We claim that momentum is ,,pz/ypop+a p nk /a2zconserved, yet most moving objects eventually slow down and stop. Explp/akn, 2yzz /p op,ap+ain.

When a person jumps from a t*. kd-tqhlwcg 66e1hv ree to the ground, what happens to the momentum of the person k.ewh 6 qv*d-g6ctl1h upon striking the ground?

When you release an inflated but untied balloon, why does it fly aqob9x q1zkt *2cross the room?z9qxqtok1* b 2

It is said that in ancient times a rich man with a6ef)hqwbdk 7 07 5vlla 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 toqh570 l)k d7ewvf6lba save himself had he not been so miserly?

How can a rocket change direction when it is far out in spaya7hz h1 2i3bmce and is essentially in m1ih bazh273y a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smallgoqg +;18)ml(zn)t g 2isudf ker the force mto () d q;gn8iksuz12gg +f)lcan 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 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 collisions. Todaqi4 zz ,ic s6cx(jd1r,uov -i-y, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this new -xr,1 qsoz 6ic d,j(iz-vcu 4idesign?

Why can a batter hit a pitcf6,7skt+p0 j4bm g9 wglt-wsj hed baseball further than a ball tossed in the air byw -7 lj0kwf9tgm4,6j pb+sstg the batter?

Is it possible for an object to receive a larger impulse from a small o +..s(eumt bkforce than from a laro+m .betsuk.( ge force? Explain.

A light object and a heavy objecc*,a ;*dxzvre8ltcq(6h ec2q t have the same kinetic energy. Which has the greater momentu r,6clvz hcqqdt *axce;2*e 8(m? Explain.

Describe a collision79qyepf(ym 1g in which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high sp0+p5l4 n7u, ppngvrla eed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water 7 5pu0 np4g+lvlrna,p is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wih7 -- )q/ j;ebn5xb6wq7 2yophshkhwb4k9naall 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 hard steel plate (fix (+(5l u dqrwre/ *xbedkic+0med 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? (xqd /i ue+0* rrwb 5mckl+((edc) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carryrko /r)xdjl 6b(iv y1/ing a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-poftw 9gzv3 vk+;jwii8l h1;v1 cint, whereas this is not truei9 8v;vf wwlgh+kct 1 ij;z3v1 for your arm or leg?

Show on a diagram how your CM shifts when you change from a lying positioumbt pj *o2l.ft;vc ira)7798n,v xbsn to a sitting p tsifbc 77*.;tunxlom 9 rv)b8jav p,2osition.

If only an external 7bta k opohr(fkd+0 ;2force can change the momentum of the center of mass of an objecthk+f0pt r;okb2o7a(d, how can the internal force of an engine accelerate a car?

A rocket following ab (l5 *kme4q6vm h,sxl parabolic path through the air suddenly explodes into many pieces. What can you say ae blkx6,m4*v(q 5hmslbout the motion of this system of pieces?

  What is the magnitude of the momentum o9yk tmj6r x,h9f a 28-g sparrow flying with a speed of 8.4 mj6t9ykm,hx9 r /s    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for6 uft9g)6zt upv1g6qfg qv9x; 20 s. What is the skier’s fqzq1tuv pu );vg9g666tx9f gchange in velocity?    m/s

  A 0.145-kg baseball pitchec vuhj wc .,*3nk.c1god at 39 m/s is hit on a horizontal line drive straight back toward the pitcher at .,1 wvnh*gj koc ucc.352m/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 th1l2x u8e3glsl rows a 6.40-kg package out horizontally with a speed of 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 kg. Ignore g 8lll2u1e3sx water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propellingl tu awx5xp0v-0sa53f gases are expelled at a rate otsuvx35a l x5aw0-fp0f 1500kg/s 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 on an x4(j e)u8ixzh r0tis0apparent 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 speed immediately aft)i 08t(ejrix xz hsu40er the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictio+q zm;s9bnn, jplf 9;ep o94wjnless track with a constant speed of 18m/s A 5350-kg load,initially afz 9sbpeq 9p +j9oj wl;4,;nmnt rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar at rest. The two st-, ymyn9j:u d *ubkense1y2 n5ick together and move eu2yd5b-ens ,:y* n9u 1mynjkoff with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horr y*u0tl 3 sr.)igwi1v*dthh3izontally at speeds of 100km/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 thehtl3t1gw* i*rv)ryh isd.u03 wind on 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 alongijlil,dd4c*a/j; f9k8n lv, t 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 3.5kg/min Ignoring friction with t,4ldd jan jlc ik8l9t*/; f,ivhe 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 alpha partzkrvh 1c)74dntg5r2 ey x6sg7icle in the direction of its velocity, and the remaining nucleus sloh65 g7xs1rtk27gv z )cr4dneyws to 350m/s If the alpha 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.p 3u ifm wwbl2/)*jv2a8h7/wkkyi 9rm0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when h wv 2wu3j //2mlw y8k bir)i9a7hmfpk*it, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a spevvot/. zfuc*3 ed 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 , c p2w/mfiscj(tni(6with a velocity of 115m/s To alter its cours /sp,(f2c(ji6twcn ime 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 tees 2bx+w0zyf kq0sj-qx89wvs5 6 vq fc) at a speed of 45m/s The golf club was in contact with the ball f-6 q5qf2ykc fj vsxw0x98sszq +)wv0b or $3.5\times10^{-3}$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 velocity ofkp q.qz:fx.m4 4ep-li 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is 4-x.:. qzkl4qeipmfpthe impulse 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 v=25m/s strikes a wall at a 4.v;3f: bhw:tt g x2drf5 $^{\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 +ojswv6e) ao5( q-5v 7m woteda-vwq/ of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 5wjavv7e ow5+/aw - 5oo ds6m( qq-te)v0km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from 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 a - z6j1ir.zzcko+jp 86w8rfelnd is stopped in 0.75 s by a head-on tackle by a tackl1oj 8 z.c6-kp+iezwfjl86r zrer 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 tennis bas81 thko:u4 35ziacgxll (mass 0.060 kg) points in the +x direction and is gs3 h ckax48:15gtz oiuiven by the graph of Fig. 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 3z.k d -yv,nkgq(c gc-75-kg person jump without breaking 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 is, in breakv k(g- n-qdycc3kg,.zing 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 directio.ub) nslwlc , 56b4 jnqg9q2nkn) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the spslknq5),c lwn 4b.ugq 2b9n6 jeed and direction of each ball 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 3m/s has1dkkrv:*ye m0z;13p gsj 5pom a head-on collision with a 0.900-kg puck initially at rest.ms rd;ej1mpgz :5*1pkk 03yvo 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 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 u m7yph: zev+n3ndergo a perfectly elastic head-on collision. If one ball’sh y 7zp+n:ve3m initial speed was 2m/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 speecz1:-+ymyhk 7tr ( obgd 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 collist k y-(yr+z1g: ch7bomion, 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 moving with a speed of 8.5m/s c+87 y:f/ugcgeeb, w,ya+ j qivollides head-on and elastically with another ball initially at rest.+buc 7,8+ggywya ve: eqj/ fi, 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 elasticawzh3b ,e7r317 lk1vve h3pslwlly 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 an3hsrwe3l bpv,he k3l17z 7wv1d 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-09cf yxz5 zul4:cn)oqogwe0)sdql8 -on collision with a second ball initially at rest. The second ball moves off with half the original speed ofs4 5nuec) qodz9 )- lcywl0xg:0f8ozq 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 aizv)n def).k7:iouj 1dr: o7 c frictionless incline as shown in Fig. 7–3oz1ri: 7n fie7dko) u)j.d:cv 5, and elastically strikes another cube at the 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 38we y t3j2kkgan object 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 experiyub,2 jtj5g h9hr*vx+ment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second prjhh2v bur*t59jyg,x+ojectile 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 trostf6h82 gt*zx 9m uu,aveling 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, whs,*f2 8uhzxt6u ot9gmich makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula4znls2ec d2g a1*c)t x c+(kjo for the fraction 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, into tw,vc4jk .umb; u45dqj do pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetij4u;jbkmud .c,qv d 45c energy did each piece acquire? (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 rear end of a 230r -ecnfe*8ab.0-kg SUV stopped at a red light. The bumpers lock, the brakes are lockede*. nec8f-a br, 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, 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 z*e klay83uhjsg1/sme- /:j kof 1.50 m and rebounds to a height of 1.20 m. Approximately how z/ks3 * 1gs:lej/muk ayh8ej-many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision 4vf4w2 m5tgvgof two objects is the coefficient of restitugvfmg4w425t vtion, 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 ttjo;:rdt y x,zzm1(g y 70j(tdwo pieces, 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-surfactxy1zzrj0, gd7(d:tm ojty(;ed 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-orn7 ,e3 anh+f5gpx+i jn with a 10.0-kg object movix+a, n7nge3 +i jhrp5fng in the -x direction at 4m/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 nucleus, an ele k1w9l3ap9eue;y qg(9wqu7c 5od htu ,ctron, and a neutrino. The electron and neutrino are emitted at right angles and have mwdu1 3e qhg,9kac(tq 95 u 9ue7wlyo;pomenta 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 maied; y3jzno to(9l n1-ss $m_\mathrm{A}=0.400$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 betweeu/k1i1l 9jd+y htw+,7w lj mikn two objects of equal mass, each having initial speed the two move il,ywim1w1h tjlj79/ ku++ kdoff together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of eq389ds1dsr,)ed mi pnw ual mass move at right angles and 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 e 3srwdidm9p8n,) 1sd 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 po ( ap+k)txdp1 v6qksth-y:i(erfectly elastic collision with another atom at rest. After the impact, the neon atom travels away(dptskyt6ah) - + xop(v1k:qi 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 with another atomyr hc0p1bw, b)cdz z/ed+g0 pv/zl;j/ at rest. After the impact, the neon atom travels away y/0/0p1bz; z+gzwc del,/ rb pd)jvchat 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 three-mass system sho ns isrdh(.2f,wn in Fig. 7–38. Specify relative to the left-hand 1.00-kg mas2n(r .h,fis dss.    m

  The distance between a carbon atom (-64n lbqmq4k;p6cg cz $m_{\mathrm{C}}=12\mathrm{u}$) 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 behind the frua;wh x q(qi)l4x6rz61mdw6p ont 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 hdxqaux;r 661wl6 zq(mi4 wp )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 mass 6800 kg, is u-lotu f*f4vevd4u0- 2cjq+xused as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determin u*-+qd-u f2xjocuvet lv44 0fe the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side*+e8tapu vi xv2k) ek,qmel2- s $l_0$,$2l_0$, 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 cases of totqa*b (g2vq pz0+7o/ ,2mztxs3t0dcbl c0 cflmato 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 th(ba+ tc/q2cbscf0 l3p7*zv tdz02 q ,og0tmx le 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 hole of rabcctf/ y7tzbh;dux h1/;5h . ,nrzm;idius R cut out of it. The center of 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.]uxb 7hdim/ ,c/; f c5.br;tnt hz;zh1y   R

  Assume that your proportions are the same as those in Table 7–1, and calculate 3h r od26dhq/g.4esq hthe mass of one of rh o d/q3gs.2hdeh64qyour legs.    kg

  Determine the CM of an outstretc0avwrdgi( ;v+hed arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to cal)sj76wiji2vi2c 0l.zri l dk( culate the position of the CM of an arm bent at a right angle. Assume that the person is 155 cm t2w.z s ir7id6cjkvjl)l2 ( 0iiall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a positiju/b.s2/ d x8lwzl 6dai*r d+won 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 CM be outi//* .+86 bzljdd wduxsr a2lwside the body? Use Table 7–1.

The masses of the Earth and Moon are 99xl:7b)3vgs+yb iqr bx. hrl)o 1fxu$5.98\times10^{24}$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 mm24.kmc 6wadcan stand 10.0 m apart 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 u5-t b0oq 1d xi,jhrt2aniform 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 lengtrxi 5tbah0,jd 1q2to-h 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?    cm

  A mallet consists of a uniform cylindrical heaio4c4dbz9y tou i0 ;l9jnxb3 1d 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, how far above 3bxzcjtbon;1yl0o9iu4 4 d9i the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–1cf,2n,4t g ri m-5ceaj4 (Fig. 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 andmwm ,7;0fg-txl uda 5z its gondola, of 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 uf7ltam5 zdx-w g;0 m,measured with 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 bat and is popped stradrucno3aa6.dt-so g(rl/ z2 ,ight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the averca/drr t6( 3 sz-ga2ud .oonl,age force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speed g-zo zf/:cl0p: k6jr p$v_0$ 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 shotpzav; s)+p;y y*+x85wpp(ngm qi9fup shown 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? Gin9+u wf va5y; pzpi*+;)xypp(ps8gqmve details.

  A 140-kg astronaut (in+4g(+nl8 ycdj7syuw ecluding space suit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-kyl7s(u gn +dy cw4e+j8g 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 80 kg, akbpv) ddqb;spwhd) r2a8).1pre initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut has pa)1 bp d)ddphbsvq.;w 8) r2kmoved 12 m?    m

  A ball of mass m makes a head-on elastic cu5 wexywd*q4uvq :(5l1 edq :aollision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its origina( 5due:qxuqq15d4w *wveya l: l speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert:-a)yq+u0tnkbvf; d, jv ,pvz witness 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 t-,)nv djuv , yqfbk at+zv;p:0he 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 off the top of a flight of concrete stepsz-zemhytvpb qsj 1**-1 tf3 5- crlhn- of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all coltv z1 t3qb-h5z-*1ysemp j--cr *fhlnlisions 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 blod: 02pil xrj-fck of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how xrpld -20if: jhigh will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and beco6m2s:ck7yzdfcnx(n 2eo 7nt ps9-n3j mes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetke3ns6o: ncxs72nt ndfz2ymp( cj 79 -ic friction between 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 hhx)4r4h 3 drad:oa:5h wo xg:and the other of mass 60 kg, sit in a rowboat of mass 80 kg. Withhaxoh4xa4d ::gd rw :h5h)ro 3 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 was abou. r 7ezt5dko)zt $ 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 qi6w 98sr ;f)v xi)ifutwo fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the rif 8qs)vfu r;wi9 x)i6atio of their masses?   

  The force on a bullet is gyo:8 weq, qs6 3iexr2yiven by the 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 massessnvr /:feabu9,0*6sa jbu : lt $m_A$ = 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 radrx+m/v .3fp3o5ahn b jioactively into an alpha particle and a smaller nucleus. What will be the speed ofv +x5fbr/oa pn hmj.33 this recoiling nucleus if the 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 fired at aq4f, n3f4k,y*rkvg1( z pkbi fn 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 slides downa;z,k peq23z gh;a8r6o+ sd) h hg0hkp 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), whaxzbi.n; 4yw1 at is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the i1 ;y4i.axw nzbncline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Sfyhz8q o ej f1*:3*w pkw :k,d/3 wusp1jjlyf;aturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Satu:jw1ujys ko8dy,/lwf;e f3z: q3 **pkwhjpf 1rn 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