5 21

21 6kg 5.0 p = 30 Kg v o p = 46 Kg t h u d 2 6kg p = 16 Kg p = 16 Kg v o = p Kg 46 = = 23 22

22 11. A 2.0-kg object oving 5.0 collides with and sticks to an 8.0-kg object initially at rest. Deterine the kinetic energy lost by the syste as a result of this collision. p =10 kg 5.0 8kg t h u d 8kg p =10 kg 1 K i = 1 2 ( ) 5 ( ) 2 = 25J K f = kg K Lost = K i K f = 20J ( ) 1 ( ) 2 = 5J 23

23 12. A 1.6-kg block is attached to the end of a 2.0- string to for a pendulu. The pendulu is released fro rest when the string is horizontal. At the lowest point of its swing when it is oving horizontally, the block is hit by a 10-g bullet oving horizontally in the opposite direction. The bullet reains in the block and causes the block to coe to rest at the low point of its swing. What was the agnitude of the bullet's velocity just before hitting the block? 1.6kg 2 v Bi = 2gh v Bi = kg v bi t h u d v = 0 24

24 #12.2 p i = p f p Bi + p bi = 0 p Bi = p bi B v Bi = b v bi B v Bi b ( ) 6.26 = v bi = 1.6Kg 0.010kg v bi = 1002 ( ) ( ) 25

25 13. A 3.0-kg ass sliding on a frictionless surface has a velocity of 5.0 east when it undergoes a one-diensional inelastic collision with a 2.0-kg ass that has an initial velocity of 2.0 west. After the collision the 3.0-kg ass has a velocity of 2.2 east. How uch kinetic energy does the two-ass syste lose during the collision? 3kg 5.0 K i = 1 v v K i = 1 ( 3kg ) 5 2 K i = 37.5J + 4J = 41.5J ( ) t ( ) 2 ( ) 2 h u d 3kg K f = 1 2 v 2 K f = 1 5Kg 2 K f = 12.1J 2.2 ( ) 2.2 ( ) 2 K Lost = K i K f = 29.4J 26

26 14. A 4.0-kg ass is released fro rest at point A of a circular frictionless track of radius 0.40 as shown in the figure. The ass slides down the track and collides with a 2-kg ass that is initially at rest on a horizontal frictionless surface. If the asses stick together, what is their speed after the collision? v B = 2gh v A v B = 2g 0.40 ( ) v B = c 4kg t h u d 2.8 4kg 27

27 4kg t h u d 2.8 4kg p = v v = p v = 11.2 kg 6kg p =11.2 kg v =

28 15. A 70kg an who is ice skating north collides with a 30kg boy who is ice skating west. Iediately after the collision, the an and boy are observed to be oving together with a velocity of 2.0, in a direction 37 north of west. What was the agnitude of the boy's velocity before the collision? (, at 143 ) = 160ˆ p = 200 kg ( ) kg i + 120ˆ j 37 30kg 70kg t h u d 70kg 30kg v boy = p v boy = 160 Kg 30kg v boy =

29 16. A 4.0-kg ass has a velocity of 4.0, east when it explodes into two 2.0-kg asses. After the explosion one of the asses has a velocity of 3.0 at an angle of 60 north of east. What is the agnitude of the velocity of the other ass after the explosion? 3 4 kg 4 b o o 60 30

30 3 H 4 kg 16ˆ i Kg 4 b o o 3ˆ i Kg ˆ i Kg 6 Kg 60 3 Kg 5.2 Kg V ˆ j Kg 5.2ˆ j Kg p = i ˆ 2 + ˆ j 2 p = p =14 Kg v = p v = 14 Kg v = 7 j θ = tan 1 i 5.2 j θ = tan 1 13i θ =

31 17. A 4.2-kg object, initially at rest, "explodes" into three objects of equal ass. Two of these are deterined to have velocities of equal agnitudes (5.0 ) with directions that differ by 90. How uch kinetic energy was released in the explosion? 4. b o o 5 1.4kg 1.4kg kg 5 p = i ˆ 2 + ˆ j 2 p = p = 9.9 Kg v = p v = 9.9 Kg 1.4kg v = 7.07 H 0 7ˆ i kg 7ˆ i kg V 0 7ˆ j kg 7 ˆ j kg 32

32 K = 1 2 v 2 =17.5J K = 1 2 v 2 =17.5J K = 1 2 v 2 = 35J K Net = K K Net =17.5J +17.5J + 35J K Net = 70J 33

33 18. A 3.0-kg ass, initially at rest on a frictionless surface, explodes into three 1.0-kg asses. After the explosion the velocities of two of the 1.0-kg asses are: (1) 5.0, north and (2) 4.0, 30 south of east. What is the agnitude of the velocity of the third 1.0-kg ass after the explosion? H V 3 kg 0 0 b o o b o o 5 1 kg 1 kg ˆ i Kg 3ˆ j Kg 1 kg 30 5 ˆ j Kg ˆ i Kg 2ˆ j Kg 31

34 3.46ˆ i Kg 3ˆ j Kg p = i ˆ 2 + ˆ j 2 p = p = 4.58 Kg v = p v = 4.58 Kg 1.0kg v = 4.58, at

35 19. Three particles are placed in the xy plane. A 40-g particle is located at (3, 4), and a 50-g particle is positioned at (-2, -6). Where ust a 20-g particle be placed so that the center of ass of this three-particle syste is located at the origin? 50g 20g 40g 20g 1, 7 ( ) x CofM = y CofM = x 0 = 40 3 x = ( ) + 50( 2) + 20( x) y 0 = 40 4 y = 110g = 1 ( ) + 50( 6) + 20( y) g = 7 36

36 20. At the instant a 2.0-kg particle has a velocity of 4.0 in the positive x direction, a 3.0-kg particle has a velocity of 5.0 in the positive y direction. What is the speed of the center of ass of the two-particle syste? v x CofM = v x = ( 4 ) 5kg v x =1.6ˆ i v ycofm = v x = 3kg ( 5 ) 5kg v y = 3ˆ j 37

37 v = i ˆ 2 + ˆ j 2 v = v CofG =