We claim that momentum is conserved, yet most moving obwyvs )aro023 kjects eventually slow down and stop.w0kvyas3 o)2r Explain.

When a person jumps from a tree to the ground, what happens to the momentum yj zyent/8 24pv+g/cu of the person 28gtjcey/npz uy/4+ vupon striking the ground?

When you release an inflated -smzmp+8ni81; 8z p xtsvdd0d but untied balloon, why does it fly across the room?8; + t1ssdp8dmnzm0vi xp-d8z

It is said that in ancient times a rich man with jzq.- m denxh3tp+z7: a bag of gold coins froze to death while stranded on a froz - 3dmeznq:.jx 7t+zphen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change directioi at*,pyha4:x n when it is far out in space and is essentially in a vacuu axa*:h,typ4im?

According to Eq. 7–5, the longer the imub hypk 3gusm dyz959+l8n ,1hpact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to h+3 dpkmgn1uu9y l8bhz,59sy inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as ri0ns pn(jk16f p9 ,algigid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapj pp (n lfa91,6kgis0nse upon impact. What is the advantage of this new design?

Why can a batter hit;ic;lc 8qyii 4 a pitched baseball further than a ball tossed in the air by theiqc;i;yc 48il batter?

Is it possible for an object to receive a8 zwn/ .uy 8jxb,qwgp6 larger impulse from a small force than from 8wn jxz 8/ wy,p6guqb.a large force? Explain.

A light object and a heavy object have the same kinetic 4mp6t* yh juo0bz+c7 wenergy. Which has the greater mw4jm7z+yoct*pu0 b h6 omentum? Explain.

Describe a collision in which all kinetic enezbxrozrg st4( w,ckp6*;;5 27lvon ihrgy is lost.

At a hydroelectric power plant, water is directed at dv6vn45 ktj2z; c)za qhigh speed against turbine blades on an axle that turk6nq; vtc z2)zdj5v4ans an electric generator. For maximum 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 w z4;cis,h )4gjpt mdwoei3 z35all 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 c5/u9d 0w4ob ujs, gmm(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 that falls and sticks to the steel plate.c/uums5 db j0 4,w9gmo

Why do you tend to lean backlg,9:iecz- e oward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-pointqxtqlp7oeu/ kox ul zsf2,6, 51;m;dz , whereas this is not true zuqs, kz5pe xlo/md172f,l6o;;txq u for your arm or leg?

Show on a diagram how your CM shifts when you change from a lying position to pp-9rzm oe*:lt4cp.xi6owlzz7tv /. a sitt9o m el7: tzp-l pz ot.pxvicz/.r*4w6ing position.

If only an external force can change the mome1a3a7u jatte 9ntum of the center of mass of an object, how can the internal force of anaa1 att3 e7uj9 engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes in, 0ly(wkmszo 9to many pieces. What can you say about the motion of this k(yows,l9 0zmsystem of pieces?

  What is the magnitude6n uoyr rwpr+(oh;/ f-n67 ap5fe*gfh of the momentum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 /zga5a3k-nx*5c rx)zb8wp cj N acts on a 65-kg skier for 20 s. What is the skier’s change in velocityax g558j*bcr3p zxnw/zcka-)?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive vo1agps;+4 * 3* wuwpkpqz g)dstraight back toward the pitcd kowp41;z3wsp u* *+p)gqgva her at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a speed of nlg,ahp50-fwrq (bx8ka( 9an 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at ren, kx05 gpa(8n afhwb9qr- al(st. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gykvz;p:-:ccl eaz q7 1ases are expellee:kzq yp- v:c7zl ac;1d 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 movib: 7+yi xsjr(t z(i*glng 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 trav /8+7ty8:b6n gvieqwky d/hstels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is droppgd ise/ :y yvqktw h/n8876t+bed onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traf)z ijy d1k8q3veling 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 wh8:icx-y)i jeafxs ,2h*l9 a whip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per squ*2-i w i:lj8ha 9sfch)xexya,are 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 alons :crz oa,(l5jg with a constant speed of 8.6m/s on a level track. Snow begins to fa,5j asclz(o:r ll vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initiallyl-k6cym-e.a0cpnuvhi yi2e 85-bkk( moving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus hasyv-h2-06 .8(ckuyak c-iemelbpk i5 n 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 pe ins:w ,2ze/ o/z(x2*v zriyg 1qjm*ilnetrates a 2.0-kg block of wood and emerges cleanlysn(z/2gm o* ljv iwxyzri21/ i,e*q:z 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 tra5 9w oc(aej58xrbce 4vveling 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 velocity of 1bnj.91p vf o0e15m/s To alter its course by 35.0 j1vb9po .e0fn$^{\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.n6aj6 ;slp6 .e-vi )7 xdkxrswkk88f v045 kg is hit off the tee at a speed of 45m/s The golf club was in contact r6)jx 8ipkx vk sfke8a6wv;.7ls 6nd-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 7p(l;igg/v c yvelocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) Wh7c/ yglpv;(g iat 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 i,zs+iy)rom1rrs4:f speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashwp)c*,+let:dh 2a*m *(d3 zhlqrljr nhorthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takh2dt:l)h3(ad+ m*crzqnj * lr*e,lphes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in 0+al2p xp o.p1.1oeajgudce 7-.75 s by a head-onlcaxaj1p71e-2doo ep+p ..g u tackle by a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points in the +x direeop vyrjkzzgw e o1;3m,+b3s e+39 t7 4mylq6oction and is given by the gytqy6zo9 3m,o m 4 l+7wposgb1eejr;3vke3z+ raph 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 perso7giel g ljv8xgkv85x hrg;*.:n jump without breaking the lower leg bone of either leg? Ignore air resistance and assum.8g :x5v*glvxk ;hir78 jgglee 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 (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with rxn89, q+e mvm 89mjcua 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 reprecxe89vmju+9nmqr8 m, sent 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, movofez0p0e4 r6b ing east with a speed of 3m/s 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 dirope 0rbfze604ection 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 ehrxu ;ga:p.2 j/79 h9es kvsstlastic 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 bax9 29:7shs p/t r e.gjuask;vhll 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, mf e*e n(i6fs** 4gg)l4x p d.gkx h3a9gzydy-zoving with a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.09 gy** 3) ly-gixhgdx4s9azefd4fg*n pe(6zk.0-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg x1rrl0,s7wg 4q hl d88z9 qaynthat is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bw1lrq r 98y70s a84z gdnlxqh,ounces 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 3m*cj41d* 9niheqlu d :,zradamusement park 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 dm1z dhl*ajuq3die, * n9:drc 4ifferences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a sen 9v:+x6 xdfdlcond ball initially at rest. The second ball moves off with lf d9+xdx6n:vhalf 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 shown in Fi;ulvjb)drk; tae- f-s ;f/kn4g. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [ ba; djnu-f)l;; ftk4ve /-krsHint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an objr2g2p h r3 fy2*yi3fb-;o fe5)earsm fect 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 expepf8y-o1 b ve 7.dt g8 :-kydcpux6r1nyriment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A se-xy:1d 76ngy ty bdp8erov-uc1f8p.k cond 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 it*k gec;rk) r1a2ru7uy d-z7qkb4g 2 xhself 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 horizontk) bg dy4 rr2ue7;7c21-xu*az q kkrhgal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for thedu l:hi.*ewiu,1 +,k6vg gcpt 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 an ob:ese5my3hetkgm7v*wfp kt, ; *2kk9uject, 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 particle, and B repry:m, f2v eekpkmtgs7 khw ;kt*39e*5uesent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stoppedi6rmfj (ain)* at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m beforea 6i( )nj*firm 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 the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height of 1.20 lq6a.s .n syos8f0p6ym. Approximately how many rebounds will the ball make before losing 90% of ip nys0q.sa yo6l8fs6.ts energy?   

A measure of inelasticity in a head-on collision of two objects is thqiw8 efb mvsy-/x3/ 6gkpe(-i4xa zt. e coefficient of restip(zx egi 8 6-xykmwi/eqs.-va43t b/ftution, 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 timeslyh2rscy *ber*u 5( o) 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. What is the rati(r 2b*y 5elhurs*c)o yo of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at egu /.mboq(m7n5 .tacz8:koh 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the fina neqh 7(.muoz: ot/8.ga mb5ckl 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 in x 8bd -nymto7a6sh2)zto a second nucleus, an electron, and a neutrino. The electron and neutrino bod xn -t7a6h28ysm)z 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 massrox 4 .+,u-rcfazpbrwa id :)/ $m_\mathrm{A}=0.400$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 colli-prob0 yw-grhgp : 05 sk)2gjksion between two objects of equal mass, each having initial speed the two move off together with speed v/3r-5po k)b2gwjk hg-yp s0g:0r What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal el (+l8wc9c5pscwg2oir3;u t mass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upw suicec;35(clo w l2+8rt9pgward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision kctu -t oqnhngc71*vpfx-mg5+ t:7h .with another atom at rest. After the im 5hcg-7t.m* f :kv+ptqnoxtc-1ghun7pact, 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 perg8dmrse1x7 7w t1pkw7wj n4kwd2je8u b.9 g v)fectly elastic collision with another atom at rest. After the impact, the neon atobew p gtgnws1.wdm2)v8 jd877k49 r7w 1euxk jm 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 /j73xx-dv h2ciz5wh1ag0 km w in Fig. 7–38. Specify relative cizj-amwhxgdh/30 7x2v5w k1 to the left-hand 1.00-kg mass.    m

  The distance between a carbon atom (ga5dm e;f3( sp,/d:tuhnv/h sg 9mo9ivth p+7$m_{\mathrm{C}}=12\mathrm{u}$) 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 r:sje*q-xfoy m326 hlkt 3zm4 is 2.50 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and *me3 zk lsomx4h:r q6fytj-32three 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 m, of mass 6800 kg, is used as a ferryboa5j3 9xrh54*dgiqmu3 -t4eqqs 4xx hbat. If three cars, each of mass 1200 kg, occupy its NE, SE, andt4 bqerh5qs4x-aiqdjm43 9x*hg 53 xu SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides qpo b:qq:m g1+$l_0$,$2l_0$, 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 pas/y-ti :nfu1h gte (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-nu iy:h 1tf/grane 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 * 1tpni3nz0 i 8cbhfl4radius R cut out of it. The center of the smaller ciclf40tnz3 i i*8pbnh1rcle 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 proportions areoi 1p;xhh xd2q3d +v6l the same as those in Table 7–1, and calculate thqodd2vi6h1;x +lp hx3e mass of one of your legs.    kg

  Determine the CM of an outstretched arm using g +5 suzdw:hv6j0hvc5Table 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 at a rig. d8 :4f)wgj(arquec-1s guemht angle. Assume mu)8qe:g 1d wgr je-a4(sfuc.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 3f-heg tu8/urand legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’st/h fur8-u 3eg median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and w)j41v3 bw bxci el;zolf)q )-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-k+9v b8 v6ny m+dwyram9g man stand 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 cylindrical head of de1b 8w35gn hhyz8 d)d.nijwl.*fey) mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of massnbdezi8 d )lw1e3.*nh jwyd8f)g.5yh 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?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 k4l*a i9 xo*5xqeo,ibf +9fr nkg 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 wl*q*,xo+ fe49 9xirboknaf i5ill follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig- k3ul: nq9r.jf ned6j. 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 staxqk rwpk ybh0,z.e;zyaw*74+la 7/d jtionary with respect to the ground. A passenger, of mass m, then climbs opd hlxk +zk7w7z,*.rya jqe y40aw;/but 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 pitched hori+k0h(( qmgc lszontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the bamk (cgq0l(sh+ ll during the contact.    $^{\circ} $

  A rocket of mass m traveling with i0c- rcq jkbt8xru:d i1 8)ck3speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown in Fig. 7–43. Ru,yek 4q. vpvz(la::yelative dimensions are also shown. Should the player be worried about this being a “sc: v4yazyv (uq,plk:.eratch 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 2.5 )6.ep nj3cms 0ip4zuq7tky(om/s by pushing off with his legs fpcjt4)7q(i 3 6u0poysnzme k .rom an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are initr 9yo)-llwh;.fi p 9f rgdfa-q44d1s iially at rest in outer space. They then push each o pr9ff qls-ldag9-. i y 4wd);r4i1hofther apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second y;d :mg* fun3zball (at rest) and rebounds in the opposite direction with a speed equal to one-f3fuzdy n* gm:;ourth 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 expxr5nknq 8uld5 */bs7 mert witness in a court case involving an automobile accident. The acmqxkn5n*r 5 sb/l8ud7cident 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 the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of tota7cm3ge l:frh j;g2lwwuknv d:6t; a)4l vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a differentn4hkl;c:2 :t 6we3l wa)gf7rv m; djgu 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 7h;d(l tkskmkva1h2(7/icra 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 after the bulle ali7sdh(h 7mv;r a(/2k1ktckt becomes embedded in it?    m

  A 25-g bullet strikes and beco8fg(h3p7zotp /vd s* /bzzx1 qmes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction betwee8fhtosvpg(1 qzz z d/*xb3/p7n 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 7/t8lro 6ou sekg and 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 sittingsuo 867r le/to at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abob,l+wtejpxh92 2 yje6 ut $ 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 sa : jjmdkh)hw x1o2pan *yyy::, mty+9uddenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the othery2h19n)m k:odyw*m h x+yaja,: p t:yj. What is the ratio of their masses?   

  The force on a bullet is given by the formul5hk;ls*j f7vhd7 k5wr a 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*+t4 (qynidta b-;mw3bbfx2c $m_A$ = 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 alplx2i9ff eba (l.) y9f*vl +amnha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of t )a9inyl +(* .lfmfv a92efblxhe 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 firedxne :0:.m p83heh5sjnqj i gc qd1e(1k 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 ukqbq7+r9 tc5jdpvl ) 0kluao( c4t/ 5slides 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), fqths1yo;ahlh ,u/27 i ,oe)ywhat is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incyq;7 21elu/a)yi, os htfhoh,line, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshoqsi j3uvgch p*2 uto0s t7(2d ;i98mpbt effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Suc308p h2potbvm *susd(qig9; 2 uij7 tn) 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