We claim that momentum is conserved, yet most movingco2 b4vg/t-oh7 u8vg/c;se wq v7fi.wko* 5fa objects eventually slow down and s*i;qe2 wvgahtwvo 7fv gc/-/o f 7o85 .4cbkustop. Explain.

When a person jumps from a tree to the ground, what happens to the momentumii0 a/xzxp)7 o;t;fv w6b/g op of the pers)/ 6b7 zwox0oai;ppg t/ ;fixvon upon striking the ground?

When you release an inflated but untied balloon, why does it fly across theb-sf f*,j , b5.gdfvap room?bpvbd j, 5sf a*.f,g-f

It is said that in ancient times a rich man wl*2*x3oub.vh,sp vk qith a bag of gold coins froze to death while stranded os3qv*b2 ovpx.hk*l ,un 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 miserly?

How can a rocket change direction when it is far out in spac pvx(2zd ue63j,bzcc2e and is essentially in vx2jc e dzbpcu,3z62(a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller t-flzs ,m4j i-b4.eue 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 during an automobile collbu s z.j4,4emei-lf- tision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisiocjt-daowe;t0 (z .e1d ns. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this new desidce( wdatjo10z t.-e; gn?

Why can a batter hit a pitched baseball further than a ball tossed in t- zjd/w4suo*8 kmd- f/7h ktj5yc4ntyhe air by dzd7uyt4 4*n 8tmck- yj-ojhf/k/s 5wthe batter?

Is it possible for an object to receive a larger impulse from ap0krf 2is wra9l5ii9z 3cr*1n small force than from a large f k c1s9lai3pn0 i2rzrriw*95 force? Explain.

A light object and a heavy object have the same kinetic (0 r/ f;6 r2puw+/nsjckwy0e-fcloaxenergy. Which has the greater moment/0cxy;pw ef2+l njws ru-(f0c ro/a6kum? Explain.

Describe a collision in which all kinetis/,6 e a9o:prkof:ygmo7yb5 nf*x-v rc energy is lost.

At a hydroelectric power plan nf6o7ew -re8zt, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximue-ofw7z6 n 8rem 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 8k .lt+n;1xck tk gx8: ubwd7dwall 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 s6 j- z/xs2sjbuteel plate (fixed to the Earth), fromss u-xj6bj2/ z 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.

Why do you tend to lean backward when carryings(s2yukqmx2, ) thjo: a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas hlk+tp:gp bim 4+rz .8lsmf/8*eq1vhthis is not true for srv .hq/ft88 +ppih4lgeb:z1mklm + *your arm or leg?

Show on a diagram how your CM shifts when you change from a lgi5jn;rd; t9ek t0r d6p- 4eweying position to a sittink 6w ;r-;d5p4 geetienjd 9t0rg position.

If only an external force can change the qoz(5n7ogym.th 5 +gi momentum of the center of mass of an object, how can the internal force+h5. 5tgqyz(7gio nm o of an engine accelerate a car?

A rocket following a parabolic path through the air/p.x.396uc ca*ckluyq1h gw p suddenly explodes into many pux1u.3 lwy6 hpac*qpk /9c .cgieces. What can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flyin l)4zre 1,jc/l7td1gwob-xcj g with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 1tbww68ke4od.lv 8 s ur*x+ pc20 s. What is the skier’s *kpw81bd4slt.+ eru xw8c v6o change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a xn;hswt/hw d)38rfn*x2hh 4 uhorizontal line drive straight;h*wrnxw /h ) xh4dsun8h3f2t back toward the pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a speed of +; (zn :krhbjr3lnmcq*o9+gr 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it w+ qcjhm3br*9 z;(:g+rlnnk oras 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, given that the propely jvev:+w 8l9vling gases are expv jywv98ve+l :elled 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 nfg5(;.aoh 9jn y1jp iat $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless track with ajiy5bi d afw7h++7ky) constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s newk++f5y i d)jhb77aywi speed?    m/s

  A 9300-kg boxcar travelg )rwe- )95gu lrvgcqz o4(j/ding 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 whip horizontally at speunsx0nh+;gpxbqcg)lb. )og/2,t +mc eds of 100km/h If the air strikes a person at the rate of 40kg/s per squap,cu20nb+qtn gs+.;oc )l)m ghgx/ bxre meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along wiquewy85oo -0 lth 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/-oqy0w5o8el umin Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alphaoel29b(rf76u 2girngo89uu k particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a or9r8 69gubuo7u(nie2flg2 k 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 penetratwi4m.+ 3f7c wip.lo*sbg ob9y es a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on m s* c37w4.9g bfopb+ yi.wloia frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speed ugs.w 6j1,hnngs0akma 0r*.s 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 + 086/i*0j tt:e ;tq4up6 frnkht6afj uuxucr a velocity of 115m/s To alter its course by 35.xtu+4: jutu/6 kp e qunrc0 f6;tf8ra*it6hj00 $^{\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 kgu,6f3o7)lp4rk xakb n a.fu) u is hit off the tee at a speed of 45m/s The golf club was in contact with thn3r.6 )akuxf 4ob,a7 ) uupkfle ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and c(4 wal1ptb ql*mn32st omes to rest in a time interval of 8.0 ms. (a) Wh(st13 nwm*ap 2lblt 4qat 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 vxe( q zy(x-;rf=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 engineey qo0i hf5y)8dxi8hutm- 7xr3 7 (mi:hkfl gj8r in charge of the 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 from the th0 q7:xo8(yt8dh) fiimjf u 3ki7 l-my8hr5gxime 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 stocyej;/(m)r 0deag zh 6pped in 0.75 s by a head-on tackle by a taczm()6ee /ay c;rj gd0hkler 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 / z w o19hm2ex;fz0q/mlqh:et+x direction and is given by the grhx1/ otfm :w0zeqlhme 9 z2;/qaph 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 without w g7w 4mi/jd.bbreaking 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 brj7iww gdmb.4/eaking 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 movi vv (k,4,ybag(vnz 15g9az uzhkmsa*+ng east (+x direction) with a speed of collides head-on4z hzm * gzkk+u,ay g5vs,(b91v aa(vn with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a sp0sb 77sr0ojtc/m98 j kz,rjljeed 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 /sto z0jk mj9j8r077bjl, s rcobject 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 undimw2c varf5, kfe lm)kf3z/91ergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball) mv29fr3ef5,kl1i c /fwzakm 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 head-on withl.(bgy nvu/j1w0n5l kwboro6/ 0 g;qh 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 an./lj0 1l0bvh6 owk qwgnr ;g5noyu(/ bd direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s coozna (enm+-,av*uq3l s :lc p+llides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounceaqmo+nzlsec-3(l :p,ua*nv + s 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 amusementi7t)6l gt zy.z park ride collide elastically as one approaches the other direztgl6. yit7)zctly 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 elastic head-on collision with a seco jzf /bywoad* s)n8cd(rl (v9+nd ball initially at rest. The second ball moves off with half the original speed of th( 9f zs*yl c/db(arvwo 8d+n)je 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 snf t(:-,wl/0ue) qpvbq)yqbw,8 aheihown in Fig. 7–35, and elastically strikes another cube at tt (qbynalbi:q 8 qu)ef),e0v,pw /-hwhe 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 object ofj-z0/xf 0xa- bptog, u mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 r*1r6cu:5xnvt 3pz oqfy6c u) kesults in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twk1 vy o)6365*prftcx:unuzqcice 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 /-kfmwzrbqd8b c;7/s 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the swcf8/br /kmq -b ;7zdpendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energsz oa)*mgcjsw(d 8 -f2y 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, initially at rest, into two pieces, oneenhsoy:;u-k 0,a6 syi of which has 1.5 times the mass of 6koy0 -uenh ys;as,i:the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end )e +:mv*s o;g ecirii d7c/4svof a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent thr):siiev 4e *ic v s+7d;cgmo/e SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height of 1.20 m. u4 55ixyx (q 9bjd+zpmApproximately how dxi 9+ yqb5j5up 4zm(xmany rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision ofq ps4;w0 58iw cxl(iap two objects is the coefficient of restitution,p(wl;40a8 5iwpqx cis e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times thw01x g kuieh6 h78aqtm8r-e+ae mass of the other. A depression is made in both faces of the cut, so that a firecracker can be p+irmwa81 guak 70eh6tqe -x8hlaced 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 ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object movinz -reo53oadw 0in0hg :g in the +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/-ro05 gwd3 0neohiz :as 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 nucleus, an electron, +t )3.n2sx+7zfl h eleeja,cjand a neutrino. The electron and neutrino are emitted at right angles and have ,t+jesz+fn x2hlcj3 al.e e7)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 massi2 2u(pmrc*ch $m_\mathrm{A}=0.400$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 inelaf753;.pbcze jvefzdyrqq4 7 55a dz/rstic collision between two objects of equal mass, each having initial speed the two move off together with .7e/vp5r 5zd7qqejrc 3ba 4;zfdz 5fyspeed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles ando:t5 m4hfb. ,n3mzmke 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 collisi h:mfmt4mz,o3e.n b 5kon, 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 with another atom at nx4gu1bbdt ;6rest. After tbunbt dg;x4 16he 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 at p8u,d3/gnscxfs k. kj r;t2+ srest. After the impact, t2k8+f k;j u/gpr. t3sxcsn d,she 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 system shown in Fig.h+lo5/- kqqaz u*cq5m 7–38. Specify relative to the left-hand 1.00 5o/aq-lk+z5c *mqquh-kg mass.    m

  The distance between a cara :g6s5t0:c kjp*h. jbmcp,fgbon 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 ikq pma5pgf(gxk b v68(nmx 64;s 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 three people sit in the back seat 3.90 m from the front? Assume that each person hax(6b nv5pmgxmkkq;g6 a4f 8(ps a mass of 70.0 kg.    m

  A square uniform raft, mp-*d w +)vl :9b7mvve jf(;otkdr9k x18 m by 18 m, of mass 6800 kg, 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 loaded ferre)9 v*t7 d op;jr v-+v (w:dxb9kfkmlmyboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidey;:0 l1wp n 5r8jhtemts $l_0$,$2l_0$, 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 xw.0-msmpl/bv k 9wr8 has a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal pla0lk srw-.pw9bm /v8xm ne, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a cirn j,o 141udh+ vuj1oascular 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 m4ujo1s vadhjo ,nu1+ 1ass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Tabe7pa+a5mq d64 e avm-wew 10egle 7–1, and calculate the mass of ovw1pweea5-deg7mea 6a40 + mqne of your legs.    kg

  Determine the CM of an outstretched arm use pn5w 7ww)pi*ing Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate q 9tuxc/j n2t3m.zi4b ibfc- bo3*c3gthe position of the CM of an arm bent at a right angl-j3n*cqc3t ub29 m iox/bc 34i.b zfgte. Assume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a pos: 4lflhm4dp:zd g2w9kaj1(i rition such that his arms 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 body?(k4ghmdp4i1w2: llzr d f9a:j Use Table 7–1.

The masses of the Earb*ew0ogl) s 2gth and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on frictionless j;tv /0o7 epqmln01d0 scumum 80in7eice.
(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 he1gffm ha 5cs30g(bt2bh+1hj x:b*iiqad 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 parabg :1cfta3 i b+mxqh1g0(hjf2i5h sbb*olic trajectory?    cm

  A mallet consists of a uniform cylindrical head of bki/2zbl(x x;: oav 3wmass 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 mawo zl( x/3b2ika:xbv;llet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29),a+)nwxwwie)5/ pws;z) 8ah o u $m_{II}$=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 tht5 wfrs fx4qkop6n :pf)*, d(ee 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 balln*oeq:( pskrxf4tf 65 ,)p wdfoon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontxja aogcb d3n5l6p n0y5upw,(m 1xw 3,ally 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 fox (0m5n3a ,g5xy do 3a,p lwpj6b1cwunrce on the ball during the contact.    $^{\circ} $

  A rocket of mass m trac2v7gbw)sk7: sg jx )qveling with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is89;ijj (kif4in c*mu b faced with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “s j(8ijuinf;bk9m i *4ccratch 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 2e kou(42+dnhjd w)p7h.5m/s by pushing off with his legs from an 1800-kg sped( u4wpdoh+n)jkh72ace 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 oh x0p ay++te9lh6m :r37pg1by q lb4vcther 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they w3 byp:t 17 4 c+xg vhl0qyep+b96mlahrhen the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elasxqah /;, ip ko0gc-6hgtic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass o iga x,;6hckh o/0gq-pf the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as anvqals75 a3g /fhkt67f expert witness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, ck t3/vgfah7aqs 6 lf57ar 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 ofn,hv7tl1r;atg :u * b yoab33e concrete steps of total vertical height 4.00 m. The ball hits four gbb;3anve7tt:o h r 1a 3yul,*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 a 1.40-kg block of wez+j(*7n6 w3a wfadbt ood at rest directly above it. If the bult73*+bjz6 aen wf(adw let has a mass 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 strikez 7mf /azb0yk/8g8hsj s and becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of0 j8mkbza7s/h/8f gyz the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass,,6: p*gf rs on)5 j :bs,z8afvqfwxdk 60 kg, sit in a rowboat of mass 80 kg. Wito8*6fvjfaq z:b, :x r s)ns,5p, dwfkgh the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abq 1;5qp gte*roout $ 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 yy61pxbomk-,1, ks m xs9a/fmtwo fragments by an explosion. One fragment acquires twice the kinxm py a ,my9ks 6-b,1f1/mksoxetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is givgeq2e0ui -p3 tm yi9)men 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 q fe5l8wjnj-7 $m_A$ = 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 particlejn qbf9hi 7l7p */tyqh-0z(gl and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha partictjf/*-qgqlhhb 9 (nzy770i plle 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 a0f1l vw bv)lz u)a.) lmq78qf oh+p)zvt an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 3 0y;asl sbd696i*o vsn0.0 $^{\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 4n;b*ym zg 3jrcs2by2on mass m if it is to rebound from M, slide up the incline, stop,4rny;2y mc s*32zjgbb slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn vzdp2 e9he9 1mmoving in the negative x direction at its o9hpzde1 m 9ev2rbital 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