We claim that momentum is conserved, yet most moving objects eventuaw/yin3ycqvjtp )2g3v0y m ,oe40ai65s 7ij ijlly slow down and stop. ijp wyevny2/3a005)o mvjj ig i4iqy3 7ts,6c Explain.

When a person jumps from a tree cp/x9ne o5e je1c:n6gto the ground, what happens to the momentum of the person u1e:pg x9ecj6c5on n/e pon striking the ground?

When you release an inflated but untied balloon, why does it flyxg7 e8g;- ie)1hu js6a:r xsae across the roomseeax-j g:8)hs 1 eu6rgxi;a7?

It is said that in ancient times mh mil o4dy95qzn-,4 ba rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the icz 4h9-lo idm qy54mnb,e was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is essems0) uqtc jr ..z/ggh0ntially in a vaczumt0sq rgc 0. /.gh)juum?

According to Eq. 7–5, 1s1y7-os 9jo clrci0x the longer the impact 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, explainl90is1co 7r1s-jxo y c 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 withstan1 g )-si)i;mizyd +gned collisions. Today, though, cars are designed to have “crumpli-; ) enggz)sdy +iim1e zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in the a5:95mc-epu-v6cjlj dtl o8 twa/ k5axir by the bat-/ej mtjv6c8 5utx-oa 5wkc:5dlpla9ter?

Is it possible for an object to rec9s ppm)wcypcqj /4u(,eive a larger impulse from a small force than from a large force? Explayj/c4sp(wu) pp9 c,qmin.

A light object and a h ou+em5mr y+0teavy object have the same kinetic energy. Which has the greater momentumut 5oy +e+mmr0? Explain.

Describe a collision in which all ki 1e avfd17gur/netic energy is lost.

At a hydroelectric power plant, water is directec 80 c)b6 ogpeowh5w:y3l pfy-d at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a wow epyc 5f3-po80h):l6ygbc dead stop, or so that the water rebounds?

A squash ball hits a wall at am3-76a ldua qm 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 (fixed to the vc x r)ro)w;40x* rczpjik)6mEarth), from which it rebounds at very nearly its original speed. (a) Is the momenwpjx rm c)rioxv)6; 4zkc0*r)tum 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 o86ey kslm7)b/;q +:jnuf iyhbackward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of piz- 3i:tlqq y7rpe at its mid-point, whereas this is not true3: ltrq7q-i yz for your arm or leg?

Show on a diagram how your CM shifts when you change from a lying positio*9g zfk7c lu y0q8ua6xn to a sitting positionyuagx678uzc 9q l k0*f.

If only an external forda:nh kns)kqce 3a;igwhh di+x n fq(w0-4,.:ce can change the momentum of the center of mass of an object, how can the internal force of an engine accelerate ak-+c4(d:aghsa0h hnw e:q3. xidi, f) k;q nnw car?

A rocket following a par;pg lqlfc1o n8qnho4t6++y) aabolic path through the air suddenly explodes into many pieces. What can you say about the motion of this system of pi6q8;h ++t gfpn4lyloo c1) qaneces?

  What is the magnitude of the momentum of a1rb6/ )xj*o xwd)l,q2hhc yrc 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. Whatk( 0:9mnejc l8rh0:4g wooyls is the skier’s change in velocity (o kwn8jr0: yg0h4lsm9l: oec?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive straighlk 8u d1k7gkd9t back toward the pitcher at 52m/s If the contact time between bat and 87l1kdu kdg9kball 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 1kz)n.sm9v -bram.6 po2h u o6;qmmgo9sv2;hl0 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. T k vs2 zq .6mbs9h; ono9)lmp;.m vhg6oa2mr-uhe 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 ofptx;pwh;m2i.k9qs779 kihn n a rocket, given that the propelling gases are expelled at a rankkmftpp;q79x 9 sh;h 2i wi.7te 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 mov v2njk r23)b/ccbjs l.ing at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels +v u; *q*szswtalone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,init qs;wtvu s+**zially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar trave qk/7;fjq t15+4 p+hyoinyqm mling 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 stor0)7j joa78 elxexo*t lm, winds can whip horizontally at speeds of 100km/h If the air strikes a oe 77 txjxejloa)0* l8person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical 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 c4ni.4fyx rlriy(-1d of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate yicf4 l.yxr(d14 ir-nof 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 initially moving at 420m/s emits an alpha particle i sfd50 ,cs7flhdb ,:idn 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 has a mass of 222 u, what speed does the alpha partf l7d5c: 0dshb fd,,isicle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood2q))/aq(y+i* wi+ /l+fjotjg4uub q:qnm fqf and emerges cleanly at 170m/s If the block is stationary on a frictionless f4++qn ju+lbyf ftjqw / ()qm/ :aq2*gqoui) isurface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage roctq,7 )yo i/tilket is traveling 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 ln*7peu:b ul /space with a velocity of 115m/s To alter its cun7:elbl*u/ pourse 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 t/;j:ngcjois-q 2 q x+45m/s The golf club was in contact with the ball for tjjq-/ig: 2 xs;+qcon$3.5\times10^{-3}$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 velocigv8 6d0y twgq:ty of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a)tw d: v8qy60gg What 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 ht);y)wcpq hc.ohl.*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 the crashworthinnpp-+go vuu, s8 ds6 oyzr6r(.8mhc5ness 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 theg+ nmz hd8su rpn u8o(c-rs.o6,p65yv 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 ea lp 2o2bij(g4ost and is stopped in 0.75 s by a head-on tac2 ojbi lp(2og4kle 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 o;s19ja02 jq+(b edqd wd/blp kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimq+p 9q ;d e10sjbbjwl(oa/dd2ate
(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 heightb v35t8at:x oc can a 75-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assucovbtx5 a t:83me 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 collide0((pb/qrm2nlp . vy z5 ts7twds head-on with a 0.220-kg ball at rest zqy/vptd2s. twmp(05l( nrb 7. 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, movr frde.4-9sjxq(rke, ing east with a speed of 3m/s has a head-on collision with a 0 f.d,rj9s( k-xq4er re.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 represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastic nf6t do0 :8.eh,m kof(c.fg wuhead-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 moving at 3.00 m/s in the oppositug ed hk.(:wc8nf6 mft.of ,o0e direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a sfy /4(j-d mcjb*j0hyepeed 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 reprey0j4d/c -j f(yh j*embsent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is bw-er, h/mvy 19k,v jcmoving with a speed of 8.5m/s collides head-on and elastically with another-c ,,k mbv/9j1vherw y ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement pau3qi :x.-ovcr rk 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 .3quo rcx iv-: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 bal4 a-hdu jd3fig.l0u-dl makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the oriu-gduh d 4-i0 3.fdjlaginal 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/xiwi2 3dazn0ekr id;( w;0oe slides down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land?i i knee;2 3i(r;da0wo0 d/wzx [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an objeikp-67 ml7;v*nvn kract 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 1 reikz1x1x.lp( .bkn3fpsults in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pb.3z1i.pn plxxf (k1k endulum 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 travelivkf(2fqi)h 5sng 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pf25h i()qfv ksendulum 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 fro(ow-ao55ipvxc9si w 605 e xtaction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into two pieces ptseexe e)a af5q865(, 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 represf5aqea8 x6es)t (p5 eeent 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 atj; 7r3x:)xuiz2t zbg red light. The bumpertxr zgt3:72b; i)uzjxs 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 the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and reboue.5x gw ++rfch ggd8wy /qv:z:rs;zm(nds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% oex(5y wvw h:mrzz/+q gd:8+cr .sg;gff its energy?   

A measure of inelasticity in a head-on collision of two objects is the coeffi l6qh b1 vv4rhmdu;97icient of restitution, e, defined udr1vvl9b764q i mh h;as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the massrc8 )c9d;/scrs h yyh.zqg4m; 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 8hc4ym;sc9qhs./z rcyd;)gr set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on wfcyi0p. s6tvi q,f.*ycx-zv +vj/ n32t6 nebw ith a 10.0-kg object moving in the -x direction at 4m/s Find th w 6,nsxnfi-t6 30 2+/*pyvjt.fi.cyzvqcvebe 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 decays6hvh9 fnvih3 7cz4b *n into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momenc6n9hfhi 3 *7bv4v nhzta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of mass(xx4v m0nis .k $m_\mathrm{A}=0.400$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 equal massk g30/e5hfzuux;,y /e.n fkfcm3 uej5, each having initial speed the two move off together with speed v/3 What was the angle between euc feu0;fk/3uxm5fhk .3 n/ ezg,y5jtheir initial directions?    $^{\circ} $

  Two billiard balls of ezmw+.xom/dhh m ;m5 d*qual mass move at right angles and meet at the origin of an xy co;m mxz h/h5m wm*do.+dordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed 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 pe.rj( 5wj 5jmxpndlyrl2 x2e;-rfectly elastic collision with another atom at rest. After the impact, the neon atom jnr.l5jyxp 22 -;dwxej rl5m(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 wi:btk3u q:fgq llc+:y y;y7fj2th another atom at rest. Afytq y:+7fgj2 kq;ucl 3lyf::bter the 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

  Find the center of mass .yqa h22yi0yg1wtcv1k3gy /d of the three-mass system shown in Fig. 7–38. Specify relative tog k 0yawqy vcd/2. tgy311hyi2 the left-hand 1.00-kg mass.    m

  The distance between *.x/9n i2wwz qdlcbc 4a carbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of the car. Ho-ji 5:z4h fxn0tnmh; dw 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 has a 0nntm;-j 5d hhf:zxi4mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a p pevltsle 25/.(ui3 b e*iy9hferryboat. If three cars, each of mass 120y uhpe/2e5. l(3lt*e9bpvi si0 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides tcl):,,:az: +qngzz l yh1fug $l_0$,$2l_0$, 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 casevg1o p-,ryx. vs of tomato paste (see Fig. 7–40), e -x1r y.opgvv,ach of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hq pwpm-8. ,ortg z-tl)ole 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 o 8qppt-,.r o-)gzltmwf the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as thos (jbghh 96 /kft-9lvwlfxa* u6e in Table 7–1, and calculate theuxak-9hj g 6wl* 9/lf(fb 6hvt mass of one of your legs.    kg

  Determine the CM of an outstretche0g, :a/ylzldhhpa1sf* 9g3 b yd arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an sxjj 7:qh .rw8ogb3ng- kl9j8arm bent at a right angle. Assume that the person ib-8j 3gq:8ks9jgn.j7 x ol hrws 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is injx s /rjo77x+n a position 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 ths7xx/nr7jo +jis CM be outside the body? Use Table 7–1.

The masses of the Earthj9ora,y1xzr *p20ez1p (gof t 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 z05mdlcgw u9*:j0w ry-kg 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 cylindrz-hd hkth)+(e ical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectoh hdt-+ (hek)zry?    cm

  A mallet consists of a uniform c9rg,)rxm (j5v fbba. oylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that(gbr.m rfa9x ,ob5v) j will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14w 1yfvcdg(e 8+ (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 ap bq-lfajh lu4a8( ox 44/eyq.nd stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed meaj .(py l-uo4x84 l/a4aqhqe bfsured 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 horizontally at strikes a bat xrokb x 7(b+9-g/qc jgand is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate tho9gxjcrx(k bgb7+q/-e average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m trajb0b8il 6k,a gvx8 jm2hq /.v4q. twmyveling with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown in Fig. 7–43. vz:-u jb;):xfn p0nsg Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue baj;0::n fpzubn xg-v) sll will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of)vjml l++ 4s.qwgedfc0af0 5;8whfu t 2.5m/s by pushing off with his legs from an 1800-kg space capsu0;m+) w+u 0fqj54ltv g8eldc fa.fs hwle.
(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 mmv1 xwmh w0)ock.,6lq ass 60 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut ha 0mq1xow6,vkhm l)wc .s moved 12 m?    m

  A ball of mass m makes a head-on elastic collision m/o58k- n- )gtkzbf uct*hkj( with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speeo k8 mutfkc)t/z5g j hk-(b-n*d. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an4j(tx6nm8i4tg,k stdxru6hi 5 :/f j g 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 applumi: ,kjh6rtit(g 865j x gtfxn4d4/sied 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 fligabpt z1 0;n3w): iclge0d7k vmht of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the boug:b1na; 0)7 vwdztp icm 0kl3ence 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 yh 9 ,61cjens( p1mlwa14dlnh of wood at rest directly above it. If the bullet has a mass of 29.0 g and a sah,e9(4hplcn1 1ln1yw sdjm6peed 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-kg bloca 2dktvq bc( jgj,28n-k of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, w jvnb dg82,k2tj -ac(qhat was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kgy9ylps+zg: a bs *b-k)6lh4zd/y k n+auqfw39, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sittinp klk+q4*b)3+wz d/6z9 usn:fl a-a s ybygh9yg 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 i9kamr q;wd;/ 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 sudd :b8;mtbo0vu qy/e n;r;n:wzvenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic m8 tn vn :vb qe/zry0;bow;u:;energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formul7d ,s ijo fi9n59fxjzza4vblc2d; *+fa 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 b+ +ebhgsts- r:qq,f*$m_A$ = 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 a yk.;:nuws1 , l:yvqaupd4 h-ln alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the sp;hkvqp.1u-s ny ,llay:4 dw:u eed 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 aqp s6rep4,pwgb1pss3r9u0z 3 n 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 tlt5k8:3dqri slides down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), whatoj6loz* pg cj 2*3 kis52 peo2m.0gkfz is the upper limit on mass m if it is to rebound fr 35izk *m*ojf g.c 0k2seop gzo262jlpom M, slide up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slin5ywp r xgfwa+5r e.tc)oe7h 8gz7e5r0gshot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with fh)p w.grr waro8c77555xez tye+g e0respect 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