We claim that momentum is conserved, yet most moving objects eventually sloiubt2,q +xi hy 0x,5cow down and stop. Explainbt+,xcyu2o,xi h q50i .

When a person jumps from a tree to the ground, what 4hxxx 59f1d o1b,bs dq,i/lvovwt7z6 happens to the momentum of the person upon strikinv7qd blbw5 z fxosd,/x9h1,to1 6ivx 4g the ground?

When you release an infl (kn*fuj 95ag-ms1p plated but untied balloon, why does it fly across the room?js-1gpaul 9f (p kn*5m

It is said that in ancient times+ (yd svp34+webn 2iek a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could no e+i+sk eyb3(ndp2w v4t push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and isf kaa.z/r l0f5 essentially in a a /lraz5fkf.0vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smallerca(: /ta qb0xmrgs5( - wljt,k the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended tt5q/k bs :ja lg,c(axm(r-tw0o inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withsta :0riop,qppwy jqcwn :pn248w e71 bb4nd collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this nby q rbjw1q 4c2i:wp po48p n,07npwe:ew design?

Why can a batter hit a pitched baseball further than p:2m ,g5ms 0um6ccu hkg*;onl xob:c 6a ball tossed in the air by the:6c ok mb c: 5u2hmgmu;cp60,slx*ogn batter?

Is it possible for an object to receive a larger impulse from a small force ttxcapg 410jn5 han from a gj5x1 4cpn ta0large force? Explain.

A light object and a heavy object have the same kinetic energy. Wh0pyk *s1,sb j*hnay5 njr79zeich has the greater momentum? 0k,y1 s5nebyp9*r jj7a s znh*Explain.

Describe a collisioneo za*itw9kd- 0s *0fmsjv7h0 in which all kinetic energy is lost.

At a hydroelectric power plant, water is directt acub36s da,;ed at high speed against turbine blades on an axle that turns antbduasac 63;, electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wa4+r *b 0di9tgwckd cot. ;sy(eruwk1 ;ll at a 45 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a harr)4p z.8v:xqaw0: l yqw2aot ud steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks )au.t o 8lpwvqqa 4x::rz02ywto the steel plate.

Why do you tend to lean backward when carrywlo; ecsh11m 2ing a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is not true9u5w gemul6jj;:sl p: for your arm g6 5e 9s jp;:wlluj:muor leg?

Show on a diagram how ; y:k: j; jjcmyb: dab7ls-k-vyour CM shifts when you change from a lying position to a sittiy ;skj-dmlv :7bck:;-jjba: y ng position.

If only an external force can change the momentum of the ce 7qy hsqm 8)bobkn1,)j;oi+iqnter of mass of an object, how can thokq +s) i;,iqyjn1mhq )bb 78oe internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes int;opcq/biuh lf29x8 7g,s 9)wok js, cqo many pieces. What can you say about the motion of this system oh cgc;kfb9uq,ps,ls8/)qooj 79ix w2 f pieces?

  What is the magnitude of the momentum of a 28-g sparrow flyi1ryyhk1qp;/ b-/r ngjh8 a,xpng with a speed of 8.4 ak g/;xb8hynj1r y1p hqr,-p/ m/s    $kg\;m/s$

  A constant friction force of 25 N acts on a 65 0l(yt ( /op2ae: qumt4fsr6yk-kg skier for 20 s. What is the skiuk:et(2q/m0 4aty y lo(rspf6er’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drivcv76 pzz1wv +z hj;g6me straight back toward thepz 71g 6m+jwch ;v6zvz pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a speed.aj dz4wt0j2;a)kol0ha- js e of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the chia0tl4 jjj-a.; eozswd)a0h 2kld is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the prope6nfb oelvq: 8)4x:wcxlling gases are expelled at a rate of 1500kg/sf 8c:l6 eboqv:n4)xxw with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s od qg6 d2*kyg ;hne)t+gn an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual spengq26 ge+k*;yhd dgt) ed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictionless track with a 4zz;ti+th u:zconstant speed of 18m/s A 5350-kg load,initially at res+hzzuztt: 4i; t, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling atzd(vivwkycuuj7;;2s x7o d iz*t4/ :f 15m/s strikes a second boxcar at rest. The two stick together and move off with aw 4cjs k2i;zfd /;i:u vzytd*xou(v77 speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speeds of 10mm19y k/ut kk(e5 :knx0km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind t(k1um:m k95xkn/ yk eon a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along )ymv*bw s 9fd+ ,)hutpb82dsc with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a ra) v ,s dfc8s2bw y)*btu+9mphdte of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initiaxz0bc:p8;sr4s rz: vl s6z 5bts9b8lally moving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, wha98zz5t vss :;blz 4sprl: s08r xcb6bat speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet travelinga.y: :ga, h g6vkrj2ek 230m/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stati. ava2j,:r :ehgkky6gonary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speed of 5o .72zmwgtzhfue* 2i$5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass-p 1ew pcdpl4akd:- 7w 3180 kg is traveling in outer space with a velocity of 115m/s To alter its coura7 :ec-pdl-p 4d1 wkpwse by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed of 45m/) 9;yqe- o1axo)um ezys The golf club was in contact with the ball o)ao)me-; 19exzuyy qfor $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a vel+aec b+8 r yil se)kh,q v6tk+w;fjp--ocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the im-t fce+;bvjqep8a w) +ks,+li-yh r6k pulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed vidgn) 2 n bo.0sfjd1o+tjf t7-=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the cyqybv*d,boe q6o in-xy 8d)9 -rashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s fromdd b bq -yn) v6-8*9yoqoyeix, the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east anj,o5 fmhgd +lo )9nnqd6wq9 q3d is stopped in 0.75 s by a head-on tackle by a tachq dwq 5d9mo )lfo9n ,+qjng36kler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennisws*ej7 esy x2gccb)6w,u5 m,a ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphicacw62gbx5, mc ewjs e,7s)y*au l methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-e m4+*vshd p7akg person jump without breaking the lower leg bone of either leg? Ignore air resistancep4m+avhd 7e*s and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of m )*5iokfs)qch 9 5peyx cl2kl67pdc7collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each balpp cs6f2iy*7xkqk lcm)ch7l)5 e9d5ol after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3mtbpy-3e l/in+qso .) t/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg pui +.q en-st/p lo)yb3tck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass unde3;2 m.7fobv m:dx wyvbrgo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the coll;2xmf 3w .o:vyb7dbvmision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a spot2sbrc- 3pz* es9e/feed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision r2f9p3e/z* ebsc o-ts, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is movin ljdex: rb9z21g with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. x ldej:1z2 9brAfterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as one approachl.ge+k*dr oz7es the*7.erg kol+dz other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collisu.g 0dfo0a ac:ion with a second ball initially at rest. The second ball moves off with half the original s.aufg00 :o cdapeed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides dox1 .e;r cy gh5z/yy: 8szwdgb0wn a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the tah /0bz yywrxc8:gs;e.dg51 yzble is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an obje16gpqkt9ir 6sct of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a maximum height h an9- zf.qx e2h0r:fcjof the pendulum eh aqn9:0 .cx f2j-erzfqual to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling (r fb1j:px(cl230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Detec1f((x:rlbj prmine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fractydb,dk+yn 7w3,y 8*cdn-g o:exi+bz aion of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, incryt 1j:,5lz- 8nd swo (lofm:.e f e8zmccm:6to two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acqj z:zd, ll6(c58cmtr. 8nmem s f-oo1cwfy:: euire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rvzd 34 +cpb)4jb jx*jpear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80,jpc4+pb3xdv4 z)jj b * calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rf( 2fm*kr8ely,l:. gsr. oji cebounds to a height of 1.20 m. Approximate*(l.g 8j eory m:f 2ifs,clk.rly how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the coeffihhiq:4p**r e i2e dd3wcient of reidh2hr4dq epw*e: *i3 stitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one witj7l 0k k8o ox5jvg hv,/3ra2luh three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in 8u0357lhga jrk /ovjlvok2,x it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-om z0 s9n9:nyefolb0a9n with a 10.0-kg object moving in the -x direction at 4m/s Find the f: 0 m0slz 99ybfnno9eainal velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a seco.-nk6l5jjkybq* 9 (lylx9 mtmnd nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have mome9b* kl6mj -y.tlnljk9m5 xyq( nta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of mar);4g* c)zwn sq xuk+mss $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between twk y,3*xnc0fwuh4r 9noo objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle beth nw0 knfoy 9,r4c3*uxween their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the origin ofky1ebg lyix 0 .lawq6q**n.e8 an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the rel.yg.e *8 nwy1al0 iqqk6b *xight along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with another at-q q ,vapis,rpsm;c:4ii ;n. dom at rest. After the impact, the neon atom travels away ria: c;v idq.,n;is4mq- psp,at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision withnv3d jdebgz-,y9pgn b+vf( /5 another atom at rest. After the impact, the neon atom travels away at a 55.5/3v (fpdzv9n y-bdbe n,j +gg6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of maoz1nn6mg qr*: ss of the three-mass system shown in Fig. 7–38. Specify relative tmg*q1n6 on :rzo the left-hand 1.00-kg mass.    m

  The distance between a carbon atoo(5ab-4featf m ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m 46yuc )/dievr9axsbve5,* nzy3j/ k cbehind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the f*/ ec,3 /n4eik yj5vv9s6 a xy)rbczudront of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mas.9mqhj1qs: 7j,st f/db*hd azs 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE,q,.bhtjd/smfqhj *7s19 za:d and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides z. q+wqch qgf:otd/5antt/ n6uph-/ :$l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identzfr yax2 zxnz4 p3(-zw :6m4juical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so thatn6ma4x wfzz4(rp zu2 x:y3-jz the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular h) bd1 cg*ruvz6k.ho 1zole of radius R cut out of it. The center of the smal*.1uod hg1bzckz) vr6 ler circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and c sq5m4t5, aaitqr6 dz3alculate the mass of one of your l5 43i6sdz, rtqtaa 5mqegs.    kg

  Determine the CM of an outstretched arm usin 4t 4no orkcx0,:9ukawg Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent at a righl )jbdq t2)l*idakh496fxp8j t angle. Assume jdb8t4diajlf)lp q kx6*29 h)that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a positioe*cc8 ed: qo 04zle/a6qa mc-kn such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this z/q l eodk6mc*ec: qec-4aa 80CM be outside the body? Use Table 7–1.

The masses of the Earth an3ucxby,, q g6hd Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on frictionless ice.z5e0bwq 8+ccv
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head o0x; vq83; )ukrcab 8or irfe6wf mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of th)8k;frwaoq8x 0 ir6e3v; bcure handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform c(hnq)qkks5dp:cvt3-fle 8 haqsp./zmp. -;qylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.5.-/ckm) l qdtn8spfpq5.q;kez3qpa hv(:sh -00 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29)-bnxq 9x17qb ck rg.3c, $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass 27oup vic.hu2M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured wit uip.2 uhc2o7vh respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a ba 8oa9 s2fuj;gqt and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the a2 q sfoua;g9j8verage force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speed*9,rpik mh:b l $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown ik-t jb8, gpk;tn Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue -g8 ,kt kjp;tbball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.std 8 bapa* lbnjb-j 6bu4i.29v(7cbh 5m/s by pushing off with his b9b7sh jl*bija(v a.n68dtbc-42 ub p legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and tha+tzvd . 8kym -sqr1xtuj ss04)pu0.ze other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter . d ya)k4 sz jp vm-xs1r.8+tsuu0tz0qastronaut has moved 12 m?    m

  A ball of mass m makes a head-on elz9ss q-kq7r;pastic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is thep-qqr9 sz;k7s mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involvingbk01aohi5ndhv4(w - b an automobile accident. The accident involved car A of mass 1900 kg which cra 5kb bvi0o(h-w4n1adhshed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls of-7kc6gsr 8ld uf the top of a flight of concrete steps of total vertical height 4.00 m. The ball hits f7u 8dc-g6k lsrour times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest gg mki*(z r8qih+(,d xdirectly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the (+kxhi,(mdzg ig8q *r bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood plabh, ;jjl 151pklh k,mlced on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it come ,1kll1lb jk; 5ph,mhjs to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and theg-h :3kku.esnvw/ s p) other of mass 60 kg, sit in a rowboat of mass 83.)s gnehpwk:/ vksu-0 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass wa79 kmnaymv4pk7s c/k7s about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenlnmy)u3 u,r6h jdy +mt,y broken apart into two fragments by an explosion. One+ )m h,rjnud,y3ty6mu fragment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by thev ;fun:r hiu3u zke368 formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses zl tez++vz +m4$m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha particle and a smavyz/bnsiihz39wp .w3t b yjf vq9:)gs/d;* p3ller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is 3d/3i/yi) 3vbwpsn9 ; .qpz hz sy:9gwt j*vfb$ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an ij*d.pw(:y jaangle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.oii d;jvgb t)l (055ra5vle 5cj.a.bf0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upp552ujm3llf fh0*vr cw er limit on mass m if it is to rebound from M, slide up the incline, stop, slid *h v3fjrw5lcml u52f0e down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot eff cbnzu -xq3iq9o a)4mdb*f/q;ect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbit/ u -bonib mdqzq)x3f; ac*q94al speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s