We claim that momentum is conserved, yet most moving objects eventually slow4u yjjy(l5w tlhc8v8* down and stop. Explainlyhy4vc*j8 5u8lj ( tw.

When a person jumps fhd2j . nvczkloo3. ;p4rom a tree to the ground, what happens to the momentum of the .z cl3jpok4oh;.vn d2 person upon striking the ground?

When you release an i;s wcsz+,;lsmnflated but untied balloon, why does it fly across the room?+m,s;wz;c ssl

It is said that in anm5 -fnn ,a8kgpcient times a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so 8ng- a,nmpk5 fmiserly?

How can a rocket change diree).a)okl r/o7a d(lefction when it is far out in space and is essentially in a vacur lo) /(. ako7d)aeelfum?

According to Eq. 7–5, the longer the impact time of l9vb n 0swgs-:xhr g*dz*u2.can impulse, the smaller the force can be for the same momentum change, and hence thdgs xu9h2g .l:**vwb-n c0rzse smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions yse204zl1to1bfg d k jxd2,nhy1(.xf. Today, though, cars are desih1dfdl1s f1tyzen2. (k 4 g0 oxx2yb,jgned 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 dd xm )tnxtfb /inw/6j5x6ia(8n*r y( 1l/kbqthan a ball tossed in the air by the 5iix1xn*tf 6( ltyw/dkqb)/(njx 6nmd ra/b 8 batter?

Is it possible for an object to receive a larger impulse from a small fx lj10s;m2juj oy a):dorce than from a large force? Expj sm:10a;u2 y)jljdx olain.

A light object and a heavy object have the si-51ps ndz6-slfm,j cpa45cxu() r baame kinetic energy. Which has the grea-xj m)5cs,p( lfbp6u nia-cd15 zs4ar ter momentum? Explain.

Describe a collision in which all kinegnq . xpvdgv:vp*upn,q-b/7c jhi. 7 4tic energy is lost.

At a hydroelectric power plant, wa gvq/7d4(v ysyter is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the tury 4 gvq/(yd7vsbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wala1m. p pc ;bkcr,2vdnp o1gd10l 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 h z -p-in3k,zhtard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piecpth-z-ink3 z,e of putty that falls and sticks to the steel plate.

Why do you tend to lean backwa r(y8 qh pbwx()io-6rfrd when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas thzl zz (*g3w) hv.++zd6gtmfguis is not true for your arm orf(l.+z)mu6whg*z+ 3v zggzt d leg?

Show on a diagram how your CM shifts when you change from 3y+ jfo9)t bp rz+ cdlzvg/ a+ph/97kba lying position to a sitting pospt7vgy9 3jhczzb/a/)lfop+ br+k+ 9dition.

If only an external force can channlwf96))t-ay - is z6v x2tljdge the momentum of the center of mass of an object, how can the interd f)j) yxw-tz6 a9v6n-stll2inal force of an engine accelerate a car?

A rocket following a parabolic path thro :2-ogtgj y1nrugh the air suddenly explodes into many pieces. What can you say about the motion of this s12 -tng:y jgorystem of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying+hqdx;a8m r7d 6bv(z htsst 08 with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kk:dq0 tn7 z 5ns6t sq-6leq0qcg skier for 20 s. What is the skier’s chal6 tq7t6qes0nzs 0 q5: cqk-ndnge in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m(poy-9(qkay x /s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the c(qp ao9-y(kx yontact 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 horizontf-qqeqn)p)fo61 a rs+ally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it wasoqa )+rspne) f61qfq- 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 ach:241bos -g an7xurm rocket, given that the propelling gases are expsxcna g :u-r4 bo21h7melled 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 moving a l x::x4df4q95ioso owt $4.1 \; m/s$ 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 ca8qf ,r 2jnlx*pr travels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is r fpljnqx, 82*dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling am,j/lidn/g, l t $15 \; m/s$ 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, windh s4wu/v; tjz)s can whip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high ;t)zsh4/vu wj and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of 168 -5chhorj u.ukuc c8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after - c6u j5h.k 8uuh1ccro90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an al2ds;4zw ivf 5fpha particle in the direction of its velocity, and the ;v dz5s fwf4i2remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penoibk80qkkx1 (etrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surik0 1bx 8qko(kface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is trave1rscr*goe6 *bf5w1,ga h2 hxfling 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 +ge/ )qbow2ncnd,p h3with a velocity of 11cw/d n+e2qg ohn3 p),b5m/s To alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed of 45m/s The golf cl0y *i:t-gkh eax93+hkvcaa9xu fc a15ub was in contact wihh1c*aafkak t:i x59+ -9xg3ycae uv0 th 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 uyha *:ld-y56tnpi0 h dg na,(nail at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the naiyy65tgnu:( anpl,0-dd* hh ai l?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass s jo,:. 7pzsbp- ua5jum=0.06kg and speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of themr6 4edhh i;(xcnjnzir9225k crashworthiness 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 takes 0.15 s f2;h459rrz2 jcmhinin(e k 6xdrom 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 gs7uhy; (bdd9 in 0.75 s by a head-on tackle by a tackle79dsg ;bud hy(r 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 tenbh 3g2l+k u+krnis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function ol + ghkb3kru2+f time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking the lower leg a+a sh,vr9 ycs(v l15cbone of either leg? Ignore air resistance and assuca alv1hr5y,s v c(s9+me 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 a speed of collideuzb 8g1gie+t 3nva,/b-v zzdb6p( 8trs 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 Bgzarz (,z1bnvd+ 8bv6i p/-8ebt u 3tg 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 /x.vcwg/sa 0 l7p3v.itodz 9hv5ly4r 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 direction of each object after the collision?Let A represeyl/vxi hw./34o p9 v 0tc5s.zavgdr 7lnt 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 ol(rq9/ s+;qis vg6nktf equal mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collisit(9/nsli+rsv ; 6qgkq on?(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 of 2.5m/s collides w-xnp1 xehgkwl kh(htq 0fi7gi-7,r,w/s 5.dhead-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.,qhx-- fe 0dlw/pixhg w(sihgt7nk17krw 5, 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 mxlg 568(qee6z snjo j(oving with a speed of 8.5m/s collides head-on and elastically with another ball initially j5xol8g e6 6j (qzs(enat 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 park ride collide elastically as on *xa0kq21fikplf q,-p2gnt k9e approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 *2 1gfkp, -2fxp liq 9k0atkqnkg, 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 elasticc1 c aq +*y.,v5jyh4gzp.*1rt kd8gl mp ryv6l head-on collision with a second ball ini*4dvcgpyhm rl qz6j k. y.tl,8+ 1p5raygc*v1tially at rest. The second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictinuak74 d.) layonless incline as shown in Fig. 7–35, and elasticaya4l7) a.dkn ully strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an ob2+i)o5k x o9k;p:mvbw mx .3*nkumm cjject of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile )h nm8-d)2+ydoqllhb 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projn+hd 2dmlbl )y-q8)ohectile 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 penbh1y 3ss2,fq sdulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine t hsbqy,3 ss12fhe vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the8pqpj 4 )xrzj aj43e h8z6fx4r 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 oblkzl k.tufm 7)y: f-r8ject, 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? .rtzfku)8- 7lk l fmy:(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 rear end of a 2300-kg SUV stopped at a 4mvd qk/i1rp w(/wxn7red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic frict4/7vdxik(/n w1 wqpmrion 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 fro rru8)j7f)vfs9dye 69 ipan6am a height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the bai6pvs frauaf98 6))y7 j9nrdell make before losing 90% of its energy?   

A measure of inelasticity in a head-on collihe-id qi5 topt 31-,gvzf,ib 2sion of two objects is the coefficient of restitution, e, dedi,z 5tg,i ve1oqtp 2b- i-fh3fined 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 int6-j.ij el01l ,hl9z0 ic u.em,uuzhb th.t:ofo two pieces, one with 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. W lhu1eh9clu.0:06hzi i.,f,t.juez mjbot l -hen the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x directil )siaa u0y:)o5sp b*jon at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of ea )supy s )oa:b05*jilach 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 nucleubovl+y ac lacf4j5;1f t6a*7rs at rest decays into a second nucleus, an electron, and a neutrino. c* 6tlay fjl7o5 a1+4;bvrcaf 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)d)ttzl yb.ad, g,p9cw, q;an s $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equalcso r6dg,o)z0nl m2 tx./;dx o mass, each having initial speed the two move off together with speed v/3 What was the angle between their izm6 2x)r 0ogx/dsl. o,t ocd;nnitial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the 7cm ;z o rnr;8 vh88hm8w6alamorigin 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 t6 z cmrw7a8hln8ah; m88vmo;rhe 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 2 zpgsxf aj-1p6g 9gk7perfectly elastic collision with another atom at rest. After t jk 2-6axgpgf97 s1gzphe 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 per 57bpyz ( ex4xor a,;ukm7tvpg764 dmyfectly elastic collision with another atom at rest. After the impayyamkmz6 e7txorxvp457(u d b; p4,g7ct, 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

  Find the center of mass of the three-mass systei ot )hngy)q -qb/8ho. lyt,n:m shown in Fig. 7–38. Specify relative to the left-ha qyb)ottqyh.:) oli/ ng-8nh,nd 1.00-kg mass.    m

  The distance between a carbon atom m)clh24jr7fw0:m z da($m_{\mathrm{C}}=12\mathrm{u}$) 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 ckhdy4fqaa9 qbpq--p:-2 g0tt,bew9 bar. How far from the front of the car will the CM be when tw-f-q0kp t:92gyh-a dat9bb 4epwqq ,bo 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 m, of mass 6800 kg, 9-gsf)sm 8wtt 8gzi v:is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the g98tt)s-z w s:m8i gfvloaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidel/k/ bs+ht*ykehls2y02g 4k ks $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases ofl /xy9pps k*y: tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of graxly*:9p spy/kvity 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 p 7qo5eo)g3j jmhq) le*late of radius 2R has a circular hole of radius 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? [o7q 3) eqmgl ejh*5)joHint: Try subtraction.]   R

  Assume that your proportions are the saaoghh) 2pv3piy lvv:d; ;h)b5me as those in Table 7–1, and calculate the mass of one of g): v 2dlb;yphi)h3pvo5h;va your legs.    kg

  Determine the CM of an outski+h*;1v/m qj 1 b9fftjpqnh5we 5w. wtretched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calku-/gw) lit49lf rn1ae w:nn1culate the position of the CM of an arm bent at a right angle. Assumetnl:l4i1w-ng/e a ruk9 fwn)1 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 s3ohajv38as)qda2u ly. l)r3 and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the l)2sar83l.ou 3yd hsqj3av) a body? Use Table 7–1.

The masses of the Earth and Moon are/h r:c6y1: uzrdnw;k n $5.98\times10^{24}$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.klx 7 kg5n+ psvd35c2lwl7w4d0 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 masj ip3hj*l cl20sr8tf b1n,l s0s 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 parabt ls1shl* 38pj,lfb r02j 0cniolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass m* 2)d.mpqc zj2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 pcm.* jd2mqz)kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in E.wkkeo(lpao-p,a k3x r)e) b(xample 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and mjiu oz.:)qq(i a..- kwj(azqstationary 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 mov(qo.zu jki.:q )-iazwm jq(.ae? What happens if the passenger stops?

  An 0.145-kg baseball pitcpirppuv8 :1hhdt+srpg,,)u ) hed horizontally at strikes a bat and is popped straight up to a height of 55.6 m. If theud)p:,ir h8hpprtug) vsp+, 1 contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with sp0pz8pa3be)(oz-oa apeed $v_0$ 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 ss )ao5b3hxxa 1hot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball) xbx3a sa5ho1 will also fall into a pocket? Give details.

  A 140-kg astronaut (6*)qhx( 5 kmpvk /2ay5yc.jz(kdf fedincluding space suit) acquires a speed of 2.5m/s by pushing of(*6 /e. ajyyzdm 2fq5xhv d5k kk)pfc(f 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, are initially at r2u nld51zp jc9(q2lngw j5v jeij7 67qest in outer space. They then push each other apart. How far apart are t5lecwqv(9226n 1ujjjp z7 nql5gdj7i hey when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision wiz gez5uvx:-qr6f s.6i),swnv;g gk8nth a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the ma8k 6xng :i; ,f.v5 gnz)qzw-vs6seugr ss 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 auy,hg )(5ez xbz1 3o8v ozvw0xotomobile 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 driveox0o)g1yx8zh3 bzveozv5 , (wr 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 total ver; o8(auecob1htical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part ouo e(b8oh1c; af 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 bloc nq0j51:of9;kg novjwk of wood at rest directly above it. If the bullet has a ma; kjoq:o nj1n5vg9w0f ss of 29.0 g and a speed 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-h; ff)r om0:;o mlm6do23juyn kg block of wood placed on a horizontal surface just ino)6rj;omfm m 03ydn;2 :uohfl front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other ; pj mwa54u;xsbw3* laof 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 exchange seats. How far and in what direction will thew;awbmx 4 u5l3sa*; jp boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was9 q2hgky0na 5n about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments by an explosii75,oc,ew7j qc +qcd:y4jk jk +jz3ipon. One fragment acquires twice the kinetic energy of+ 7j,5 ij4e+pc kwo jc cqidj37,zyq:k the other. What is the ratio of their masses?   

  The force on a bulletzv6 hbtc(* y8o is given 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)de/6bj9bpar l-loz mdj dw4t3a-j4 . $m_A$ = 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 rad9;r+(mr;bep y+z /ieqr9qv0qe,i s uwioactively into an alpha particle and a smaller nucleus. What will be the speed of this re/q ; +rmi +pqr(eibzw0 ,s9eu;eq9 ryvcoiling 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 fired at an angfu) hu 6 g4lbwn*xcgf+ +jty+/le of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.dov *1-gk yy-ubpu*7m 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 rebouty 1 0/n4g8rv6wxqe .li4y4uav-r *m2p hltlbnd from tvll /p8.vtx4i6bw q l-m1nru4r4ahyg0y*e2M, 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 tj1d ig /0rnr5che planet Saturn moving in the negative x dir/jn 0 rr5id1gcection 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