We claim that momentum isy;3 huypnqu6 : kwzlzjh:7 hm31yv-n) conserved, yet most moving objects eventually slow down and stop. En6-hhyv:1 ) k37 u3 qhzzmw:y ;jpyulnxplain.

When a person jumps from a tree to the grou lqxfh1j2rl-(o ax9r2 nd, what happens to the momentum of the pershx2r9 -qlaro jx1(lf 2on upon striking the ground?

When you release an inflated but untied balloon, why d fbbh,w9+d* owoes it fly across the room? 9*bwo,dhfbw+

It is said that in ancient times a rich man with a bag of gold coins froze tof7dgln )r4stc*o.dz ( 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 so *) o.(dt4d7 nfzcrglsmiserly?

How can a rocket change direction when it is far out in space and is hmq 23(bt5 1xfos mxc(uh/,lx essentially u/x(bxclsh ,2f3 1xh(q5mo mtin a vacuum?

According to Eq. 7–5, the longer the i; 0mpq as34/th rf4cagsrjs 5)ui( q:vmpact time of an impulse, the smaller the force can be for the same momentum change, andmq5vschs3 t)jr4(g04iraq: fa ; s/up 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 ri i4 drn1 un9s27jkp :ar,li3gpgid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse u23 ik4g s9:nr1n,7irdlpap ujpon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed (v,a91qwaprj7j-gwo in the air by thejw r(1waq,a9p-7 gvoj batter?

Is it possible for an object to receive a larger impulse from a smalli )1 zy wnj/)b1ieh16roiu9md force than fy) w/o9n6zeim ii r)111u hdbjrom a large force? Explain.

A light object and a heavy object have the same kinetiew t45eq0-xsf3bpl7*c,of6bl hk(av c energy. Which has the greater momentum? Explain.pobls w fef046xla(khc35qvb t7e, *-

Describe a collision in which alcqmdko9jrj+l)j(q0m az46m/2f bi6z f9 0cval kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against tu1xxm d3j 0bz//kyoy605kn3autgcw b. 3)ose y rbine blades 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,yyn/xkg5ty3jx b b. oe u/k0o6)13mcs0d waz 3 or so that the water rebounds?

A squash ball hits a wall at an pntg, :9oh*3kry9th 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 (fixed to the io .n.rn 7*7hwyk*d hekynv81 Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of thirikny*h k 71vy78.d*nhen ow. s 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 to the steel plate.

Why do you tend to lean backward when carrying a heavy load in your arms2vp/a ps ry, puel)a9-z8lnf(?

Why is the CM of a 1-m length of pipe at its mid-point,m; v73 ss 3kjwi :d4(tkc(vtij whereas this is not true forw k;3(tk47sjt(3:mijsi vvcd your arm or leg?

Show on a diagram how your CM shifts when you change from a lying position to /odnr+ u4nr1g-g*qc k 8upsg7a sitting pongng pq ru41+ o-/g7dr8s cu*ksition.

If only an external force can change the momentum of the center of mass o; qaqiiz/4 f8uf an object, how can the internal force of an engine acc84iu/aqqz ;if elerate a car?

A rocket following a parabolic path through thet0x6- axffr0m air suddenly explodes into many pieces. What can you say about6-m 0ta0r fxxf the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed ofr jdq4vb1re,qb46 u+5+mzya k $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s.r 1zizsz-zz ma7 -r2( en/3x7thlgd 7g What is the skiernzz21-gtdagh 7x37 /zrsm7(riz -ezl ’s change in velocity?    m/s

  A 0.145-kg baseball pit .oj- qsev9)mvched at 39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52mmj.o-v9s )v qe/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 throwsnovcs; q37t q7 a 6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the t;qn7qsc73 v ovelocity 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 water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases s icdsqp*hp6mk4-u rk5 q8 z*1are expelled at a rate ipd 5*ucsk8*41 z6prk-sqhqm 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 moving athp 9*0 9.ogbqn i96jmxgel1 av $4.1 \; m/s$ 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 alone on alevel frictionless track w 3pm9qdwy 26*yijw)kzi4+ uqo ith a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’sd3i q wyo)p6kyj+ q29* wim4zu new speed?    m/s

  A 9300-kg boxcar travelim, zlsb -a5 :*mam(pifng 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 100kmdcwi8 38u.jqpsj:o;d /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 is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of frict8w: 3d;sojjpud i. 8cqion $\mu\approx1.0$ 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 with a constant speed of 8.6m/s on l;p9kryhc8d jd1ddmo;b , 6 h:i4k6ixa level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed odk6ob h;6 d8jlmxi4hk9i; dpd: c1 ,ryf the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in tpoo+r y6gv*ttp2u0; 9zl fc (she 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, what speed does the alpha particle have when it is uzrpct6o 9+*t g(p v02lyfo;semitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and emerges 5 4)0 oag(xuum8gixrx:vmo;ecleanly at 170m/s If the blo04ea v o(; 8i5rom)xmg:gxuxu ck is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is travelinggi8:ikiv+ vyxk nz ;8gd;gn/- 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 outerbc +t qy/pms(;r : zf*2xjf.yn space with a velocity of 115m/s To alter its cours (r. bmqpy;z*f :yc+sjxn2tf/e 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 spee:v5 r/fmvo7 hd vti:s3d of 45m/s The golf club was in contat o3 vmsr75di :h:f/vvct 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 na-s1nw e (9 zawtz:kcm,il at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse giv- 1s c(:zem,w knz9tawen to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass vo8;hpeb*.0ci 8 so*vmk i-t wm=0.06kg and speed 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 nav+:gush a* v1d)6z8re cfxgi3y36o xew 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 from the time of impact until it is brought to rest. (a) Calculate the average force exh:y+xgv38) 6g * as31c e6ridfv uozaxerted 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 0.75 s by avah7z0zm yhr q w(n,o+:f g-e3 head-on tackle y7e m+h3h z-ofrgwn0zqa ,v:( by 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 tennis balkdrs pp4abpaq8r(;9;l (mass 0.060 kg) points in the +x direction and is4qpd pp 8;s9;aa(brkr given 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 75-kg person jump without breaking the lower le ;ct9vw,)/mc( lupdq cqk59z rg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from th,zcrw ;5(p)/q lucvdt9k qc9m e 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 e j/.2laq;kqjh zz /g/kg moving east (+x direction) 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 speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent thej2qhjz l;a //. qge/zk 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 speedkjv iid,6xc+:1tyi k 7 of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be th+ kkv,iix:j67 dicy t1e 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 au8k9yaiu/ l+fdvo u4fx47 0d l 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 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 d u4f4d8kdu9viya/ o x+fll7u0irection. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving wit/43k ,ks66 (as8 dijfeaqdfp ch a speed 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, what are the speed and direction of each ball c f3a8k/de6qj6i(pak df4 , ssafter 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 speft dgax9 2rt/c6,l62hy vjz0xed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward jf x2x6cht/gryald 9,v 06t z2with 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 collimv/ y2 8dp7u6wsl t-rd:8mch nov5r2cde elastically 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 t5:7n-mhcosm l6r 8 yuc/vdd8pvwr22.5m/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 elastir, dapm8nid. vv: l*c ;u,tf. quom7;bc head-on collision with a second ball initially at rest. The sec;,vli,*;f7 abutpod .v cr.d8mnq u:m ond 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 sh ak55wqq 6l7 u.ybqh(i5l umv*yz*.pkown in Fig. 7–35, and elastically strikes anot(q5 v*aq w5*ipq5l byk.k76m.u yhzulher 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 an o-k sm) 5reln8bbject 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 maxiyjs0y ao-; i un,r1xm,mum height h of the pendulum equal to 2.6 cm. A second projectilei o-,amr,xyy0 u1n ;sj 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;ujx z mwa 7ympl( ao.,i/ goz)v 8wlo538c4wp buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, zygcpx 4o5j 8mzl,./7via)8w o l(3w mo;aupwwhich 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 formula for the fraction of kinetiszs;6i+ 4 z6ek d f:tnip2q9wrc 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, iw-j )py0gkxs(:(y chj nto 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 ene -(y)gsphjk: (ywj 0cxrgy 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 2ey f1q b1o--di300-kg SUV stopped at a red light. The bumpe ob-dyei1-f q1rs 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, 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 rebounds to a heig2-uy y6 j pwknhku2*o)u0d.gfht of 1.20 m. Approximately2 kuok20nf )-d uj g*yy6ph.wu how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on cz rp5gk23xuf4 zs6 y,nollision of two objects is the coefficient o,2r3 ugksxz5 p6f4nyzf restitution, 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 with three times the ma4tpd)qkhyh)2z(b /cru/(d3wxjm 6o n ss 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 reassem ph(b hq / u/x)ddm3t2coyrk)z(6nwj 4bled. 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-on wi j-dpk 4barl)ll5a*/1 et saj7th a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of eak)7l b / rsj4j51aapl alt*e-dch 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 electr*5/wvph 9rp8nu7l4f zfvpt ;mon, and a neutrino. The electron and neutrino are emitted at right angles and have momenta vfmphpr pv4fl9;8u*zt/ 7nw 5 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 masy6y8agume z* o4krq(; s $m_\mathrm{A}=0.400$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 collm4 speb.sxx ),ision between two objects of equal mass, each having initial speed the two move off together w sx4s.,x ebm)pith speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass mo :ls vs32hu;dnve 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 th:d2 ;ssvhnl3u e 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) me9..+7qz2t2jlq t gvin mknx ,k4d6vmakes a perfectly elastic collision with another atom at rest. After the impact,7v2nmgj6xi4+ zqk.9ketmtl2n,. vqd 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

  A neon atom (m=20u) makes a perfectly elastic collision y s8* nsn*d.h55p-lpdh mr .),v lihmiwith another atom at rest. After the impact, the neon atom travels lh n.*dm ypdvs8 mil*5,h) s.hrp-5inaway 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 three-mass x/zrcl d5i+7 5cz3xlk system shown in Fig. 7–38. Specify relative to the left-hand /z 5 ldlzc3kxr5+7ixc 1.00-kg mass.    m

  The distance between a carbon 6bzxq m70t t9zatom ($m_{\mathrm{C}}=12\mathrm{u}$) 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 cjlne-8 b) l;vnar is 2.50 m behind the front of the car. How far from the front of the car will the CM be when two people sit bn8ve l)n;-jl 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 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mase iy(k,php q;9 1a/rlzs 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the ryapz,/pk e1i;hl q9( loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side9erg3eq jbe24su 9a*z 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 ident:f3gtos6(xl iv*) i jt tk(8ybical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizofl:t3osj ivgt(ti) bk6yx 8(*ntal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate ofhsh7:,bl) n)2hx2s qaa.hdkr radius 2R has a circular hole of radius R cut out of it. The center of thx lr)hahb :.nqh2, shd2sa)7ke 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 calculate *c wkwstq ze0 ph.)2;vth0svtzw qhpck;e2.)w *e mass of one of your legs.    kg

  Determine the CM of an outstretched arm using Table 7–1.fkv6:ee-m+ i;nw/zuhw n:) ho   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position oy fz8 akdpw4e)nl,1y ,f the CM of an arm bent at a right angle. Assume that the perso py)f8ly , a1wkd4,nzen is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that ((1g2k2u3pd mpakkjt;9nmt rhis 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 outsjnk2rmd2um9 p13 pg; ta(tk(k ide the body? Use Table 7–1.

The masses of the Earth and Moon aret;uex*kf ( r)szay l6ov gw,)3 $5.98\times10^{24}$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 standn w;ezsvn (:j4 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 uniform cylinw 0:g kixfcdv586l *j8fty ji9drical 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 x5:*k6ji08ffyt 9jcdi8 vgwl 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 cylindricc:b g.j y/okr *emc;, .-bobmaal 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,bo :* m- /egybckrbj;,.o.cam 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 (Fiipl;4p3yun) jg. 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, of mass M, are in the air an -5lyk gb:6qlbnk58 ydo5;qijd 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 balloon. With what speed and direction (relative to Earth) does the nod -65kyqibljl:5 q5kg8; y bballoon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched hemh(()q9zob .tu2eea7d6 k f norizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, ca )d97mqn h ((b6fek 2o.atuzeelculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with sp3tnmxpv.vy3e43 d /fe(4,scicp/ s lqeed $v_0$ 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 wp q2; lwd2uazs)wgz2+p4 i 9nyith the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cueqwzg u2)aw yp;2 lsdp nz4+i92 ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of t e:aje +hqu4n mv(3:4/z6fq3daenvfq8onz3 2.5m/s by pushing off with his legs from an 1800-kg space capsule. :uqj3hz e6vmn e8f oq( n+va:q 4zt34/ad e3fn
(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 ka/zacxlc7 )r ,v hr-6yg and the other 80 kg, are initially at rest in outer space. Thev)hcy alc ,r 7xz6-r/ay 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 head-on elp 4t)kyclxli9 9bb+l2astic collision with a second ball (at rest) and rebounds in the opposite direction with ablxpl+4) kli2c y99bt speed equal to one-fourth its original 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 wqnboo+i/audyi sfb)jzt7 b 71.8)c6 bitness 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 of car A was exceedi+zjb f oauid q)76bbi.7tsb1 8cy)/nong 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 vn0dl:; s+-jqjxq3 x fcertical 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 collisions are perfectly elastic, what is the bounce hdnx+ lsj0c3qj-x;fq:eight on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40uazj q. e:h)f6 9+lvtn-kg 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 buu z6a f)q+t9njevl:h. llet becomes embedded in it?    m

  A 25-g bullet strikes and bnb66;ee(v*wy ieoph 0n4t2ib ecomes embedded in a 1.35-kg block of wood placed 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 drivbb *oeevi(thn wn46eiy 0;6 2pes 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 t)/v+(x a0 j9mjexel yvhe other of 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 boyjav/eelv xmxj9 (0 +)at 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 ayhw 3 w46ra)qk-r7t nxbout $ 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 g)ym44e ztmq3j0at+ xbroken apart into two fragments by an explosion. One fragmen4x0t)gma ty3jz qe+m4t acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formur61x )/aqlgh ty)ela7la 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 massesn+n b; m7u.bqy $m_A$ = 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 radioactivelytun)4 e8zqehk+ lnx6; into an alpha particle and a smaller nucleus. What will be the speed of this reenz;8 6e hukn)+4tlqxcoiling 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 u9p3) p4kxhlw7wf/ ,qrx+o dctarget) is fired 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 sli gu l,5tzxo):vdes 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 up:n.h(ken43yddu x5 f-w3c:c g; cywvvper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down t uwkd5:w -(yvxv;:c ge3ynd fhc4 n.c3he incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Fc1y.iex 1h *y:zw*irhs4xx 7 tigure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The7 six:*41xcxyr h*iht. y 1wez 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