We claim that momentum is conserved, yet most moving objects eventually sloww0w,-,taq k*yawg e-r down andyqwwwg t-0r*,e ,k-a a stop. Explain.

When a person jumps from a tree to the grouniv .rr8p cr+o-l 5i1gad, what happens to the momentum of the person upo8r- a.r1vi gorl+ i5pcn striking the ground?

When you release an inflated but untied ballo;(mle:j (c1eiz xam++3e0- xqtcbwh 8eoidz. on, why does it fly across the rooma 8- eemx+ +cqx; ( wlib:3zcmoti1ehzj0 (.ed?

It is said that in ancient times a rich man with a bag of gold coins froze tf6)m:ds ak0u v;v0idmo death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done 0f);kmsium0dad:vv6 to save himself had he not been so miserly?

How can a rocket change direction when it is far osfs3)ns)itxlcq s; 1( ut in space and is essentially in c l(1fssqxs )s)3;itn a vacuum?

According to Eq. 7–5, the longer the impa,3qdom0 qiq*cwf 96tf ct time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the obje3ow0i6cdfm* q qf,q9tct 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 possible to withstand colli 2xe6 :ny2z :zsyhonw3sions. Today, though, cars arenns3:zwx22z y y:h oe6 designed to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in tao2/llk x:5fr4z: w l3chr, aqhe air by4qlo/ azal:,hl 32r wcr5fkx: the batter?

Is it possible for an object to receive a larger impulse fro-(og g/p:k2 j:hfxu qcm a small force than from a large forc( hxg ufqk/pog :c2:j-e? Explain.

A light object and a heavy obj *d:z;8(ds:mnpganubect have the same kinetic energy. Which has the greater momentum?pma8dzg ndu;n :: s(*b Explain.

Describe a collision in which all kine m 0 wh1p9(h:9dmpqf*vxwu1bitic energy is lost.

At a hydroelectric power plant, wate*t9jgaiy2hn c9g 0 c ).h/rnzucxqz54r is directed at high speed against turbine blades on an axle that turns an electric generator. For maxic*crc5/9. zhz ijn hyaqu2g0x ng9t)4mum power generation, should the 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 walwl6:d2) -fj 9qmerqbh o.9xcz l 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 from a height h onto a hard steel plate (fx, es uzv2kb1dn6j8 )sr li+1sixed 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 prskn sbsr),l1eu2+jd 6 vxz1i8 ocess 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 7zdtv*3r9 binbglf6+3 jgb .lload in your arms?

Why is the CM of a 1-m length/ x j,5d5,ddphw,jclhk 6s5ne of pipe at its mid-point, whereas this is not true for youpw5hkd/j 5xcle6s,5j n,,dh d r arm or leg?

Show on a diagram how your CM shifts when you change from a lying positin 59d0q :-,uzrvlmswion to a sittidnl:r, -90 muvqizsw 5ng position.

If only an external force can change the momentum of the center b +c+t7/)t*uf n9ty jp7 kjdofof mass of an object, how can the internal force oft fpfkttjcn 9/7 b7*uo++)yjd an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes a+ (vc2t6m.ou hawxd(into many pieces. Whatv6+ux(m(c 2.oda wh at can you say about the motion of this system of pieces?

  What is the magnitude of the momentum ofkcmjz9h2; amhdi:8njz 3 jq*; 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-j1 ,ks,2 :rhpq-fcimlkg skier for 20 s. What is the skier’s12 r:j-s,i,lkfhq pm c change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on -;6xdy(g3 rk wx it5zia horizontal line drive straight back toward ti5 (;rkztgi wx 6yd3-xhe 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.b1vw lkfyn1 0340-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, andkl3fb 0w1vny1 that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases kh6z c1ats(/p are expelled at a rate ofs /ak 6h1(ptzc $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movi ecxo4yl nqie359 +1xcng at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless track with a consyk8v7 io e3dcw*a qj;3sl xu5; /5vputtant speed upjqwa* /iyuv3s ; odkex857tv3lc5 ; of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelin)v iw yigmv(4 7cce/h1g at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can wsky5r lq5c. h,hip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s 5slqr kc,.yh5 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 w9ge0c jace/5 lurqlr.y3k) k 3ith a constant speed 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 the35r 0kqy akj3legu. 9)/crelc speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in p iqnv v)9qz6a97pd4hthe direction of its velocity, and the remaining nucleus slows to 350m/s If the an h9pq6dva7 9pzq v)4ilpha 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,cj8 usb -wn( i9wt,fp.0-kg block of wood and emerges cleanljcb89 w(intw p -uf,s,y at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is xi4*(a ve27 nl k1yrautraveling 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 ve 5l f0uvw;l;fvlocity of 115m/s To alter its fwl0vl5u; ;vf 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 theq ,nm/d81ojyf.surk ro7c1n - tee at a speed of 45m/s The golf club was in contact q s/cjn .r8u o7m-o 1d,1knfrywith 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 8.5m/s and comes tozztdffq (; .r( rest in a time interval of 8.0 ms. (a) What ir; fzd.qfz (t(s the 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 z1s b(e2qub8qgwz *6l(kg s(ba wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthiness of njy9gp ks4 -z+0vhdw: sew automobile models. Cars are tested by smashingw9 -s4 kvsgyz+p0djh: them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is runnit n29 zp2/vv0 tul efw+dij 9gw7ipf53hycl5 /ng at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler running dughpy/l/z95 2n vd9w52lpjvi + wf tf7cei03ut e 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 th dnh4ap( rwnayy qk, 1,:gn ((oft+wm1e +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical metnyr1,fdo+aa,gn yk:1 pnw4 hm(( qtw(hods 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 br)o6+ ;pj c7qtv -pp*q9pa(rm-jli ecqsax1d.eaking 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 the6)dc pxs+mqio vj a*1-a;( tppj9 q-cr .7lpqe 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 direc dnjr;2 9-kvf7:tguybd y ,0fotion) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent tfjyy ft: 0rgu v-7bodk;9, n2dhe 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 hed4 (ilr4 csc*wad-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and directis r4 lw4(cicd*on 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 j2w4dwu bhanq1s h 4h5g)pj+/undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and thu/sjhww jh4a1qd4 g2+p)n b5he 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 ball, moving with a speed ofj 6sbuk+1t/ xf 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Le6b1 utk+x f/sjt 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 s ,h 3 n(b1(tdw*ydk1 wg5wqfrspeed of 8.5m/s collides head-on and elastically with another ball in tf r wh151q(3g*wsbyd,w(kdnitially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement p a)9t41fd 7pwa/ oo:;wzdwuyr u4b6un ark ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate6;44aurw1wufbza yd:/p t7)dn9o wo u
(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 ba93rd+ v6x*p duykz 1kofdd ;4sll makes an elastic head-on collision with a second ball initially at rest. The second d*p1 d fkyvd;dsku9or+x63z4 ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as 91uxy ;/ie)w c bgf1irshown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-halfwi1 /1)b icgu9x;yf re 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 a2 ba5dy4yklga+pl 55q n 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, projectijs;w5 kgwup-j upw0 64le 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice ajkpwp w04-jsu6g5u ;ws 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 travh672(u3f z/ plqpujv eeling 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components2f(uehvpj3q up/z76l of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for thj3kc;q/8dipja)z0 4 ,v lvc g2mr fqz2e fraction 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 ann 8z ish1**rpnbuf 6l: object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much ks6h:zi lf*p1b n8run*inetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the reazjmmcp1:6 0vt cs+2 arr 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 co0as2rjvzt1c:+ mp6 mc efficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height of 1.20 m.raf+0s+o v-x6b9yic k Approximately how many rebounds will theiyx ac vs9b06+r+o-k f ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objoltl +h/rgw5 +ects is the coefficient of restitution, e, dtrh+ l w/5o+lgefined 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 wp a7t +kyxo:el;.gjh3ith three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. x.po h3tay+le:;g k7 jWhat is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the sg ;6+7bfbzv r xc0e/w+x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction arc67 z0;bvs xf+g /ewbt 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,n2yu m6 wq*(jqbugp+r q;kr7 decays into a second nucleus, an electron, and a neutri6+nu (q7mujrg2 k*rqq ,wy;bpno. The electron and neutrino 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 mas:l8ubur: 5z7myye ,r*h nr6x ks $m_\mathrm{A}=0.400$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 ca7p3ega4 saw3 ollision between two objects of equal mass, each having initial s34seaw3g 7paapeed the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls ofbxm9tz::b mb2 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 :zm 2btbb m9x: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) ezl8 co/ eol)4makes a perfectly elastic collision with another atom at rest. After the impact, tlo/)co48zee lhe 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) mad:s:cg kg(xqy.21 p whkes a perfectly elastic collision with another atom at rest. After the impact, the neon at1sgpx:c:2k. w (y qgdhom 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 u ort7qd((5 mu6(mqg ko 8pb6jthe three-mass system shown in Fig. 7–38. Specify relative to the left-hand 1.0qomu p 5k76btudor(j 6qg8m(( 0-kg mass.    m

  The distance between a carbon atos ;wz0.uvx de9m ($m_{\mathrm{C}}=12\mathrm{u}$) 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 bpko5rgsyh e4/2ulr/c52d;8 w6fug bkx5k0bgehind the front of the car. How far from the front of the car will the CM be wheyrrhpguf 5 0cx26/ u2w;s g4lgk5/okbbd 58ken 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 that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 fd6/f+ivrh9-1shrjs onvu+ + m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, ni9u 6+hsrfj1 hrvf sv+do/ +-and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides pt lb+hz1 ;en3 ,:nh+(h gtkzf$l_0$,$2l_0$, 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 loadf(e ny7+8u z:nubrv8 q of identical cases of tomato paste (see Fig. 7–40), ez(nr 7fqbv+ e8u:y8n uach of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radqlv1zyw+m0 /1ce808 lqrm ondx edq*8ius 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 of the center of mass of the plate? [Hint: Trv8*1eznqo m +yce rxd /d8qwqml0 0l81y subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and canq;m o/b34o.8tgi/ah 16pcg tph gpc)lculate the mass of one ofchgpootp ) m.g8b1/qin3 ha6c4gt /p ; your legs.    kg

  Determine the CM of an outsdetg a n7e(b,x(2zpe3z (m4xu tretched 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 6ei 01rw)2p k5i7p vjc86evyugcm7yjat a right angle.7r02jwic16 c5i7 pepgmv 86ejk)y yuv Assume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position e1 n;mx6 l1;n4euy2 yv 3plphgsuch that his arms and legs are hanging vertically, and his trunk and head are horizontal 4 e3ngvppnum;yy6e11llx; h2, 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 Earth adm cf/ i:az2, :4zbvoknd 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 stancl aj;mt54p6 tz8ea(ls5t832di :n+x qnzoc vd 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindr2w36oe3 *vm,oto3bnh4xyts xical 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 that will follow a parabolic trajec4xn m3ot,e b3ov3o2 *ys6wxhttory?    cm

  A mallet consists of a uniform cydu2zwh(3 k(mj0s4axjlindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length23zmsj (h k(aw0u x4dj 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– jh:i;k i5yce,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, are in the air and stationary winpg8avnxz 5c/5c l7l5th respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth)lng 587pcvnc5 lz5x/a does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at (zav :o t 88.b6sknklzt*tn-ld0bc8q 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 l 88q(z.db:c*att zk 6tkonv8 sl -b0non the ball during the contact.    $^{\circ} $

  A rocket of mass m travelasdpq);n 1bc(wwuj 6(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 faced withc7;*/m1uxfya/ vpx ct the corner pocket shot shown in Fig. 7–43. Relative dimensitmx7xa *1/ycu/; vcf pons are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by pushlh p9fom:a32iing off with his legs from an 1800-kg space chof: iplm2 a93apsule.
(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 k,6bbnpb.5hbu;z m m* rg and the other 80 kg, are initially at rest in outer space. They then push each otb h m .;6prm*,nubbz5bher apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a hq*4 xi)y )jbshead-on elastic collision with a second ball (at rest) and rebosi b)q y4xj*)hunds 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 coyb)mbsx (3cnc l+4fv; 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 frictic;byl3b fsn)4+xcv m(on 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 to )wt0hdq3idmw7nj/7q tal vertical height 4.00 m. The ball hits four times on the way down, each time striking ti m7qw3)j/d dw htn7q0he 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 directly abov6tvl/kp olmz6 6:n7ks e it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded inpllo:vz6/kt6s k 67 mn it?    m

  A 25-g bullet strikes and becomes ez2d egro; j8p1 hwuld5bq 3b,kjj,9,umbedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it cz1d,2lgu53qhjowb jdku ,, ;8p 9ebjromes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and jbslf+m*0r6k the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now excha frsk*0+j6 lbmnge seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was aw0-p,aok-esvbpe69 )kws ex ( bout $ 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 g7,iuroj a k-,fragments by an explosion. One fragment acquires twice the igok ,-7ra, ujkinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by s lboi5c2q-1:qcj)h vthe 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 masseswpj;sv /1;z fc $m_A$ = 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 recci5;g2 9pgynj-oib:vy:kj 1 st decays radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiliy 1:j obgcpynjgv:9i 5 2-;kicng nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is 7wxfd n+:c +l(rf5ltofired 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=2.5l0 t*;p*xx z4luvf2tl0rqnx 2kg 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 upper limit on mass m if it is to rebouan.671xnxf x hnd fx7. f1 xhxna6nrom 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 slingshot effect. Figure 7–47 shows lz izon5.8n67pne6i3yj:p 5u.4(nliaudo a wthe planet Saturn moving in the negative x direction at its orbital speed (with respect to3du.uaw8oipj ni 7a(6i :znn e5nlzlo4 6p5.y 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