We claim that momentum is conserved, yet most moving u+(5n tzx hvux20znsk+)vw.k objects eventually slow down and stop. Explain .+t5)vuk (uz ns+hwknxv2x z0.

When a person jumps from a tree t0bfp v,+md-mg7. ,uac 8i hc savv61iqo the ground, what happens to the momentum of the person upog +6-bum8 ,m1afc.a,ihs7vi d0vcqpvn striking the ground?

When you release an inflat9l ;b wjcvuniq9m;))ped but untied balloon, why does it fly across the room?b vwnc;m)u9;il9jq) p

It is said that in ancient -2 y *6fb0urog.-utz3hbcy dttimes 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 not push himself to shore. What could he have done to save himself had he not been sood gbt3byf-6 . hcr2utz0y*u- miserly?

How can a rocket change di 9u9mdbx1 i .bkchj)0xrection when it is far out in space and is essentially incb0dx 1im9jkxu )bh9. a vacuum?

According to Eq. 7–5, the longer the impact time o13vooy.sz5:/zb t 3f8fck yaqf an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation ocb vosz5yzyt.1a/3k8 qo:ff 3f the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand col szce; pq;1jp3.gbc ;glisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is bc;j.s ;p 1pgge;z cq3the advantage of this new design?

Why can a batter hit a pitched bas4e 8y7e;mg z o e2f4j;v/g ure9e6fuxl81xzcgeball further than a ball tossed in the air by the ba1j/;cu 8orzf4 g9u8ye6 e4eze; ge7x vf lgm2xtter?

Is it possible for an ob980*nr k1wilb6tc rfrc 0rm1y ject to receive a larger impulse from a small force than from a r 1ml*iw018crrtr y6 9bcfn0klarge force? Explain.

A light object and a heavy object have the same kini/mli eti,1d q dk-1,cetic energy. Which has the greater momei qetk-,ii,dmcl11/dntum? Explain.

Describe a collision in which all kinetic energy is ;0no;ng8x zmb lost.

At a hydroelectric power plant, water is directed at high speekqiy71i0 c1px+hff0 a1 exi-ed against turbine bafc7fxpi i11 yq+0 -xk0eih1elades on an axle that turns an 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 wall at xstc g7;di/u7a 45 $^{\circ} $ angle as shown in Fig. below. 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 hard steel plate (fm;nuc 7weq--mv 6l1/g+izi ti2u wri *ixed 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 paw-mmi+q*6z; r1vuii elcu /n27 -igwt rts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a v w0w5fl / qpp ,2n31jijpvfh:heavy load in your arms?

Why is the CM of a 1-m lz2)t f . 1nys5oxhuco/ength of pipe at its mid-point, whereas this is not true for your arm ou/ft5n1shxzyc2 . o) or leg?

Show on a diagram how your CM shifts when you change from a lying knh;r1s .cib 2position to a sittiis.c k21rb;hn ng position.

If only an external force can change the momentum of the center of mas5)exm2fcb*- yza4 kz d9bx+d9lcj gu- s of an object, how can the internal force ofydcbx e c9bg9) 4fud zl-xmk+-* a2j5z an engine accelerate a car?

A rocket following a parabolic path through t*sq;afhe,zt cp5 mr 2mv(qshv1+; g8d z5 q4dghe air suddenly explodes into many pieces. What can you say about the motion of this sys5*s, qfvh2hqz(q8;g4ev+z p;g d tdamcs5mr1 tem of pieces?

  What is the magnitude of the momentum of a 28-g sparroprx 4 op o9dipldv)g/ 4 elf;k7byg,4*iec)t) w flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier fory l p1q6qa4.;inl xx5p 20 s. What is the skier’s change in vel1q5 ;6a4.nl ippxlyxqocity?    m/s

  A 0.145-kg baseball pitched at vj258 ojorz-w) h z5aq39 m/s is hit on a horizontal line drive straight back towaz8jozq5w ao-h5 v)jr2rd the 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 of sslj:) s xra*b/vaanzx5s- 2, 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 r/*a5x2lbvn s ),asz assxj-: kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling lst- .fwv*x.q gases are expelled at aqt*vsf.l w-x . rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback mov;q43px :csi6(cxzzb sing at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels ch 2m1 fsuc6z1alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speeu16 zs1ccf 2mhd?    m/s

  A 9300-kg boxcar travelif-bu s:s/*t m twjax9sk9t(x4ng at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of m.zrcuu50f, o rw2:bo100km/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 on a person. Assume the person iscrrufom5uzbo:w 2. , 0 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 al ds:si2 /bwwy5k qok-8ong with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 382 -iw oy5sq kk/bdws:.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alphv;0) w c,m rj5ezv;7uly4geadn zj:7h a particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the ymaewz czje5:n,;4;v0udh ) g7v 7jrlalpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block9hjd-qsdk97wc 4u jj2 of wood and emerges cleanly at 170m2qu j j9s9whddj-7k 4c/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rvp:(h:g;8 it y xyx*2g)q nodyocket is traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ 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 3180 kg is traveling in outer space with a x l3aejb 5*-ymg 717z.e gfxrovelocity of 115m/s Toxgo bm* f5ryeja1-gxl7z e.37 alter its course 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 0.045r yrxrps5 m0 :vu;:rq7 kg is hit off the tee at a speed of 45m/s The golf club was in contr:q 75vr0yrrsux: ; mpact with the ball for $3.5\times10^{-3}$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 velocityds:jlo6 qvn1zlhp, iu8c i-v+25xvu) of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse givelvpz56i+uijnu)v8l,c2- x1svd h oq :n 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 ha2iy ir2 ;8)co munwlu9 h 78azqsv77speed v=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 crashworthiness of new automobfaf:7aw,uuu + ile 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 , +uaa:u7fwf ufrom 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 and is stopped in 0.m-kv/t3q e6td 75 s by a head-on tackle by kv3qm 6td-t/e a tackler 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 ten3en9g vaa0)iz eoz q07nis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig.i qa0a)vz eng7z 390oe 7–33 as a function of time. Use graphical 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-kg person jump without brea949rqw;qo/u5js5t yy p o k3dawx6 ae4king the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that /6j;wqqako9e t 5y53 auoy4r w49dspx 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 ;b gv ( zjnt1peq,-u6vva) i9w collides 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 ball after the collision?Let A represent the 0.440-kg balta9(),qzeu pwg b61 jnviv;v -l, 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 c :fks2. kfi +,qofxpf(f2ef6speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, wf:kfpq(6csi+ fo 2f 2.ek,f xfhat will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, 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 undergo a perfectlg3ihfq7 i;4p2xbos uz/z ( k)ly elastic head-on collision. If one ball’s initial speed was 2m/bo32/fzis( z uhi; qk4p7l gx)s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(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 speed of 2.5m/s collides head-on1u n j7 kzv,h*kolg1f5 with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represe*zu17 jl5v,nfho 1g kknt 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 moving with a speed of 8.5m/s cj1zs; ;t)d;m mwh7 wawollides head-on and elastically with anoth1)zjs7 ;m;m;dww whtaer ball initially at rest. Afterward 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 elasticall-gm k/jw)u /qw:- wht pz07rpry as one approaches the 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 i krj ppwt/w-uh/r:0)qzw -mg7s 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 colliird1ewv)pq7) rg f(8qsion with a second ball in7r) dgrvwqe1pif8q)(itially at rest. The second ball moves off with half the original speed 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 down a frictionless incline as shown in Fig. 6;a8 5p)l,iidib/llaiuhz f /7–35, and elastically strikes another cube at thlba5h6p u/alfi8;z i,ldii/ )e bottom that is only one-half its mass. If the incline is 30 cm high and the table 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 op+r(vp9m 6 lt (4jjcynqn-+zybject 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 rvteq / /j*/n vvs9vk)dwcv: ;gesults in a maximum height h of the pendulum equal to 2.6 cm. A second projectiledv s vvct ;kn*:gjw qv/e/v)9/ 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 230m/s buries itself in adu c(37r 90elh-inx ss 1fri,k 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward shlnxe1d(9f- 7r iuc ,3sk ir0in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lwt-, ;ojdltvdud*/-ky ew l:/ost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, inity8u-zf 04x.ni-afz: fmnhl2s ially at rest, into 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 acquire? (Let A represent the he0- af 4uhf: lz8i2y nx-nzms.favier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into aa5mt6oq,jf;z gr4, -pdws 9pthe rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2frq,6-,spa jgz 9t;4wo d5mpa .8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, 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 1.50y- )b heqqb-gvj. 6as cguxy a7m-:9+f m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball ya yx-hc7g.6:vqbb )sgju ma+q f-9-emake before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is th0a:dq: tdnd*y+esp)z e coefficient of restitutio a* :tdnzs:e+d0p)qyd n, 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 pieceali*nr5j-o : ks, one with 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 it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecrla *:oij- kn5racker 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-on wit ou j6vzvhodxxhu 8k::8(.98f ;auxe gh a 10.0-kg object moving in the -x direction at f.;9x:h u a:8j vvue(xxzukdoo68gh84m/s Find the final 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 second nucl /z+n nunmoj45*52h9w:nea bzy kra+keus, an electron, and a neutrino. The electron and neutrino are emitted nhy+r 9z mnz4kwa5bkno:a/5nj 2*+ euat right angles and have momenta 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 masas5hgz1 ;jg. bs $m_\mathrm{A}=0.400$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 i0jzd7 4, d/ejtlh 1hz.ma:bhqnelastic collision between two objects of equal mass, each having initial speed the twoh0jz 4b7h,ad:t/jdqz1me.hl move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles avvve wf7ia a- 0 w3*t7r3 n;iko9a5 lz.zaweo,nd meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right 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 t a397zv eav,oiea-05 a;fkn*rwwil7z3ow v. 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 perfectgetxe zw8u8 / 7r0ehf5ebrd..1b2e my ly elastic collision with another atom at rest. After the impact, the neon atom travels away at a ee2zrwd e088g 15 /e xbb.yuehtf7 rm.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 cy -6l osmxj.8m uj4zk .ff(2gqollision with another atom at rest.jk42-q fx(zg.l fyo um6m.sj8 After the impact, the neon atom travels away 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

  Find the center of mass of the thrc(i vh8ji2,;r ucwi: jee-mass system shown in Fig. 7–38. Specify relative tocj,:(v w i;rciui28 jh the left-hand 1.00-kg mass.    m

  The distance between a carbon qzpa)n, 9v8wsatom ($m_{\mathrm{C}}=12\mathrm{u}$) 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 mtddpss3-k 103mug 4an behind 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 front 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 701atkn3ug 4d 0-dsms p3.0 kg.    m

  A square uniform raft, 18 m by 18 k/t. gth -vvuio j8j7+g*xa+hm, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, ak- g+gh8jvi.t+hvjao7* t/x und SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides 8 33q3 cljcwzl$l_0$,$2l_0$, 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 identical caseuss +( o2 yiuxsm56f(fs 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 that thmy s 5s(6u2x+si (uoffe 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 akvn*67y17p*gb 3 p.jqzqa xl2tu u+vhole of radius R cut out of it. The center ku n g*q2avy3t67x .+1vp zub qlap7*jof the smaller 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 calcux*hpp)2 nvfn/1k9 a hcom.pj4 late the mapcm n.*p/va ph1)9fh4 nx2jk oss of one of your legs.    kg

  Determine the CM of an d*-yr6kmee/doutstretched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculateheks/v 3b 4n5l the position of the CM of an arm bent at a right angle. As4 bs5nk lvh3/esume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such tha7tm9e0 t4jr 7(l8z/y ac ziefdt 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 CM be outsid9(0ae l/cmj iezyrtz7 7ftd84e the body? Use Table 7–1.

The masses of the Earth and Moon arbhv -hz-c0 r.r-o wb4oe $5.98\times10^{24}$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 abdq gx825b()h: oqnogpart on frictionless ice.
(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 of mass 2.00 kg :/cnamejp82riwt5 t,ad 7 ;qaand 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 the han5t,nce;2/t a i jd7 arwq:amp8dle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a rd::l*8p)k7znq x hfb uniform cylindrical head of 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, h dxh)zb * 7p:qf8rknl:ow 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.*-o uupp kq.r/ 7–29), $m_{II}$=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, oo/5wuy*o;2/wf en fglf mass M, 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 with respect to the bal *;f wofeuwlo25/ g/nyloon. 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 atk/w0owdlq/3 at/z xu+ strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contkw w//lt+aod3q0 uxz/act.    $^{\circ} $

  A rocket of mass m traveling with s o(app2yvo5, rpeed $v_0$ 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 show+dqvfp/+4 y n(mqf7b( z3 ooceuey :(m68mpsvn in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give deta +b(q/c4mmop(yuns+zm3 qyd76e v8e(f :vfpoils.

  A 140-kg astronaut (including space suit) acv e8+w6xj/c)i )luktgquires a speed of 2.5m/s by pushing off with his legs from an 1800-k+)k v/tg6jlceuix8 w)g 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 the other w2+ vgms.m i9g80 kg, are initially at rest in outer .vmgsigw29 m+ space. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a heal rnzk9 3xbz52d-on elastic 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 the mass ob3r zx92nkl 5zf the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert wo cu t(3)r*iyuitness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed 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 oy (ui )*utro3cf car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total vert33nw lb7jb(bgical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.7 wlbjn33b b(g0 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-z8dj8rzsc(b 4kg block of wood at rest directly 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 bullet zz8js 8(b4crd becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood placed on ap w)1 i+qone/ p6,:1mz rwgt6fihe)ia horizontal surface just in front of the gun. If the coefficient of kinetic friction betowr)g1a,1hf:i6 t i 6i zwen/eq p+m)pween the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of: uzb mkw*h:hi z+b.,g mass 60 kg, sit in a rowboat of mass 80 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 u b .*g,:b:zhi+ wkmzhboat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass wasbu280 o/qdbdqtrd3 ;h d6v3jk 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 suddenly broken apart into two fragmentsb:k4p o)gir2p s2mf )e by an explosion. One fragment acquires twice the kinetic energy of the other. k2o )m: 2si4rfpbpe)g What is the ratio of their masses?   

  The force on a bullet is given by the formulquui1 v j3k)y exglco4;g qntrx+-/)vr .+6pga 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 masses0/+c w2 rm* ,unewy2ozlr/xiy $m_A$ = 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 radi /9(jusbb we.voactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the /(uws vj9b.be speed of the alpha particle is $ 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 fireddqm 7p0:il6ef/b94 w)eyekvw at an angle 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 slid 0vkhnl.x5kqx* 5xm- ies down a 30.0 $^{\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 upper limit on mass m if it is to reboi 27xosjpw 6o x:p5y:e1ho h:pund from M, sli2h:eox:7y5op xwh:s61p pjiode up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effecpl,)s 2:bx wa lqs/;tx1e9p)lcoed )bt. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect1p pc9t)lbl a l;w) bed:qxo2/,xses) 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