We claim that momentum is conserved, yet most moving objects eventually:4 g6.mfvibvt;8u jp:aq )vps slow down and stop. Expla vuv;fastmq:g 6): pbp8ij4v.in.

When a person jumps from a tree to the ground, what happens to the momentum of tk 6* *osgjvp 4(mcl2xyhe person upon sxg46m *c lk(vo*y2pjstriking the ground?

When you release an inflated but untied balloon, why doep,mavny 483d es it fly across the room?,y4e8dn va3p m

It is said that in ancient times a rich man with a bag of gold v0wnx) *.di lhcoins froze to death while str*l id)0wnh.xvanded 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 miserly?

How can a rocket change /k. jle5ar 6gpp-wmb 9direction when it is far out in space and is essentially in a vacuumb-9j r/ gam5 6pwklp.e?

According to Eq. 7–5, /vcm ru/ b,t-hthe longer the impact time of an impulse, the smaller the force ca/h c/r u,mbtv-n be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as poz10ir+t1ta-jgp z*kn *dgi w. ssible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantgrin*+ ztzigt d-0 kj1.p*w 1aage of this new design?

Why can a batter hit a pitched baseba2rtzv+u,,bzn ll further than a ball tossed in the air by the bzub,n+tz ,2vr atter?

Is it possible for an object to receive a lrx8*-zx9 fodh o4/dnjis5 vo)ej)t1h arger impulse from a small force than from a larj nxv/9hzo -to d4eh))* s851odj xifrge force? Explain.

A light object and a heavy object have the same kinetic energy. Which has t5 4w) pfwv:5zhbae 3;:bhitywhe greater momentum? Exb :tw3 5f5hpaeh4vb)i:y wz;wplain.

Describe a collision in which all kinu 1)cfq5d eresbc/j d/) ytdh7g 9a2e0etic energy is lost.

At a hydroelectric power plant, water is di/2q xhtqd7;mv 7ggba) rected at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so thathxqq; 2m dvg7b t7g)/a the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a 4tpgs 3 k4:r0j,ft.gcm5 $^{\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 ;*h/wiu+d cr 7+wfkvbplate (fixed to the Earth), from w ;rcw*k/++fv u hw7bidhich it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (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 v yjxn 88)zkz: qyuna1h4jj(6your arms?

Why is the CM of a 1-m len b6s(eg/ve zllb+c* er;aai a1j2z2.c gth of pipe at its mid-point, whereas this is not true fe+a*ccg b/1rvz 2 . a2es z6bj;eil(alor your arm or leg?

Show on a diagram how your CM shpjomp8 pz- 3sxc;* 4arifts when you change from a lying position to a ssx rm 4opz-c8* ja;3ppitting position.

If only an external force can change the momentum of the c jqizt 1ce+jq,sb 3c2l,clluv8 l/n8*enter of mass of an object, how can zc,3+lcvsnulcl 8/2 ,1b8 jie jql*tqthe internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes into maycl:.c*lg h5 jwo96irny pieces. What can you say about the motion oylo lh.wj:6i9c cr g*5f this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed o8z/a+ /x5gtxsxei2 x kjh*r(x f $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts o:thxg rs n:vts4ahbw: 6xz:, 9n a 65-kg skier for 20 s. What is the skier’s cn9 6t:trx vwzh h:a:4gs:bxs, hange in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit o0lim+xsjemdnp: -9xsc2i:x / n a horizontal line drive straight bam d npscmi2l9ixj:x/-0 +exs:ck toward the pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horiz3/ oa +nk(xtmqontally with a speed of 10 m/s Fig. below Calculate the velocity of t/qx(3 tkoma n+he 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 exertev:1l 4.ow8oh a cmelf6d on a rocket, given that the propelling gases are expelled at a a6m:.l8 wv14oochfel 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 moving at wonr3 yg)gi4 o i96/j 7s6 -yq6kbgnfe$4.1 \; m/s$ 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 withape:jf2emc u cpx6 :b5 h-32rj a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will cr::m jeb63fupj2c 5hxp- a2ebe the car’s new speed?    m/s

  A 9300-kg boxcar travelingn2j jvjy.-);;x- ughiggu5jm 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,(+7ccgh u3k tpqe.p8k winds can whip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is bro8qk+cu.k( ce 7g h3tppught 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 cg7 vwex(iuj 0-onstant speed of 8.6m/s on a level track. Snow begins to fal0j-xv ig7 uew(l 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 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at b-u96hn.lcit 420m/s emits an alpha particle in the directinb-. lc h69ution 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 emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and emer,p,xd(bd4c bp e4dpz4ges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move ,de(xd4p4d, z 4pcbpb after the bullet emerges?    m/s

  A 975-kg two-stage rocket japil sa1is*mk8e,om+ 7pv/rf 3yf/; is traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a tdah+ij( c169*awhg avelocity of 115mth*9 a1+jiagwah6c (d/s To alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0md8l8fi 45w cf.045 kg is hit off the tee at a speed of 45m/s The golf club wasi 8f5l 8dwfm4c in contact 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 velocity ,-kqwbr ux7t,qhn68 a of 8.5m/s and comes to rest in a time intern6 w8xhkut, aq-rqb,7 val of 8.0 ms. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of massipv4 nq :d2uree91yx: m=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 :j- 6dg/lz /ojjpxh j6of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A nezhxglo6:pj j jj/d/- 6w model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/ 8by3v09qz8c s-cjw .irs4 duzs to the east and is stopped in 0.75 s by a head-on tackle byc sbd43 9j-yc.wui zrvsq8z0 8 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 ball (mass 0.060 kg) points in the +x dire.wp4tg z2 fmd0ction and is given by the graph of Fig. 7–33 as a function ot pwdgmfz042 .f 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 breakings8cut ot8dj*: 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 brea 8:utjt8sco d*king the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed off;b/ddd 8np; p collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direct8dnd; p;d pfb/ion of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with84mu 1qin4j.zs474j5olil,bhv q njd a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfe8i1d vj 4,iohz ql 4j bnm45slnq4u7j.ctly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectlnwcn: o)m6 ,d h+gw3pty 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)w: n,t +dmo ch3wpng6 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, v+ijsu1h+x y1btb: 8l moving with a speed of 2.5m/s collides head-on with a 0.090-kg ball iniv b+b 81huxl+tjy:s1 itially 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 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 that5onw ci3m 1u.a is moving with a speed of 8.5m/s collides head-on a.uc5io3amn w1 nd elastically with another 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 amuseme0qul6m/hq k 0gnt park ride collide elastically as one approaches the other directly from t6gq u0/qm l0khhe rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B 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 collisio)q, l b;g9geag3 immro;1uu ae2 wy32 p,zim7en with a second ball initially at rest. The second ball moves off with half the original speed of the fimb,y9,la;e2 z7g 3w)gormqi1 uaeg p; 23eu imrst 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 lr /.rzy)or ky(b8+lvslides down a frictionless incline as shown in Fig. 7–35, 8 r)l( + okyzy.vb/rrland elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object olmh9xw6nrxs(eq w 14 :f 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 maximum /3 w 2:tvg ltxm r8knds3:3utxheight h of the pendulum equal to 2.6 cm. A second ng x3l8:2:3swtk/dxm vr t 3tuprojectile 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 3.6gv rnlv5mrf f)(yj130 -kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arcv l10j(5r nf fv)gmyr3. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fractiojr; at.l ,02q2 biywbrn of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at /cm(4jtg -eyp rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and Bgcj/m(4 ep- yt 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 at a reo(adv20d otup1 f.)8qtu.jwg d 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 ti2w.ugf 18o( t0) dpavoj.u dtqres 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 h9,8u/u yeh/zu 3htffy s( dqhqved71/eight of 1.20 m. Approximately how many rebounds will the ba8//7 qvuu ed d ut(hqez9 fyf,yshh1/3ll make before losing 90% of its energy?   

A measure of inelasticity imyd5er-n jf/ 8n a head-on collision of two objects is the coefficient of restitution, e, de5n/e fmry-8d jfined 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 mas ftpjwrorjco r5r/ ::ef60 wg 30*udd6s of the other. A deprept6g5owufdrrj30 d6ow *r::/ r 0cejfssion 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 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 a jhuqytm 0n709l tbjy(5i/ tggt-4ce -t 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final vel7j -0cutn-t ilq(5 mbh/egg9 4y tjyt0ocity 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 inyhp d tb8) 46:*lensxxto a second nucleus, an electron, and a neutrino. The electron and n4e*)6s 8xtnhyxp dlb: eutrino are emitted at 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 maokh ryh7 i 5ec27lk(oq u-80mlss $m_\mathrm{A}=0.400$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 eq ygxj3 j0n nuhit:jx3 k(lh,5:wmoj 9(ual mass, each having initial speed the two move off together with speed v/3 What was the angle betw t j0h:uj3j5xk(m(,3hj ny nl9xow:igeen their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles a;5: kbg*mh prxy.uncg. )1vfmnd meet at the origin of an xy coordinate system. Ballk *.yg x);vmuncgfm:p. 51brh A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A 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 anothezrfppip hi8x3*yr0ze w;/5b6s; qg .cr atom at rest. After the impact, the neon atom travels away at qp;/zh r cs3i;b 0gpp6.5 yf8iwz*r exa 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision with another ato un 0k6tbpb.p-m at rest. After the impact, the neon a-pbbt uk0.p6ntom 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 system showo d 1ip-mw1frto l)sx;*re9sb v26cdjyf4h *:n in Fig. 7–38. Specify relative to the left-hand s4ox)ydbi1 dh1v9m6c* ;2p slf:*wrrfe j-o t1.00-kg mass.    m

  The distance between a carbon ato otlrp.:)2xyz m ($m_{\mathrm{C}}=12\mathrm{u}$) 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-or4m f vg*0 2p1yz+lbokg car 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 in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from0 4zm2lg*+o pyr bo1fv 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, ishy3pqdglnqu3 /542he used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboahd ep34u2g nhq53 lq/yt.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sideu tym,t :j60aqv j-*s h)lp,pks $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of tomatf0c0 tpif5q q1fp -jz4o 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 operat ifqpf4q5-100j tpcfz or can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular ho1ir o- d*2 qzilimh5i2le of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the l-mq * z5ii2rh 21idoilarger 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, .r)d.pq,a nldand calculate the qa. pdldrn,). mass of one of your legs.    kg

  Determine the CM of an outn s;: iqax-(e*0)n0awet gtxcch ,hx -stretched 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 the CM of an arm bent at6c qpn0atvh2; a right angle. Assume that the person is 155 cm tat6 h;v pnc02aqll. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such thatb) 3vg xf: s9fytct6dss9y0a1 his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM1b:dttfs)sv 9sg 9 yca0x3 6yf will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon sy uvt p1/xx-k /kx(;;gt6wmkare $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on frictionlessyd dce asd;3-0 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 diamt*m(l1 uow(gd 5ca;bi eter 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 c g*uit5 a1wl;db(m o(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 cyl, eg, ,amjhle+indrical 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 showajm,ge hle+, ,n 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 Ext64q.getl n+i ample 7–14 (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 its gondola, of mass M, djxwpnwd;0d879h si +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 and direction (relative tohxwd0;s +8wnjipd 9 7d Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched h- s3tgl al: i:hir 5dq32tzyl8qq 7sr*gn)ju/ orizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the bl 2lgi jsiuh)trz: ady37snlq* g-8/qr5q:3t all during the contact.    $^{\circ} $

  A rocket of mass m traveling wibt4;ct*u*d ba kt30pxth 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 in4y8 hlul:iq4j0g x d:m Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” inuxyld q8l: :4jih0m4g which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.oaddlu) , *3+1 1w)apym dpnhr5m/s by pushing off with his legs from an 18uh) d a1 wrop+1p*yal)d,dm3n00-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 mas d 7,s-p4ofqycnrl2, ws 60 kg and the other 80 kg, are initially at rest in outer space. They then push each ot7ypdcnr2, wq,fl o4- sher apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-ci+ z(w)(fk7ls/j6 / + tyn c/qqnt qp7zirtf*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 s/c n6//pqz kc7i +j (nzt)q(+ t7 wqlfi*yrftball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as c t5*8r+pdm, ale si8b5aetb, an expert witness in a court case involving an automobile accident. The accident involved car A of mass 190 aba*br5e+c88l,,d emsp5itt0 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) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete .6kfdok y i 5z-qv*fx1steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fo .foz1 x-6q yk5*vkifdurth 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 8 wg)4sero7r ndirectly 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 t)o srw8 n7e4grhe bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood pl-iv4 :brnvz.t aced 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 9.5t4 i.v zn:-bvr 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, sit in a rowboa+iamc: c6jw1 it of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will movcwica: m+ 6i1je    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass wj0+mva98jmh(8iqm 0i kugd8fr h 9 j;wn /yr1oas about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two 9oq ym1gfz*r /6 m1nkfuhqw2- fragments by an explosion. Onqf /oh 11mf g2uyn-*wkr6zq9me fragment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 580-( xf -xm3/wh1h m$1.8 \times10^{ 5}$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 gf1. v8 jyioh**zdzbx6nb+ts.y0jt ad ).qe($m_A$ = 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 alpp nzpv7dc8pr , 95*opc:dhri ;ha particle and a smaller nucleus. What will be the speedpr9p857: ;v rcp*npdiohzc, d 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 (clan(m :86lwfugbcqz9 1ly target) 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=2.2k35 /x(d0fc*lfx afxcx s i,g/ 5eq0shbg slides 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 uppelc/g2se k8 r;kzwy ;*g(h(xp ur limit on mass m if it is to rebound from M, slide up the incline, stop, sl2/leg p hy8z;ukrwk( ;x(c*sgide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–*h-rq1 mtt l/ :c q5zpde1dl6l47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to:rc*d16 q5/zet1qlpd-ltm lh 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