We claim that momentum is conserved, yet most moving objects eventually slojy4 q/ux*ou97 mjabqo ut00b6w down and stop. Expltuo694* q0buyxq0a bj/ujm7oain.

When a person jumps from a tree to the *kgbxyjk4v)s, wvop547- w t uground, what happens to the momentum of theg*4ys w wxb5kuv4k,-7t) pojv person upon striking the ground?

When you release an inflated but untied balloon, why does0 zkbed k7w;*6l9njor it fly across the roomljbk7; n*r0 69okwedz?

It is said that in ancient times a rich man with a bag of d :eo -tr 14p.tmgby1bgold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been sottmboy - 4pr1.1:egbd miserly?

How can a rocket change direction when it is far out in space anpq-,sc (vsue 3 1 efqgmj)q(p-x /k/lmd is essentially in a vacu-l(m// j,f-q)q m(e p3vpukc xesq1gsum?

According to Eq. 7–5, the longer the impact 0j)97icbiehqs/. 2r- hgwkgw- s y h(e8khgc3time 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 f 78g/)-h(gyhec b9.k2 cke w0 jsigqi-3wsrhhorce acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand coj(ps-p+gmk c-)m*8e xegr3 ;unxu:otllisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is t)ju+s 3mp ;ktx ngcepu*-xorm: -eg( 8he advantage of this new design?

Why can a batter hit a pppjc12*7 r.t)sjdy* (iq uoqwzv(mf ,itched baseball further than a ball tossed in the air by (szvw2put. f*m, rjypoq7( j *iq1dc)the batter?

Is it possible for an object to receive a larger impulse from a smallh/ y+kz r5xmx( force than from a lhz/x(xm5r+k yarge force? Explain.

A light object and a h w1x1 1 rvuj,5plhktw(eavy object have the same kinetic energy. Which has the greater momentum?l51w1 hkvxt ,r(p 1uwj Explain.

Describe a collision in which all kinetic enley sa1a ply9kx+rc v+08 ;pb0ergy is lost.

At a hydroelectric power plant, water is directed at high speed againtluhhm1sq2( i(6 :c.fw r7 ebvst turbine blades on an axle that turns an electric generator. For maximum power generation, should th slhefbi(q:1c v2u wr.7mt6(he 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 wpn3 uc shyi(*85u9gs aall at 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 f2jnw-.blul *c-9 5ci(o o awharom a height h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty tluw -b2o*(chn a-j li9c5wo.a hat falls and sticks to the steel plate.

Why do you tend to lean backward when carrying(naj8y5 g) ly+f).qu tfq hd)f a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its -5d:f (7mi*n vbukecz mid-point, whereas this is not true for your arm orc* dfv(u-mbnie z k:75 leg?

Show on a diagram how your CM shifts when you change from a lying pos)pgt5n1 j0e( / orhr4b6 .nohnegqrh, ition to a sittip)g r h4ebj1,.rhr0q/ 6hno(go t 5ennng position.

If only an external force can c2y pae b ib0k0-bn2lk0hange the momentum of the center of mass of an object, how can the ine0pb ibk-2 by20l0kanternal force of an engine accelerate a car?

A rocket following a parab f70ntntvmvla9 0 b+0qolic path through the air suddenly explodes into many pieces. nf bvtqv+m0 a l7t9n00What can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flyingaf aq7wigm/2:hp1g4u-dykd/m5uo -ep( ulw 6 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. What is tc hi5f y*w9*uh* w; dgcqi2kq7he skier’s change in veloc**hikw5fq 7guc2 9;cyi *whqd ity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a,3yf tp /hz)cy horizontal line drive straight back tozy c3/) ht,yfpward 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 6.40f.ecda* kp7* 4(ytls k t6m(l5rfwy8k-kg package out horizontally with a speed of 10 m/s Fig. b 7ay s6.ktk ((*wr4m58ly*lpc dfketf elow 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. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted odp2ihc9 5cd0b/j r 9vfn a rocket, given that the propelling gases are expc fic9p2 bv9/h0dd5jrelled at 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 movi3 u3t+tojekbw2k9k n9 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 travels alone on fqs4f ,edk3.oye r0 8k/ujfg9alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto thgkyr. 89 fsuk 40ffd/,qjeoe3e car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at/wc6sujks (:d0r6iha1a: lif x6v8my $15 \; m/s$ 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 whiorcu gz6i7 :mkv;- c;:cb bjp7p horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. z:i brc:7u6mb-kvj ;c7g poc; 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 speedzxc, 4r6r*-b ftb- j7xe hmu.g of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the carmcz,t7* xu xr.be-gbr fj4h- 6 after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an a8* skk+wsm:q qlpha particle in the direction of its velocity, and the remaining nucl:m+ qk*s q8kwseus 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 s 7nt; u 6-)dptnqeq7z)yshj9 230m/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block n-t 7)t he6)qqupsz;d7jys n9is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocketql25x20lz v3gozh4qw 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 trave5 (je 1ys3cedj;kve ;lling in outer space with a velocity of 115m/s To alter itekveyjc;d ; sl1 3(ej5s 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 0.045 kg is hit off the tee at a speed 3glfgvb 3ve13xalv2 4of 45m/s The golf club lg3 b g1vvex32 l34avfwas 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 of 8.5mvvpw) 066smoe /s and comes to rest in a time interval of 8.0 ms. (a) What is theov0 6sew)mv6p impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes akhfs6o)-swvm +z 5cy b :rcp/1 wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthined tg wamm5zv5:;j 08fsss of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A5t5fv g;s:0 dm az8jmw new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running:1)idt-szm t j at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tac mj s-d:1zitt)kler 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 0.06zy eunku r*.1ncn w:480 kg) points in the +x direction and is given by the graph of Fy rnn81ku:uz 4 ce*wn.ig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking the l8inf lfs+vveayv wyy0 2p609pyvw06,ower 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 fal9vy +v w802a f e60lpsiywnvf0 p6vyy,l). 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 (6 igg,s3rp; skrl) p8ctk +maw045 qgh+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball afterkqgprhc t )m +,a38pks ; s4r65lwigg0 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/sjley 5vt0q ;pge)4 qb) has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and directio0 yq)q;5elepj4btv g)n 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 under;1c2lgnk+(qvqq pa x: ksm8 6lgo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opp2mka qckqxgnl;q1s v 68+ pl(:osite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ba(9bwa9)elfj lcs; b+ ill, moving with a speed of 2.5m/s collides head-on with a 0.090-kg ball initiall+l;a cbjw9s ()b if9ely 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 that is moving with a speed of 8.55akq2l 7x4d bhhl j2n1 43kgzwm/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.2wg q32 7lhbaxn45h4jl1k d kz7m/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 elastically a67y+ nan j*geb a(+dfcoz+z -us one approaches the other directly froma7nndoj++- z(a+g6f e zcy u*b the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s 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-ojk;i map0nc3 arnem 7hy q8/+77 qdqow n:0s1jn collision with a second ball in/0kn170 8a; an oqycn 3diqemr: j 7spwmjqh7+itially at rest. The second 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 frictionjivzb:*/ef e9less 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 ezv*b9jf: i /ethe 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 of7f wn. tp:k0blhb05 uw 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 results in a maximum height h.3xgex bw;2qhye: i: 2ab(cdj of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swinqj:.2by xb;2cw :eg x3(ih aedg 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-kg pendulum hanging cm 4b3ey56iy son a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the peny46 3s i5ycbemdulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lost,+c u1ewqtm.iw af88z f.mu ff:*/9hq e $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, inux p333 7:lahdz za:cyitially at rest, into two pieces, one of which has 1.5 timeszhaudyx3zc 33l:: ap7 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 B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into )mg c**3rzat)nm*hwry gdi39the rear end of a 2300-kg 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 police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent thed9mr) w t inmh*3 )3*czggay*r SUV) $\approx$    m/s

  A ball is dropped from fmq)am887 e m el4v:yjo .0hwba height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before74 )ehf8 mmj8bqaolym wv0e:. losing 90% of its energy?   

A measure of inelasticity in a head-omw bhb*:ougnm/r5(g 5 n collision of two objects is the coefficient of restituwb*: mg55gn(br/ uomhtion, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the mass of tpzt)x jfs 8yj.7- u5rqhe 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-surfj.8uj)tx5s fzq-7ypr aced 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 movingj/ea3icf:qi 9 in the +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the:q3fiijcae /9 -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 nucln6+or(b f5f8ym b du1teus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and hufn o+bf81 (5rmtb 6ydave 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 m6k2dh 4 jjb:wbass $m_\mathrm{A}=0.400$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 collhx 6 u:k80peq 1on0zgmision between two objects of equal mass, each having initz0nge6h8poq: uxkm 01 ial speed the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls ofs pxfqt1iaoge(/u g w2 +20yv51pscv+ equal mass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. (1cpte 22vpfa/w5squ10 xv so +ggy+i7–37). 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 collisi8ixfunbf8i +p(m f2* ion with another atom at rest. After the if i+ib(f m82*pnifu8x mpact, 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 perf+b 6v5cjar)k b8hiob*ectly elastic collision with another atom at rest. After the impact, the neon atom travels away at 6ci *)jrbvh8kbba5o+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 shown in Fi;i en*s*r;xj 0bjaw9 * kjr-nog. 7–38. Specify relative to the le ;jio*k -x0j**era;wj b nrn9sft-hand 1.00-kg mass.    m

  The distance between a carbon atom whtqnj 6/yelwh-tmas q7e*k54n *:3g($m_{\mathrm{C}}=12\mathrm{u}$) 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 tob9* 3uugixg7dgc:a *he 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 from the front? Assume to9*xbgg*:g c3a7 uiu dhat each person has a mass of 70.0 kg.    m

  A square uniform raft, r 7z4zxk jvpf1vt wknz.2: r),18 m by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, ekkn) vwrf21,z v7.rt:4 jxzz pach of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side0y)dxa c+wuu *+w bm)ks $l_0$,$2l_0$, 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 loadp f6 xk8*t.ok ue3l8nd9k1ieh 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 c* 8 .ketek1p8hi9uodnfl 3kx6rane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of rax64 w7rp)lj3ep2 yq pydius 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. Whl6yr72py) q wj4p3 xpeat is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the samesnqkq* ij lw/wj ;x:zo4+4 *md as those in Table 7–1, and calculate the mass oj 4i4d/qmx;woknl: **s+z jwq f one of your legs.    kg

  Determine the CM of an outstretched arm us9s -kw4cehiihkf pe2jh4q6*) ing Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the jpn ,w)t.gli 6ux ri3)position of the CM of an arm bent at a right angle.i,r)p uw g6.xin l)3tj Assume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that hv 2awx ((t1yn2/gbzuvis arms and legs are hanging verticabuay2w vn(/g(1tv 2z xlly, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Ear2tjg opvg/y h;8q d89suc8nw +th and 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 10.0 m9*) kojn0hbr6gwni6g 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 diametero(o gpx)au 64we-6x ij 0.0800 m mounted on a uniform cylindrical handle of mass 0x)x-4iu6 pg6oajw o(e.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?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diameter awwa e3d 8h6 .lt s35dbq,9yqi0.0800 m mounted on a uniform cylindrical ha.sw 56adydwbte 3q89ai h,q3l ndle 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 (Fig. 7–2p6sa9mi, nzv 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 statoe:9wwj+ d 5vf0m1qwf ionary with respect to the d5: 0+wfmfowqjew v19ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pz0(2 uqh2pljeitched horizontally at strikes a bat and is popped straight up to a heighu22 0lzq hep(jt 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 travelmz ar49t2zq;n ing 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 fac 7 5d-ksb,*gsxy(fgy yed 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 k5ys-7xgb(,yygds*fshot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquxrkp-o +z4fc s 1 r.x 3*t(ik/:ur2+ho wbgpdrires a speed of 2.5m/s by pushing off with his legs from an 1800-kg space capsule. x.r*kws: 4udfzo+i1obp(tpr -h g x+r/c2kr3
(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 an6 xno1alyd:,nd the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lightxa1d6onnl:,y er astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (at rest) w qbe x2,ri*g9vu3np, and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the second, b23r*wpuqg e xnv,9i ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a co57g /,jsio xdy4 tqy,curt 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 bef/ 4,7ytydo,i xjcgsq 5ore 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 steps of tota 8 g9ecoyiku+**/pfd cl 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* y* +kdui8gco9f /ecp fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block orrwcn h9hak.pxp d dd8 64 z5n)b),x9qf wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise aftaqrnk 4w.hhxp9d6) z n 59)c,b pxd8drer the bullet becomes embedded in it?    m

  A 25-g bullet strikes and become8nl1v:vs f5 qus embedded in a 1.35-kg block of wood placed on a horizonfuvql 8vsn5:1tal 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 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, sito50h1znh jc b7 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 the boat move? The boat bhch j17o05 znwill move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abouta vmre0 tm;1:45tpi kl $ 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 brokene j8su c u8wvh:g:9v,-xz1yurm pe32o apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their masw3cz :s8 yj82vxur :pu hev9meuo,g-1 ses?   

  The force on a bullet is given by tr)l7.qgg h o m4k1t0jqhe formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses*04dw jvwpoydm+xwf5;/q) wx $m_A$ = 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 int* qn6 m)e5kyedo an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha part)myek65e*d qnicle 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 ary;vmiw*qn6gacr ; :2. :(bgbmz()m pc j8amfired 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 30.00o+o .tewh3o pbiy,alsy:j. ti hu7/6 $^{\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 uph( veu3bp(-lnk 71n wxper limit on mass m if it is to rebound from M, slide up the incline, e7npxk3w(1hu (lvb-n stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Satfm apg:o43v;nk3mi vr(j9 a(furn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The omaia 3g:p r((v3 fkm 4njvf;9mass 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