We claim that momentum is 5kkzs,1yd +x watmgj ()tfjf2lw9t*,m9e o7hconserved, yet most moving objects eventually slow down and stop. Exp tfxm 5s,o9awl zk12jt *ymw+ejkg(f)hd,7t9lain.

When a person jumps from a tree tsu-4 ul i9izhy4ve pqi8(t1i : ps,xg9o the ground, what happens to the momentum of the person upon striking the grou,hu8u4eii9 :gy1pq(9vps xit- s 4z lind?

When you release an inflated but untied balloon, why uk5b lgo;h i1rsd)40 qdoes it fly across the roomo0q5dkgb1 is h)l4ru;?

It is said that in ancient times a rich man with a bag of goe wq: di y+fka,+c.u08e-af pdld coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push hims ycwd,0-i8qakud .ee+p+ff: aelf to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is essential2u wlg 7wkd+0oly in a vacu g+7lkud 02wwoum?

According to Eq. 7–5, the longer thea, (s -wdzq 3lx(omsi) impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value osx3w (do m,q(l)zs ai-f 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 a:o7ymu; yar3gs possible to withstand collisions. Today, though, cars are designed to have3ar;: 7 ugymyo “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a p+k a,e: j:k(hoapi bwgnaj +15itched baseball further than a ball tossed in the air by theh k 5j,+ek:jwa1 ongapai+: b( batter?

Is it possible for an object .i. xxlfp,m (ema3ff;to receive a larger impulse from a small force than from a large force? Explain.,a 3i(f.e lp fxxm.f;m

A light object and a heavy object have the same kinetic energy. Which 8qr ,w ,9 59(to*g ahupoldn8udjt-qu has the greater moment8pw( guhr ,t9n8 uq-ldjud ot5qa*,o 9um? Explain.

Describe a collision in which all kinetic ksush)m s 6dx-zt+tq// r4.zmenergy is lost.

At a hydroelectric power plant, water is directed at high speed a/uk i,gdf4fg pl6n02g gainst turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so thfku/glni gd6p ,g240fat the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at9v/ u9dsbf7 ux a 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 (fix jf;p0 2wkh1pred to the Earth), from which it rebounds at very nearly its original speed. (a) 1fj;wpkh2rp0Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrznn fn 0u /77eochidh)4rh*9iying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at it s kxs4:d*co3bs mid-point, whereas this is not true for your arm ordo4s:xs*3 cb k leg?

Show on a diagram how your CM shifts when you change from a lying position t, e qcwuiei *7ablv3+6o a sitting positib +76la*eeucw v3iqi ,on.

If only an external f j+pg,q3qp7/dvtul *dorce can change the momentum of the center of mass of an object, how can the interlq*3 pt7/vjdqg + d,punal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes into many y lvm-.sqa ,i.pieces. What sl.im,.va q-y can you say about the motion of this system of pieces?

  What is the magnitude0*u97f,eby x)dcumoyq s13ixam q17z of the momentum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. dig;dd80c k r,What is the skier’s change i0g,d;i drck8d n velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is ae d,w)pd) -aohit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time betwee)o-w ,d)apdean bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally wip :t:2q0srp 9e .ifumsth a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at 2e0p:9:. fusmispqt rrest. 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 t+dr578j 2lhqauoh uw ht 8)h1ihat the propelling gases are expelled 8ja71whh)tr85u +hdoh2 liquat a rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movi 8hlccs8u 6jg7psv45p ng 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 v5n 4hkzysfn (,:z5u1g x v*nutravels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is droppe,g kuns45(*zfv5vn1xh n:u y zd onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at f ak89nlu/:liyffi0 u6 z.kh7$15 \; m/s$ 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 h+lz q;5jzqw15 iei8sjwq +q/d b/9fr borizontally at speeds of 100km/h If the air strikes a person at the de+ rlbq zjzqq9sbi f5jw+q1/i5 /w;8rate 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 olmr8t s1xgkb9.*tc c2 f 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 the tracks, what is the speed of 2tc1xmc8.9ts r l k*gbthe car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially mo5oi)r v6 v+cuqk,uqs8ving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 22q 8u6,+krcv)qu soiv52 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates id2xs;2 1xfeya 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictio y1; ixsfx22ednless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a 6c-h 5wih)qw7 x,lfzzc y2l/v 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 ine(5c .8yyq.bike w: msmo1tm, outer space with a velocity of 115m/s To alter its course by :sm.,i(8ywkctb e mm . o1qey535.0 $^{\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 kgk9 75qls / y x x2ogi9arp1 (mx(uh.7xvxbly/r is hit off the tee at a speed of 45m/s The golf club was in ci2xo sulxby97y91kp/ v 5xxh m lxa.gq( rr(/7ontact 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 veloci6 oi, pcg(ao0rty of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse givenia r (p0c6og,o 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 45h5 xmon psniud)i 8226 $^{\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 engicab +5id-sy5- 7yjzagneer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new mod5z-7c 5g b i-yjaads+yel 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 and is stoppob11r kr;o yk*ed in 0.75 s by a head-on tackle by a tackler running due1;oky kr *1obr 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 (mq 7w/5:x qhmd9iop(w jass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a funcwj7x:w5q(h /p9 omiqdtion 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+(0yjhum2mqic 9eg8f h0rf 6e 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 breaking the fall). Assume the b h0uh0i cy m9+ejq8gmr6f(2 fereaking 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 directf 0mnmld::9po ion) 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 balm l9mpon d:0f:l 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 has a head-on colli2vhyxv- n6-. h9( wet pebjt3ision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision,-tye v3xv6(p-tbj nh92h wie. 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 undergo a perfectl:,bgt.t) xq wvy elastic head-on collision. If one ball’s initial speed was 2m/s and thxtb :,vg)t.wqe 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 ballz(ua qyd.dmdyz0 u2+w40q 4ww, moving with 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 sp+u0d.2z 4zww0(d dy umayqq w4eed 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 collidespzkf0gvi 3 q y.8m* hq3(igv7pt2wcy4 head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces bac. 0v2p kq4ych qit(7wfggimp*3yz 3v 8kward 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 elasticallyqiw77/z5ix ; veuqa;. ftf+ td 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. ;;iz7vfe ifq/q7+td wt5a ux to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a 7 dvlss7uq p9z,ce lv*:k6vbbn)h3+l second ball initially at rest. The second ball moves off with half the original speed of thl :n7u*shqev37zvb vs6)kdb+pl cl,9e 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 slideshxo: ( nm :il0z7(uhsp down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontamuh phx:l:0so( (z7in lly.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of ojiq+4f 8wo3o:djqe(t 3cea3a 8 4pfqmass 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 expe( t35ej5jl 7ztk -lcrrriment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulumzjj 3le7kl 5t(rc 5tr- 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 y -axwu :hn.axs.jqo22 /esh- itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makesa/nu2qs.2.xhw eo:xs-j- yah 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 kinetic2 i. ;muhhuf4b 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 two piec uq c:7/t.x5qubfj b-hes, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier par ch/xqq.uujt7- 5:b bfticle, 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-kg SUV stopped atznu2yv2*mgzsn/prx-e o)xhkx - *3s : a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact.**xeos)g32xyh m pnxs zr z-k-n2/u:v 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 height ofd gt wpn(ov7:0 1.20 m. Approximately how many rebounds will the ball ma (:7owngt0dp vke before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the cckl w4omr)j-dgvujg (y -) z( im;lv55oefficient of restitution, e, definedv);5ml(cu oi r-4 gz vyj5wgk(m) -djl 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 timesv:kr+6xw 37lob1yxuj the mass of the other. A depression is made in both faces of the cuxl3kbrjw :+v 1ou6yx 7t, 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 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 dirj ,2uezp) :wyd.(eo3u.gkv pkection at 5.5m/s collides head-on with a 10.0-kg object movin.v:wj ) guke,yk u2opp.3z d(eg 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 electron, and a nf.u+ikv*- 79gdgbty feutrino. The electron and neutrino are emitted at right angles and have momenta + yf gbv*d-i.9k7uftg 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 mo 08vn,ao)hy t)8xho/ hvtkk4 ass $m_\mathrm{A}=0.400$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,4z vi2ks9mjr/ each having initial speed the two move off together with speed v/3 What was the angle between th9mj2v 4s ik/rzeir initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at thk30d6lbg*5vlpac z ,s 5cf)yve 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,yvs* c3f5ap lkzdv6 c l5)b0g 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) m (4 rc:fyr4,o/kx7acru0t rk/y fwo3q akes a perfectly elastic collision with another atom at rest. Afte(yku/xw orfcy cr : 4tf4k,/a q7rr03or the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfe2lkab2 c ,bld8ctly elastic collision with another atom at rest. After the impact, the neon 8 cadl 2b2,lkbatom 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 systywk1v()yk-sv2 h bjb 3em shown in Fig. 7–38. Specify relative bvvj h)y3( sbky1w2 -kto the left-hand 1.00-kg mass.    m

  The distance between a carbon atom5wt 7ww4wqa v o8u60zic26bv n ($m_{\mathrm{C}}=12\mathrm{u}$) 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 th2 /cl-j 0uamfke front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in th-j2ulack m/ f0e 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, 1aobv)qp0dgpkx2o (,;t u)n jis used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of theq0vuo)( kxja)g, obd ;tn1 2pp loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides ggia6f+ts52c +a 7xaz $l_0$,$2l_0$, 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 ha:wr (wk8fk z3js a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length8kzrj(kfw 3 w: l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular pla wksz9s/7qh ne+4ks(fte of radius 2R has a circular hole of radius 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 of7 sskzse w n/kf+4h(q9 the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table sk*)hyfyr5o8u1q. xhq 2rqa/ 7–1, and calculate the mass of one of51y.r/qhufk x2 q sha 8q*ryo) your legs.    kg

  Determine the CM of an outstretchej3 )lc4wj y jrv3(ms-rd arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of theoptasjtrxf- evg,+ e0;w(/ lv eoe./ 5 CM of an arm bent at a right angle. Assume thaje/w org(vtolp -,.s+0e v;/xf5e e att the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such thata+qz5lzdn 21 sgx 2ss( 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 ou sgx zns1 5qs2da2z(+ltside the body? Use Table 7–1.

The masses of the Earth e(:a cr8yt:, +4yrrwiod8o pqand Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 1(o jobuhnfww489an /jlb;2u w b.k,5 b0.0 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 cylindz2 6f+ 7gzs8h.pb 5djem lml /:cafna5rical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point 6hl 7sja.pmazf:mz5/ d85fn e2+gcbl that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kgnkv+q;f/x /*p, ;,i zjvkrldg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow i; gjpkn rl+d v;x/qz/v,f,k *a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–;z7qqrko dj;5ld 84s3o z-upn14 (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 and i. m :p+td8g wljus;k+*up4fefts 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 measured with respect to the balloon. With what speed anupsg+uml;:t8f4w f +kpj*d e .d 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 poppmscvvk :6 ugto*(t.enf- a.4ved straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on theke suvvtg4a*6t( vof.-:m.c n ball during the contact.    $^{\circ} $

  A rocket of mass m travelc*1vsnkjglhe +d 1ykx /m. td,t3f8-ling with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown in Figfv3ij) + lm9po-lngl;o wm84h. 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 pockeml mh) +pj3o; lfl-n9o4g8 vwit? Give details.

  A 140-kg astronaut (including spacyrjeufi5i;/;xr8j n( xeqs 0 +e suit) acquires a speed of 2.5m/s by pushing off with h0ixxfs+ eq( yn;re5 ijj; ur8/is legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are ey;v(:vj ik4k initially at rest in outer space. They then puveyj4k ( :ik;vsh 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 elastic collision with a second ball (at rest)ho:sc1oa8n)8l syx8 j anxa1cs)joylo88hs:n 8d rebounds in the opposite direction with a 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 witness in a co/ exx)a dasg5,urt 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 exceeding the 55-mph (90km/h) spe5 a/xsd) gexa,ed limit before applying the brakes.    mi/h

A golf ball rolls off the to.z5ulq elkjl)))2i f op of a flight of concrete steps of total vertical height 4.00 m. The baj)q e52kz)ulol. )fil ll 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 height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest diipu8djej-4j+ q, uh+i3wx 8rzrectly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block r -3zhudqj,u+ixe+jj4 i8 wp8rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and b.b-d+ +rnmgct nu/s2 9s(zk0 i2t7 apifr7mxyecomes 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 tcxd7msi yf-9sn nrt( b7a+zum0gipkr/.+22the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg,- w.lnhbbi 1a, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will t1,.hab -lbniwhe boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass wa0y zt+,3* 4 zdnq nkis :)txxgfjw)u-es about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broke.dm-jsb 5e0nf n apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the oth- esb5nf0j m.der. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 5y)m +8g3x8uxsq6o l gp80-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses 2q ,y3os;nvv)d s +lxb$m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha particle a q6rs:+my-pt*)hwdr5iq*5rjc u bpd5 nd a smaller nucleus. rj55 *5t+:p *s )rd-myiw6urphcqq bdWhat will 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) ucgb(epe :;/i 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 slides down a 3xky4qea+3gmy1 :/f vp0.0 $^{\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), what6 cs4xlv w9/z-gd h,kp h/du1n is the upper limit on mass m if it is to rebound from ul-/cxdkh/46sh9w d,zvgp1 n M, slide up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slinqyjz+ 6 d)irxr;ka;d7gshot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital +zyia;x q rrddj)7k6;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