We claim that momentum is conserved, yet most moving objects eventuallyylocr+e8t5kz 80(vij v)mgr t0 z bd-- slow down and stop. Explay+gzk 5brz- v0t0o8l ed)ci(jm8-tv rin.

When a person jumps from a tree to the ground, w 5kvxzyvcd:mz 5: 37zshat happens to the momentum of the person upon striking the groun5 537k s:vzycv: zdxzmd?

When you release an io;qrga( r:vu;nflated but untied balloon, why does it fly across the room?r:q (;raoguv;

It is said that in ancient times a2iae/is hzc- j;bxe(1 rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the s/ehbc;1(z- xejiia2ice 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 direction when it is far out in space alfzn+ tngy4j93;ki: rnd is essentially in a v+n ki9fly3 t;gzn :r4jacuum?

According to Eq. 7–5, the longer the impact time of aus */c9/ csnufta)t 4an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate aatcsunuf4s/ *c)9/t during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possib:toy1 b8z-9rug)pxc5i msgt9 le to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impapt8sx1 bugc iyo- g9 :r9)5zmtct. What is the advantage of this new design?

Why can a batter hit a pitched baseball furt 7f ale- mj3vmc7,q(.4jnkcihher than a ball tossed in the air by the batte4e ha.fi cnjkq-m(v3 lj7cm7,r?

Is it possible for an object to receive a larger impulse from a small force th b :a 6.:zmy4rajkb4uelp9bw wte2 :h:an from a larh.pab: 2 mzwy4e:9w6br::jelu 4ak tb ge force? Explain.

A light object and a heavy object have the same kinetic energy. wrr :2/ppxip3mcw a 1;Which has the greater mo21ca3rpr w ipw;pm /:xmentum? Explain.

Describe a collision in which all kinetic energ kmr3w(d/ *bjq b/nu(bc 2fs le534fddy is lost.

At a hydroelectric power plant, water is directed at hig8z0kmgcirakq h4(x // h speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine bladhg m/zqkx/(ir0c 4k8a es be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a cb lbz jnhx 1)v768:z*(pvzzw dw,e5l1 y:lsu45 $^{\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 lhfh :2 2n9kkyh onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed.lyh fkk:92 2hn (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 j k7, 57qcw .lboku4qpwhen carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mis+,pu1)jac fe d-point, whereas this is not true for your arm ac) ej s,ufp1+or leg?

Show on a diagram how your Ct4 c3r/jbed d6ynmj2-M shifts when you change from a lying position to a jtynme j/24 36r-db cdsitting position.

If only an external force can change the momentum of the center of mass of an ob dscks r2;v jyjeb8(eg5.xj//ject, how cjdbr ves;e2x/s c/k(.y8gjj5 an the internal force of an engine accelerate a car?

A rocket following a parabolzlr* *y4w;q9cpm /exu ic path through the air suddenly explodes into many pieces. What can you say about the motion of this system of qcm*wz*;/4 yuxlr9eppieces?

  What is the magnitude of the momentum o1-bspg,. rek) kh9diof a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg sbx5w fb+0 ;q qoqp;3qskier for 20 s. What is the sk;bps b+0q wfox5q q;3qier’s change in velocity?    m/s

  A 0.145-kg baseball pitbrik08* c 9ejni6mw1 pvmvm1)ched at 39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact tvw8i11bcp v 9mk6m*iej0) nrm ime 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 p o4yu6f:; pqzqackage out horizontally with a speed of 10 m/s Fig. below f4 z:6;o pyquqCalculate 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 on a rocket, gi ++ gai06fx+ .5mnhsipc bz4flven that the propelling gases are expelled at a ri6cf+hzlmxi+50 .+b nfaps 4g ate 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 a f9t)m r8hle2ct $4.1 \; m/s$ 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 frictijq:oj iuq09/4dmmx2/fbsnwe9 o7 ; hfonless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s ne b: ndu724m ;/ofsqjhx9ie90wjq/of mw speed?    m/s

  A 9300-kg boxcar travelb.p 8dcpjc40r /qq qz.ing 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 can2kcq9-f-x r*vmz jk e/ whip 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. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximuekz m/fjr- 2-*qv9x ckm 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 cdkn/g un ho+2v4.whc: ky-d*along with 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 i4kwn*-dhcu:go v2 k.ynd/ c+hs the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alh lec 02xcbts;wm9z.f(v 3.x+ t*eye jpha particle in the direction of its velocity, and the r(+zthj3cvl 2bs..fx c9 *wy;me xt 0eeemaining 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 travelinizxn0-ef+8h9 v shqtjj ;u15dg 230m/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is statisfz8eut-5ih ;qhdj9x1 v+n j 0onary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at ab-z7 s3pz1r zn 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 travvsc8.jkrb.z;kl.rp/)x 6 we celing in outer space with a velocity of 115m/s To alter itwlrp /cz)j. ks8x.r.k; v eb6cs 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 of 45m/s The g m02 xr+b4lp3svdkh ,kl/lcc ;olf club was in contact with the ball f;+k0slbd h c3lp m,2 klrvxc/4or $3.5\times10^{-3}$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-r+-,/jv , lzbay zdd:f i3 ia6hrnt4i/s and comes to rest in a time interval of 8.0 ms. (a) Wa6zdi/ f:,ylnaij-rb4v+ t d3 ,-i rhzhat 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 mass m=0.06kg and speed v=25m/s strikes a wall at a 45 w:j 9g-xfgncek6n2; x$^{\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 newbf3tt:vdt7zi4r:oh ht/i s4p) sg +u) automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s frout)+4/hhbt r p:iftdi )4sos3zgtv :7m the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the eastst+sfn. pgcz9nh b/ ;wp, -ll0 and is stopped in 0.75 s by a head-on tackle by a tackc thp- b,l nnf.;lp 9+g0/szwsler 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 1e ey, l-d4pxbp5c0e:j8kbar tennis ball (mass 0.060 kg) points in the +x direction and is given by the graph 1jy a0e -:p85c4ek,pr xdbelb of Fig. 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 wi-v3f d7/a0nvdpw r(o h8dc2d ethout breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force8 7(0/3vprwh dfddd-2enavco 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 (.t/;l lryodr kg moving east (+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 aftl dr/;t (yl.roer 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 xy*ge jmnmj6b; s15g,.8um; klry e u*a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuu6s;mmgjx re; ,5yu * mng*e8kjly 1.bming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent 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 perfectly elastic head-on collision.h6t 6oi4 )smia 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 ahit o) s64mi6the 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 of 2.5m/s collq*nj ivu tf1k(4pfu)1 ides 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, whatifutfq1)j1n(p 4 v uk* 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 spquc3h*do,:ph31m h2b6b mnwg eed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3* hm3m dop 1hb6gw:hn,ub cq23.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as onei8cjg(s,u q xyb4t, /d approaches the other d, /,itcb gsu(qdx84 jyirectly 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 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 elaq1su. z8g/dega t: 1jkstic head-on collision with a second ball initially at rest. The second ball moves off with half the otdeqs u:gg k .z18/ja1riginal 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 asxr4 rsl0dj0qhb5;t p /s0*d 4 junl-ng shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does 0jrns/j h5nl 4dtx;b* grq00u s-d pl4each 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 of mass 0 azhaek 3i9,bm$_A$ 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, projeckiv3u,4ccl+)qu 0jn ctile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A seconi4),nqv0l u3kcj u cc+d projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg penduk:jzy(:yz 6fsgw rm3,lum hanging on a 2.8-m-long string, which makes the pendulum swing upward fmsw:r,(yg z:zkj6 y3in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fra9f;fx z z z: ;vwey9zl14aid/dction 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,(q)mpbkarj( *dsz*zj ij n/2 2o m:7ya 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 kinetic energy did each piece acquire? (Let A represent the heavier par :kr pobmda2ma(/zy*jni qz*j() j27sticle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into thq av5x- ;;e1i gzogll(e 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, knolaxe5(;li-g1vzo gq; wing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height of 1.2s6mfv y:6m1c fp5w9dn0 m. Approximately how many rebounds will the ball make before losing 90% of its6f1sn:6dp9m ywf cmv5 energy?   

A measure of inelasticity in a head-on collision of two objects is +x2(v1aw7 oujqk1 jdvthe coefficient of restitution, e, def(a 1ov12dvwuk+j jxq7 ined 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 the nx,ief5kl:,c qoch 2+other. A depression is made in both faces of the cut, so that a firecracker can be placed in iekh:,q fcnc 5l,+xoi2t 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 q-.m l4( ey cae59fmgo*z0nmr +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the - (e0m9zmygr *aeo f-qc .54lnmx 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 nucleusy5f iow j.jw);, an electron, and a neu5ywjf o.)j;witrino. 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 mass rqjf (vpm+ .ule+nc e81 i (3fwyqf)g3$m_\mathrm{A}=0.400$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 o9+r). jzj e* nyen8ctibjects of equal mass, each having initial speed the two move off teez.j*9y r+ )ncij8ntogether with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at rir/fz q(siqgl rv*2r 8; .wxno6ght 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 elastioi nrs.fqr8*rzlxq vw/2 (; g6c, 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 collisio:tmzz nh87 j/j5 ywv p6a/klu1n with another atom at rest. After tht an8v kjuj 7yw /pmz/lzh561:e impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision with another atom atih ph gx-+i3(qe8wog kfg,n*d:pmd(- rest. After the impact, the neon(:h8kg* ppiwh qddeg(g-n, x- 3i+omf atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. Specify re9(jnu6d ax 4melative to the xajmd9 6 n(ue4left-hand 1.00-kg mass.    m

  The distance between 19uqv mihjqf22.fu ,( qg/ypaa carbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) 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 the front of the car.on-kcc*ml+t 9sxal sz4 4t *s* 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 that each person ak4* * o9*tcns cm-stsx+z 4llhas a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is -1i2* dniae du(/bfg dused as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW c-d gifani/2*ue(d d b1orners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side9uai+:bs)orxe 1;dl+ 0bmdh ms $l_0$,$2l_0$, 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 tomato paste (see9ne+, j0k o,ra+jcr .lfgqr5b Fig. 7–40), each of which is jr.b,f c5+qlnk0+r e,jo9 r gaa 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(w )a/ ;oddropvg;a+i of radius 2R has a circular hole of radius R cut out of it. The center of the smalli/(p+da;w o;vd)ar oger 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: Try subtraction.]   R

  Assume that your proportionh+s5o hm .r:e;u,ol pns are the same as those in Table 7–1, and calculate the mass of pl+hhe:.;oo5 m,ursnone of your legs.    kg

  Determine the CM of an outs44icq rq/q- bn pi/jec4/au9e 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: he ;s wj)m)eb/rq0ry the position of the CM of an arm bent at a right angle. Assum:;r /yesb)qwh) j r0eme that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hanginbrwv.12q)x j hh 6*r xn- w:cd6ncnxc(g vertically, and his trunk and hrvqx.bjxrwwh( -dn2n)1h 66n* cxcc:ead 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 Earth and Moon arelx/+-lj(yp- dij xn6 g j5z2mk $5.98\times10^{24}$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 apartgbjy .ean +ez2.ruu-on- b3 j; 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 2.00zeat,8 badp d 1a3:jh5 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 handlezped b5daj 8t a,1h:3a is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical headbikome/2oo ;.g)n es. 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 para;i)mo2oge kn o.bs. e/bolic trajectory?    d    d

  (a) Suppose that in Example 0v yt p5 ( zw33+/au1v)nfbh;upkzc da7–14 (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 massp r- p3bu6 (m6dsauywy8ys78i 0saa1t M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?1i6(u07aaywbup dat y3s- m8p8r 6yss

  An 0.145-kg baseball pitched horizontally at strikes a bat ameo7ut5bycw bvq +a6nr764o ,nd is popped straight up to a height of 55.6 m. If the contact time is 1qw 5+yur,otbm o7 nvac7e 4b66.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speed 8*tw:wtc 7 n7;uaw(;q qtahk j$v_0$ 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 show;nj t ;d:zxe-on in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” n;x-eto :jdz; in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including spacemsfv96a:25 v wzni y0z suit) acquires a speed of 2.5m/s by pushing zn2svv m i50wz:f9a6y off with his legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, jyh-9bu mx+rl mqr1np(l e-;.are initially at rest in outer sp ye+1buxr.mpl9;jnlmhq- -r( ace. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a secr0 +gd e9jwp8zond ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original spe zgje rwp8+d09ed. 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 court case involving an autom1xc;lhlq- 4 t1tr* xzhobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying th 1l;lxzxt1* r 4qht-hce brakes.    mi/h

A golf ball rolls off the top of a flight of concrete;z( :t(grd4 lui jna,p steps of total vertical height 4.00 m. The bgpl 4u(ta;jrin d :(z,all hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into 0r+ 8hcq xwg.x0vat1u a 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a spe hqw80x+ agtc.vx0ru1ed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-k8 pz jrk+)ysa-0ty7jl g 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 impt)p +jjk ar7-yzy0sl 8act 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 7jjief1h/ep. 2dl 0q*)fov dqother 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, edlp7.q qjfh/)vio e2d10*j f now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abk7p z( (qyfwc.out $ 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 apac43kuo72eik b 7-oiy bs7 wdy2rt into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other.2ks-c3dybikoo477 wi2ue y b7 What is the ratio of their masses?   

  The force on a bullet is givenk n; a877nblr3ed g*xy 5p9qvk by the 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 rle5p0hix/*i og 8 lk3$m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha pae.szi bw06.k cs )irc27oa iv*qt ;*qsrticle and a smaller nucleus. What will be the qi.6q w0z* )csovi7rc;ssei*tk2 .abspeed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay targrf 4l2ju:tcg ;et) is fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg sli, bbi 6mi3p,cp:cm1bkdes 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 lim jmios*8: c6icit on mass m if it is to rebound from M, slide up the incline, st8 j*:ociics6 mop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot e)zlrs;i s3h2iffect. Figure 7–47 shows the planet Saturn moving in the negative x d; li)zsh3 irs2irection at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s