Description: Conceptual: A bullet embeds in a stationary, frictionless block: type of collision? what is conserved? v_final?

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1 Chapter 8 [ Edit ] Overview Suary View Diagnostics View Print View with Answers Chapter 8 Due: 11:59p on Sunday, October 23, 2016 To understand how points are awarded, read the Grading Policy for this assignent. A Bullet Is Fired into a Wooden Block Description: Conceptual: A bullet ebeds in a stationary, frictionless block: type of collision? what is conserved? v_final? A bullet of ass b is fired horizontally with speed vi at a wooden block of ass w resting on a frictionless table. The bullet hits the block and becoes copletely ebedded within it. After the bullet has coe to rest within the block, the block, with the bullet in it, is traveling at speed vf. Which of the following best describes this collision? Hint 1. Types of collisions An inelastic collision is a collision in which kinetic energy is not conserved. In a partially inelastic collision, kinetic energy is lost, but the objects colliding do not stick together. Fro this inforation, you can infer what copletely inelastic and elastic collisions are. perfectly elastic partially inelastic perfectly inelastic Which of the following quantities, if any, are conserved during this collision? 1/16

2 Hint 1. When is kinetic energy conserved? Kinetic energy is conserved only in perfectly elastic collisions. kinetic energy only oentu only kinetic energy and oentu neither oentu nor kinetic energy Part C What is the speed of the block/bullet syste after the collision? Express your answer in ters of vi, w, and b. Hint 1. Find the oentu after the collision What is the total oentu ptotal of the block/bullet syste after the collision? Express your answer in ters of vf and other given quantities. p total = Hint 2. Use conservation of oentu The oentu of the block/bullet syste is conserved. Therefore, the oentu before the collision is the sae as the oentu after the collision. Find a second expression for p total, this tie expressed as the total oentu of the syste before the collision. Express your answer in ters of vi and other given quantities. p total = vf = ± Catching a Ball on Ice Description: ± Includes Math Reediation. Find the final oentu of a person who catches a ball on a frictionless surface. Find the final oentu of a person on a frictionless surface off of who a ball bounces. 2/16

3 Olaf is standing on a sheet of ice that covers the football stadiu parking lot in Buffalo, New York; there is negligible friction between his feet and the ice. A friend throws Olaf a ball of ass that is traveling horizontally at Olaf's ass is If Olaf catches the ball, with what speed vf do Olaf and the ball ove afterward? Express your answer nuerically in eters per second. Hint 1. How to approach the proble Using conservation of oentu and the fact that Olaf's initial oentu is zero, set the initial oentu of the ball equal to the final oentu of Olaf and the ball, then solve for the final velocity. Hint 2. Find the ball's initial oentu What is pi, the initial oentu of the ball? Express your answer nuerically in kilogra eters per second. p i = = 4.40 s vf = = If the ball hits Olaf and bounces off his chest horizontally at 7.50 in the opposite direction, what is his speed vf after the collision? Express your answer nuerically in eters per second. 3/16

4 Hint 1. How to approach the proble The initial oentu of the ball is the sae as in. Apply conservation of oentu, keeping in ind that both Olaf and the ball have a nonzero final oentu. Hint 2. Find the ball's final oentu Taking the direction in which the ball was initially traveling to be positive, what is p ball,f, the ball's final oentu? Express your answer nuerically in kilogra eters per second. p ball,f = = 3.00 s vf = = Collision at an Angle Description: Straightforward application of oentu conservation in an inelastic collision. Two cars, both of ass, collide and stick together. Prior to the collision, one car had been traveling north at speed 2v, while the second was traveling at speed v at an angle ϕ south of east (as indicated in the figure). After the collision, the two car syste travels at speed vfinal at an angle θ east of north. Find the speed vfinal of the joined cars after the collision. Express your answer in ters of v and ϕ. Hint 1. Deterine the conserved quantities 4/16

5 Which of the following stateents is true for the collision described? Moentu is conserved but kinetic energy is not conserved. Kinetic energy is conserved but oentu is not conserved. Both kinetic energy and oentu are conserved. Neither kinetic energy nor oentu is conserved. Apply conservation of oentu: p initial = p final. Find both coponents (north and east) of the initial oentu p initial using the inforation in the proble introduction. The agnitude of p initial is equal to the agnitude of the oentu vector for the two car syste after the collision: pfinal = (2) vfinal. Hint 2. The coponent of the final velocity in the east west direction Find the coponent of v final v ϕ in the east west direction. Express your answer in ters of and. Hint 1. Find the east west coponent of the initial oentu What is pe, the agnitude of the total oentu of the two cars in the east west direction? (Take eastward to be positive, westward negative.) Express your answer in ters of, v, and ϕ. p e p e = Now use the conservation of oentu equation to find vfinal. vfinal (east west) = Hint 3. Find the north south coponent of the final oentu Find the coponent of vfinal in the north south direction. Express your answer in ters of v and ϕ. Hint 1. Find the north south coponent of the initial oentu p n What is the agnitude p n of the total oentu of the two cars in the north south direction? (Take northward to be positive, southward negative). 5/16

6 Express your answer in ters of, v, and ϕ. p n = vfinal (north south) = Hint 4. Math help Let vfinal.x be the east west coponent of vfinal, and vfinal.y the north south coponent. Then vfinal = v 2 final.x + v 2 final.y. You will also need to use the following trignoetric identity when you evaluate the right hand side of the above equation in ters of v and ϕ: cos 2 ϕ + sin 2 ϕ = 1. vfinal = What is the angle θ with respect to north ade by the velocity vector of the two cars after the collision? Express your answer in ters of ϕ. Your answer should contain an inverse trigonoetric function using the notation asin, atan etc. and not arcsin, arctan etc. Hint 1. A forula for tanθ Let vfinal.x be the east west coponent of v final, and vfinal.y the north south coponent. Then since the angle asked for is the angle east of north. tanθ= v final x, vfinal y θ = Also accepted: 6/16

7 Exercise 8.4 Description: Two vehicles are approaching an intersection. One is a 1 pickup traveling at v1 fro east to west (the x direction), and the other is a 2 sedan going fro south to north (the +y direction at v2). (a) Find the x coponent of the net... x +y Two vehicles are approaching an intersection. One is a 2600 pickup traveling at 18.0 fro east to west (the direction), and the other is a 1600 sedan going fro south to north (the direction at 25.0 ). Find the x coponent of the net oentu of this syste. p x = = Find the y coponent of the net oentu of this syste. p y = = Part C What is the agnitude of the net oentu? p = = Part D What is the direction of the net oentu? θ = = 49.5 west of north. Exercise 8.21 Description: On a frictionless, horizontal air table, puck A (with ass _1) is oving toward puck B (with ass _2), that is initially at rest. After the collision, puck A has a velocity of v_1 to the left, and puck B has velocity v_2 to the right. (a) What was... On a frictionless, horizontal air table, puck A (with ass ) is oving toward puck B (with ass ), that is initially at rest. After the collision, puck A has a velocity of to the left, and puck B has velocity to the right. 7/16

8 What was the speed of puck A before the collision? v = = Calculate the change in the total kinetic energy of the syste that occurs during the collision. ΔK = = J Exercise 8.27 Description: Two ice skaters, Daniel (ass 1 ) and Rebecca (ass 2 ), are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is oving at v1 before she collides with hi. After the collision, Rebecca has a... Two ice skaters, Daniel (ass 60.0 ) and Rebecca (ass 45.0 ), are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is oving at 14.0 before she collides with hi. After the collision, Rebecca has a velocity of agnitude 6.00 at an angle of 52.1 fro her initial direction. Both skaters ove on the frictionless, horizontal surface of the rink. What is the agnitude of Daniel's velocity after the collision? v = = 8.51 What is the direction of Daniel's velocity after the collision? θ = = 24.7 fro the Rebecca's original direction Also accepted: = 24.7 Part C What is the change in total kinetic energy of the two skaters as a result of the collision? 8/16

9 ΔK = = 1430 J Exercise 8.36 Description: A 1 sports car is oving westbound at v1 on a level road when it collides with a 2 truck driving east on the sae road at v2. The two vehicles reain locked together after the collision. (a) What is the velocity (agnitude) of the two vehicles just... A 1050 sports car is oving westbound at 15.0 on a level road when it collides with a 6320 truck driving east on the sae road at The two vehicles reain locked together after the collision. What is the velocity (agnitude) of the two vehicles just after the collision? v = = 9.87 What is the direction of the velocity of the two vehicles just after the collision? to the west to the east Part C At what speed should the truck have been oving so that it and car are both stopped in the collision? v = = 2.49 Part D Find the change in kinetic energy of the syste of two vehicles for the situations of part A. ΔK = = J Part E Find the change in kinetic energy of the syste of two vehicles for the situations of part C. 9/16

10 ΔK = = J Exercise 8.40 Description: To protect their young in the nest, peregrine falcons will fly into birds of prey (such as ravens) at high speed. In one such episode, a 1 falcon flying at v1 hit a 2 raven flying at v2. The falcon hit the raven at right angles to its original... To protect their young in the nest, peregrine falcons will fly into birds of prey (such as ravens) at high speed. In one such episode, a 620 g falcon flying at 18.0 hit a 1.60 raven flying at 9.0. The falcon hit the raven at right angles to its original path and bounced back at 5.0. (These figures were estiated by the author as he watched this attack occur in northern New Mexico.) By what angle did the falcon change the raven's direction of otion? Express your answer using two significant figures. θ = = 45 What was the raven's speed right after the collision? Express your answer using two significant figures. v = = 13 Exercise 8.42 Description: A g bullet is fired horizontally into a 1.20 wooden block resting on a horizontal surface. The coefficient of kinetic friction between block and surface is The bullet reains ebedded in the block, which is observed to slide s... g A 5.00 bullet is fired horizontally into a 1.20 wooden block resting on a horizontal surface. The coefficient of kinetic friction between block and surface is The bullet reains ebedded in the block, which is observed to slide along the surface before stopping. What was the initial speed of the bullet? Express your answer with the appropriate units. 10/16

11 v = = 270 Also accepted: = 270, = 270, = 270 Exercise 8.44 Description: A ## block is attached to a very light horizontal spring of force constant ## N/ and is resting on a sooth horizontal table. (See the figure below.) Suddenly it is struck by a ## stone traveling horizontally at ## to the right, whereupon... A 15.0 block is attached to a very light horizontal spring of force constant 575 and is resting on a sooth horizontal table. (See the figure below.) Suddenly it is struck by a 3.00 stone traveling horizontally at 8.00 to the right, whereupon the stone rebounds at 2.00 horizontally to the left. N/ Find the axiu distance that the block will copress the spring after the collision.(hint: Break this proble into two parts the collision and the behavior after the collision and apply the appropriate conservation law to each part.) Enter your answer using three significant figures. x = = Exercise 8.50 Description: You are at the controls of a particle accelerator, sending a bea of v_1 protons (ass ) at a gas target of an unknown eleent. Your detector tells you that soe protons bounce straight back after a collision with one of the nuclei of the... You are at the controls of a particle accelerator, sending a bea of protons (ass ) at a gas target of an unknown eleent. Your detector tells you that soe protons bounce straight back after a collision with one of the nuclei of the unknown eleent. All such protons rebound with a speed of Assue that the initial speed of the target nucleus is negligible and the collision is elastic. Find the ass of one nucleus of the unknown eleent. Express your answer in ters of the proton ass. = 13.0 What is the speed of the unknown nucleus iediately after such a collision? 11/16

12 = Exercise 8.54 Description: A 1200 SUV is oving along a straight highway at Another car, with ass 1800 and speed 20.0, has its center of ass 40.0 ahead of the center of ass of the SUV. (a) Find the position of the center of ass of the... A 1200 SUV is oving along a straight highway at Another car, with ass 1800 and speed 20.0, has its center of ass 40.0 ahead of the center of ass of the SUV. Find the position of the center of ass of the syste consisting of the two cars. Express your answer using three significant figures. x c = 16.0 behind the leading car Find the agnitude of the syste s total oentu, by using the given data. Express your answer to three significant figures and include the appropriate units. P1 = Part C Find the speed of the syste s center of ass. 12/16

13 Express your answer to three significant figures and include the appropriate units. vc, x = 16.8 Part D Find the syste s total oentu, by using the speed of the center of ass. Express your answer to three significant figures and include the appropriate units. P2 = Part E Copare your results of parts B and D. P1 > P2 P1 < P2 P1 = P2 Exercise 8.56 Description: At one instant, the center of ass of a syste of two particles is located on the x axis at x = 2.0 and has a velocity of (5.0 ) i_unit. One of the particles is at the origin. The other particle has a ass of 0.10 and is at rest on the... At one instant, the center of ass of a syste of two particles is located on the x axis at x = 2.0 and has a velocity of (5.0 ). One of the particles is at the origin. The other particle has a ass of 0.10 and is at rest on the axis at = 8.0. i^ x x What is the ass of the particle at the origin? Express your answer using two significant figures. 1 = 0.30 Calculate the total oentu of this syste. Express your answer using two significant figures. 13/16

14 P^ = 2.0 i^ Part C What is the velocity of the particle at the origin? Express your answer using two significant figures. v1 = 6.7 i^ Proble 8.72 Description: A sall wooden block with ass _1 is suspended fro the lower end of a light cord that is l long. The block is initially at rest. A bullet with ass _2 is fired at the block with a horizontal velocity v_0. The bullet strikes the block... A sall wooden block with ass is suspended fro the lower end of a light cord that is 1.42 long. The block is initially at rest. A bullet with ass is fired at the block with a horizontal velocity v0. The bullet strikes the block and becoes ebedded in it. After the collision the cobined object swings on the end of the cord. When the block has risen a vertical height of 0.800, the tension in the cord is N What was the initial speed v0 of the bullet? Express your answer with the appropriate units. v0 = = 290 Proble 8.80 Description: _S stone rests on a frictionless, horizontal surface. A bullet of ass _B, traveling horizontally at v_1, strikes the stone and rebounds horizontally at right angles to its original direction with a speed of v_2. (a) Copute the agnitude of the... g stone rests on a frictionless, horizontal surface. A bullet of ass 8.00, traveling horizontally at 330, strikes the stone and rebounds horizontally at right angles to its original direction with a speed of 190. Copute the agnitude of the velocity of the stone after it is struck. V = = /16

15 Copute the direction of the velocity of the stone after it is struck. θ = = 29.9 fro the initial direction of the bullet Part C Is the collision perfectly elastic? yes no Proble 8.90 Description: Jonathan and Jane are sitting in a sleigh that is at rest on frictionless ice. Jonathan's weight is 800 N, Jane's weight is 600 N, and that of the sleigh is 1000 N. They see a poisonous spider on the floor of the sleigh and iediately jup off... Jonathan and Jane are sitting in a sleigh that is at rest on frictionless ice. Jonathan's weight is 800, Jane's weight is 600, and that of the sleigh is 1000 N. They see a poisonous spider on the floor of the sleigh and iediately jup off. Jonathan jups to the left with a velocity (relative to the ice) of 5.00 at 30.0 above the horizontal, and Jane jups to the right at 7.00 at above the horizontal (relative to the ice) N N Calculate the agnitude of the sleigh's horizontal velocity after they jup out What is the direction of the sleigh's horizontal velocity after they jup out. to the left to the right Proble /16

16 Description: A 45.0 woan stands up in a 60.0 canoe 5.00 long. She walks fro a point 1.00 fro one end to a point 1.00 fro the other end (the figure ). (a) If you ignore resistance to otion of the canoe in the water, how far does the canoe ove... A 45.0 woan stands up in a 60.0 canoe 5.00 long. She walks fro a point 1.00 fro one end to a point 1.00 fro the other end (the figure ). If you ignore resistance to otion of the canoe in the water, how far does the canoe ove during this process? dcanoe = 1.29 to the left Copyright 2016 Pearson. All rights reserved. Legal Notice Privacy Policy Perissions 16/16