We claim that momentum is conserved, yet most moving ob) eqh8ey 1 mzx6k.vwy.3+wgfejects eventually slow down and stop. Explai f.6vgeme+k )wq.z1w8yxh e3yn.

When a person jumps from a tree tz8 xtzx ++qjd9o the ground, what happens to the momentum of the person upon striking thez+d z8q9xj tx+ ground?

When you release an pnmpnv*.-)dy 6 wtm8hinflated but untied balloon, why does it fly across the room-vypt. w8 )*n6npmhmd ?

It is said that in ancient times a rich man with a bag of gold coins froze to 197 vmmunxwk 8 mzw60kdeath while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he8607wmzkkmxn 9mw 1 vu have done to save himself had he not been so miserly?

How can a rocket change direction when it is far-d0rhu.zdazh)m x9oo d3+:h q.rvr:n out in space and is essentially in )rhoxmonu:-d.3dd 9z: 0.qrh zh+ v ara vacuum?

According to Eq. 7–575ma0dcd l :kz, the longer the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation :l0 dmzc5dk7a 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 rig.d3r3w2:n71*dfphbp au l nsquo tm99id as possible to withstand collisions. Today, though, cars are designed b d3fu 9 up.: 7nnqwap2hd9 31rm*toslto have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit ax(+-n/ r (bydfe5ddq g pitched baseball further than a ball tossed in the air by thd( -d5 rbnfx(/ydge q+e batter?

Is it possible for an objex+g , vkan );omp00xmqct to receive a larger impulse from a small force than from a lar mnpgokm 0)0xa qvx;+,ge force? Explain.

A light object and a heavy object have the same kinetic energy. Whic *//m3uzirxk eskc6tl228sfn h has the gre e8li n2 c3//x6fstmszrku2* kater momentum? Explain.

Describe a collision in which all kinetic energy 7e8hpx,9 9b2 jsb6qtoxkq (sp is lost.

At a hydroelectric powtwg,mewf.f4vheq ,9 t5f 7w3der plant, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should td9hee vw,,w.g5fttmf f3 4 wq7he 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 a)gy7zbv:i en(bz0y:l 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 .)yjo 9.2* x3uwt zkq-mvu ugmEarth), from which it rebounds at very nearly its original speed. (a) Is the momentum ofz*m.twmx quu92 o-g3u.j v)ky the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy lja)/ vz j*3qvr0pd uhx )7t+xtoad in your arms?

Why is the CM of a 1-m lengthgfyp;g5+ s rv3 of pipe at its mid-point, whereas this is not true fo5rs; g vpy3fg+r your arm or leg?

Show on a diagram how your CM shifts whenm0e 92stnmk)j you change from a lying position to a sittt9 nj)mek m2s0ing position.

If only an external force can change the momentum of the center wd dwgv,j//p8pu/r ;dof mass of an objectprwgdw/pu ,/vd8j; d/ , how can the internal force of an engine accelerate a car?

A rocket following a parabolic)hm ojx)k)u-3eaab sum7l), pdw-l( t path through the air suddenly explodes into many pieces. What can you say about the motion of this system of p3) -oa lt)p,heuju 7a())m skwdlm-b xieces?

  What is the magnitude of the momentum of a 28-g cd g7oyt)6e1f sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65- cjoz*2q8gl50l/m tlal s72 ikkg skier for 20 s. What is the skier’s 7k5g2 8/qjctl2lzm0s l lai*o change in velocity?    m/s

  A 0.145-kg baseball pit lcz3t47 3ue/csfzs7kijyq .-ched at 39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time between bat and ba. t7 4eu zsk7fy33/zi-csq cjlll 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 ffl4f h:l;e-wse; r4x 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 water resistance. 4;f;r4lff -h: lxseewThe magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gasejpk 6f:w(*qqi+ jd; y 3omqv,bs are expelled at a rat6w:*3bq;y+ o( qkq mj, jfivdpe 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 movlqk1 l;7ei k/eing 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 alone on alevel frictionless track with a :y /hvfh8- oq7zb9mue constant speed of 18m/s A 5350-kg load,initially at /-hzm:v h9b7qu8fyo e rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at/7t1 a(;vz c h ybf+.ze.gzg;bye bfm- $15 \; m/s$ 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 wh4xsxasyql8(e pmt15t, 2s 6x kla)2p cc c:qi+ip horizontally at speeds of 100km/h If the air str(l sp +lptqm 8s2cx 6s)ic 41cx2,:ea5qxytka ikes 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 friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of ,erylr bom5 x :*.ela78.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 9 :.erxoylemba, 5l*7 r0.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in th -h:;n grezvd6e direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha p-gv zendhr6 ;:article 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 block of wood and emersi j;ldxpgf yvn2ow 0 z.n:;93ges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emz:.yi;s fvndp39 x;0jl2onw gerges?    m/s

  A 975-kg two-stage rocket is traveling at a speedox)a2ix ab1wyv. g . ,*c6acty 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 sg(m7o4fuke* v y m)k)zpace with a velocity of 115m/s To alter its cours7*m) mukzv f k4(oyeg)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 mihcis6*) r+o h/eh)ris hit off the tee at a speed of 45m/s The golf club was in co h cmh*is+/h)rri)e6ontact 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 g4wah* yct48ho; (i8pi8jgy svelocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the hia488ytgjwc o(p hi;*g4ys8 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 uya(/)gfz4r n3c .qr-c .o(+to gutdv5 $^{\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 * xcfz-mi4q1d the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by xm- diq4cf1z*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 st.wn;+hqg63lb tgswrie jbi (9b *2r1fopped in 0.75 s by a head-on tackle by a se 3;2g 6j 1.fi+bril(h tb rwg*bn9qwtackler 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 ball (massl 0tpsl0xx;o0x4q +3i eg i8ml 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a fuxilx4m0 si0l0got3 8xq+ p el;nction 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 breakinbt 8:bpk*+ rqnx ja,.vg 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 breaking the fall). Assume the breaking stv+n bb:.8x kr*t,qpj arength (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 2ndli 042wiupof 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, ui0wndi2p2 4l 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 has a head-on collision wnm eym1 4zg:)gith a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent ynm4m g:)1egzthe 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 perfectly elastic head-o-65dcr1rjlffwx3 z:zd8lwu ,n collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the z:w ff18w 6 j uc-lx5rd,rz3dlopposite 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 an w bi:w*7y/xd7l) idspeed 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 after the collision?(Let A represent:lnd di/ yw 7w)x*ab7i 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 thp ;zw(lltehc(o 2.p6 hat is moving with a speed of 8.5m/s collides head-on and elastically with anot26c l ho(lhtp.w pz(e;her 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 rez azve(m,y2 w4 ,srv8ide collide 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 toa(wzy 2 m,4svv,r 8eze differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision wit:beq:/gev 2fz3t p 2je0dcz;ch a second ball initially at rest. The secondz ;c2:23gcpd bez/ te0fe qv:j 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 inj/j()/rsrqn ;loaq5(c ,pq 0q(sspi0.flqc e cline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the(c /p ij/jq 00p(n rs ,aor5f);cqsllqeqs(q. incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of;fu)8ft :ey dsa:t qi7 an 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 experiment, projectile 1 m4z/x:) ucr1 jg ..zdfybtk;tresults in a maximum height h of the pendulum equal to 2.6 cm. A secondufr4jx yt. 1tzc.k;bd)m:/ zg projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kgs/ 9r rt/ifuc.am2g,m pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the penmc,rm2/gf a/ 9uri.st dulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic enqpjhg7v9(,0a;xydnm n)lns* ergy 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 breaksk)sup 1, pjlwpyfe(0 , an object, initially 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, (ylp0sj),p wup 1kfe much kinetic 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 2300-k;n-+*jwlkdpm slh2/ r g SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The policm-l/ ;p+hwk*sr l nj2de 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 to9d4 xj9gtijq/l -q vc .g)cxe; a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of it txc4vjjgdx9 . q/q-9eg;c)ils energy?   

A measure of inelasticity in a 1up zb0m 9xt99 6utcpj 3tkec g)d.)zrhead-on collision of two objects is the coefficient of restitutioc1k )t3p9 b9) ez utjcz.uxpdt9mrg60n, 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 tty a1g5d .f8nqhree 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 firecracker expl1f5agy 8qd t.nodes, 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 directi v(piiw( 1a dec(ei4 tw1,or,xon at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity oa(xei,1i(w cvt1(p 4odrw ,ief 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 electron, anjps+6(grkxjq e1mj b.j:wyo 56 4/ u16pebdpl d a neutrino. The electron and neutrino are emitted .s/kumd5bg+ :l1o wp6j41 eb j6jp6yep(xj rqat 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 massal iecu px*)+htt0 32u $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equal mass, each hptf87l7uvdl c)lh-: aaving initial speed the two c-778a dlht : )fpvlulmove off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal v rm+q6m*hhm4x c-(jlmass move at right angles and meet at the origin of an xy coordinate system. Ball A is qr m6xlh-h( c4 +m*mvjmoving 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 and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with another atomo0oiup0 3z::;wvwjmi at rest. After the impact, the ooi0 0vwz;:3p:jiwu mneon 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 perfectly2 w0v- wc2.ti518lt hnlxbct-)drcu x elastic collision with another atom at rest. After the i-8xhlc d2l5w.1b 2t)x crtn-wiuvt0 cmpact, 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 three-mass*b, 5l+tdmh bw system shown in Fig. 7–38. Specify relative to the l*,+5 lwbdbt mheft-hand 1.00-kg mass.    m

  The distance between a carbon atom (611jo(krt q;vh :,nz(pxxucsu; hu xp9)n(q d$m_{\mathrm{C}}=12\mathrm{u}$) 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 cx-vwg(nfvl o8 .-e;fpar 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 si 8w.v vf;gn-ople- (xft 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 mass 6800 kg, is used as ah lh-nnqr(iwg 4i 9b-0 ferryboat. If three cars, each of mass 1200 hrbg-iw4-ln(h0n9 q ikg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side 0uv91xktdk2hw (a pp: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) palleq/ vwd)caeeajr3;ip )e pw6c (,,oe1 zt has a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.6/, dqa1c; vc)eriwae,w3jpezeo )(p $X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of rg5gjoje6b k34 adius R cut out of it. The center of the smaller circle is a56og3eb 4 jjkg 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 ashr fm*c9(h i; kaluunc-6v u.-gw86 fk those in Table 7–1, and calculate the mass of one of your legkmfv6;.c(kai-6 8*lfurw 9gnuc -h hus.    kg

  Determine the CM of an outstretched arm using Table 7–mc.sz g( 5.iloa2au)b -bz+ v i:fo7cq1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent at a rigb+d pw7ntpey +p2t(e7 ht angle. Assume t7tw+yd7+2bp ntppe(e hat the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hango8zh )jg +ci1eing vertically, and his trunk and head are horizontal, calculate how far below the torso’s median j+ o81hgcei )zline the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth ajvr e)6agcxx71wew fn ;pf0fx64dn/8 nd Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man cwt -lcwdzm7 931b0m65zucy e 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 uniform cylindrical head of mass 2.00 kg and a diameter 0/ippihsmociqk 7nzi;76. m / *v7(gy t.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 77 z /yio gihnqitcsv ;./ip mk7*(6pmair, 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 head of massjm l nz6lwbql(u73j6g ge5qj i76u: v) 2.00 kg and a diameter 0.0800 m mounted onqj6l u g7m vj( 7qbll6wj5e:)6g un3zi 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 handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Ffz0evc2 fwts 3;( tw9iig. 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 and stationary witzg*t)e-uva3 hpz1 k)rx1 gzj0w ea;b7h 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) do7uztgvea31z 0b*a;) re1p)wxgz-k jhes the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizo +au;beba0+i entally at strikes a bat and is popped straight up to a heigue0+a;b ba+ieht of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speedp4 9acb*pef+an,pim 2*s* duf $v_0$ 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 yz(/n yp wc-wnt-mto3 k:d+n4is faced with 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 cue ball will also fa-ty t:y wko-4nd+n/ zcwnp(m3ll into a pocket? Give details.

  A 140-kg astronaut (including spacez5sfr;,s p q /klz/,y1alw en- suit) acquires a speed of 2.5m/s by pushing off with his / 1e;yn/s, qwf,prz5lz-k slalegs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are initially at rest in kmu h.xoctd/swo q29.)quv95 outer space. They then push each other apart. How far apart are they )s52qkoudtho/.m9uwx 9 q .vcwhen the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a hea 7ooimn k al:uomzs.a4:-4iw-scl : h0d-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 of the second ba7m:4ki -usn -a0.l azolo:hsmo c :4will? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving an au8u*a y +mejr7 hh5/mwitomobile 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 kineti 8m+u h7amyw/r*j5 iehc friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of tot16p k1n4u9cwm ,lpx9lrpglarao :/ 3aal 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 collisions are perfectly elastic, what is the bouncl pr n9l43mwxul6:1oprpa9 a1,a kc/ge height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at red ug:cl 55c wvsnf0 1.x23dy1eqb.iy20i klpqst directly above it. If the bullet has a mass of 29.0 g and a speed of 510i1ndu0fe2cs xqcb2y5.pl 05v k3d l .qg1iw:ym/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becpkyu8lzn w 7jx dzxe(4jc(h3mv 7/- n)omes 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 drives the block a distance of 9.5 m before it comeswx(pjcn l87zj ymz) d(n/v7k43exu -h to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in aml.ph)s. chu r36ktf . rowboat of mass 80 kg. With the boat initially at rest, the two peoplefchhku..rl.p t3 6s)m, 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 ovd7p (z*je(xs(m vm. kx5 1zxwas 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 isp/s)b,s,bfyh et,6h f suddenly broken apart into two fragments by an explosion. One fragment acquires twice they)h/,6bs fpethb s, f, kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the fozr)x*q:+zm+ 5cr i, uw3syozxrmula 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 massesz5klqmk c 6ri2;yn 01w $m_A$ = 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 twv j-c -p,po2hlms*2 decays radioactively into an alpha particle and a smaller nucleus. What wils lpm, vj2pc-*- toh2wl be the speed of 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 an angle of vf43huxpys r ;27scsl nq; q3:30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.0 , ,lbgv/xcrb s*5d 6yi$^{\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 uppeb10 iu)lud.olr limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and bul) d1uo0il. 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 Saturn6cgqhvv 9 zlmb5s(.fq5qq-8 n moving in the negatiflqmg9qbc8q55 svzn6q v -(h.ve x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s