We claim that momentum is conserved, yet most moving objects eventuall+mc- b b2ewq6zo, p(pouz f5m6y slow down and stop. Eo eu52-mzzbp m,f(q +b6cowp6 xplain.

When a person jumps from a tree/ d1.41lkpr+chl* tco;m8mmcx oimr 2 to the ground, what happens to the momentum of thod;4colti+ 1m* 1m8xh mpr2 c.lmckr/e person upon striking the ground?

When you release an inflated but unm2 r5d ps4:ymcl. 4hs-j +3tijuvvwj(tied balloon, why does it fly across the room?3. -c5tmi(l4:j m p+hjdyvs u2wvs4j r

It is said that in ancient5d:upcp mru f2vo0k/ 5h)def , times a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frieu :5 v/rk d0,pp fmuo2)hdc5fctionless, 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 essentiaqj1. (hrn*c ujyv8vt (lly i(jy n(rv cj. u*h8qtv1n a vacuum?

According to Eq. 7–5, thekl2xi7zf/ t v8c rly5+p/ pg.z 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, explain the value of air bags, which ar lvg2zfzti+ /.8y5lxpr7 c/kp e intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as shiwsjfa 4/vi7 1l )z5rigid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse sjwf7za/l i5i )14vs hupon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than g g2tho.::lo oj:cn7y a ball tossed in the air by th. g: jyt2lon7:o :coghe batter?

Is it possible for an object to rece:r6see s38au(2 afm oq. t6fqiive a larger impulse from a small force than from a large fssa ruo3eqiaf(6. :m6 e8q2 tforce? Explain.

A light object and a heavy xzm+t l vpv)()object have the same kinetic energy. Which has the greater momentum? Explainz l)v)tmvx(+p.

Describe a collision in which all kinetic energy is.x+3zz j myjs;r*;67 zmasqzi lost.

At a hydroelectric power plant,ws/8s+sk jkr;:l -x hn water is directed 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 wj:ln8/ssksr+ ;-kxh brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a sn8nq9,7ie qer v5 zwxdj0q +*tkaf3( 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 ste.nikcgalt+a;z; q5 7s31ua/zb5yedmel 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 piece q5si5lea.;/ 3bu k1mz7 yz+acd a;tgnof putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load inbhsnu*1ba mt93 bj*h3 your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is not tr4du* hyqcl :x3ue for your arm oru:hlcq* x34dy leg?

Show on a diagram how your CM shifts when ( /yvanw2c97 x *0ufb159ft vwv tmihmyou change from a lying position to a sitting poamm2 u *xw5vb(w19ft0 ifcyvh7 n9 /vtsition.

If only an external force can change the momentumh7k5 xjt:0)xir is4pv of the center of mass of an object, how can tkjhit5:0 xir4p)xs v 7he internal force of an engine accelerate a car?

A rocket following a parabolic path thj;al k )j7a/w ronnp0hjs+d(4rough the air suddenly explodes into many pieces. What can you say about t j j(dp7nsw 0a);4r/lo+ anjhkhe motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a spee 7m g(1ivywzwzt3e e(/d of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. W1mi1rfs lu:u: p4mw 5fd 7uar rff/j/2hat is the skier’ ulsdpw2ua:175m/m ruf4:f r jf1ir f/s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s359 pkht9aoeg9c;z xi is hit on a horizontal line drive straightoei 9kxt; p593ga9zch 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 horizontalb tc 4og;sur a6k/2b9zly with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water u gbra/co6b9tzk; s42resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that th :nhkf fhd oi7un;x3e+*3 h0 )z7aosxve propelling gases are expelled at a rate of xx ve*;iozhnh077+o 3kna: ) fhus df3$1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving at h4u6u;ns3de3 cf *px*+mvoe m $4.1 \; m/s$ 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 ax1hn 1n/4k9qv y2kvva constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’syn9kkvvxn/ vq11ah 42 new speed?    m/s

  A 9300-kg boxcar travelib5 p/n,pn -hqdng 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 horiz);exw0r ow3tfontally 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 perst 3) frwx0;oewon 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 const g)v-o.5rsev+sk(l w hant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speo+v)5.wsv( slg -h kreed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits ad7f8pl6x9zz7a+s cpuyz 38u fzxhe 85n alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what s7 +c ap8xpd 58 x83 hf7s6fzleuzzzu9ypeed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and emerget e6uq; l*jj5d1+hndy s cleanly at 170m/s If the block is stationary on ajy d+qnu 61;e j*hld5t 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 spee4maxj 5wyygj rsp3:ic3y cqz 6 z82i/s/oi+3 td of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a velocity ofc f9; e- 5f0 tkgm)v kjq-e3bz. v,u1iuguid,b 115m/s To alter itkf9,-0 uv5 m,jq egigztevickub.1uf3d ;)b -s 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 bu)mz;h( 5k di: nubxdk,: )qxof 45m/s The golf club was in contact with the ball)b x zd xd5kk:qnu(b;):,hu im 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 comesz6-gn 54rwhlac un z6v0ju6. l to rest in a time interval of 8.0 ms. (a) What is the imagz v5.64wnhuj-l6un0lc6z rpulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes a wall at a 4 +:2;-xj y)gpiybipr 8f1q+3xndvi hb5 $^{\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 charge5zj* 4xz04 (t zmclocr of the crashworthiness of new automobile models. Cars are (z m o0c4zlzcr5*t4x jtested 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 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 an ndbf 20xpehcuw 88,6khptl 00d is stopped in 0.75 s by a head-on tackle by a tackler running due west.w h0hfp6tb ,p2xld0e80ck nu8 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) pointmitc52bg l jx8,lw*(t h,kd -bs in the +x direction and is given by the graph of Fig. 7–33 as a function of timed(5gihxbc8,,- *2 bt ltwjlkm. 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 heig((ert ch g rze1c83j1eht can a 75-kg person jump without breaking the lower leg boner3 t(eeceh1( rj81gzc of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (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 7,tqj l 99isdccollides head-on with a 0.220-kg ball at rest. If the collision is perfedit 9cs7lq j9,ctly 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 witel2 u(solts7x 4q: /wl (gg7dmh 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 represent the 0.450-kg puck, an eoxl :(usdqs4t(/g77ll wgm2d 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 under;: oar7atcwzol c 3.e5go a perfectly elastic head-on collision. If one ball’s initial spee5e.a3t:7rc ;oow za lcd 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 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 dp6 djs9:y,uz* v) elvwith a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are ,p syzdj: d) v*eul6v9the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.kr *dj tcrj*b77*4 iod220 kg that is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bo*74t *rk7obci drj d*junces 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 one approj0d4y:a3.dvsd b0kt ,4iq gt6sj x 1cwaches the other directly from the rear (Fi 4qb064,sdkdgx ijtwj0da1s.3cvy t:g. 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/w2ea8v9 .n6nhuk0c ckynu* v a second ball initially at rest. The second ball moves off with halfe 6 c9nvwnv ky*2h.a8/ncu0ku the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as shown in F-4pdta2zj2 w /ypbx m oqm2)w0ig. 7–35, and elasticall-qz 02po4)2d/ wwpja xbmtmy 2y 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 qiv: (, 8q5ypj*( ljxjsk;vvhan object 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 c/mvkz 4+ edgoa7.; rx1 results in a maximum height h of the p. 7ez gmcv odrk4;x/a+endulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s b)-f7fve0mvs muries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the penm7 vsm)f 0-vefdulum 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 enew79vm hf4qf d00 ;ynrvrgy 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 8e m1 aueq/*d7)ajnazat 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 *euaaqd)aj mzn 8e7/ 1each 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 colloy5 6:3,(xq0 g z s2kcm;pukhfvpp;k tides into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tire(gkf 5pykqs6kv2z 0u ph3 t;xm;:,pco s 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 hth*:j ;obi;1ak m dow,eight of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its energy?jdt1 ;* ow m:hka;bio,   

A measure of inelasticity in a head-on cort./z e efoo8-llision of two objects is the coefficient of restitution, e, definetof 8ro ee.z/-d 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 wv n)*ixho6z r1w nyu:r)2u*bc ith three times the mass of the other. A depression is made in both faces of the cut, so that a firecracuunnr)h )cxyi*wvo1*6z: rb2 ker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the 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 hby0*tgy d8 .mqead-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each ma.y b*m0 8yqtdgss 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, and a li nco 6;na+a (uwsjiqh*8s97 neutrino. Thqso9ws8a;c i7n6 +uj lih *a(ne 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 masw+e6pz x 8i9z:iq)aefu wc v7 b:+:oyos $m_\mathrm{A}=0.400$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 in1 :ag nunagiqcup)(/- jct) )gelastic collision between two objects of equal mass, each hqu n/i-pgg(tcjacug:a)1 n))aving initial speed the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equaltjf ,9flrc t576ul w*n5l, uuf mass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the r ft7556f,lncju9w r *f,t uullight along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collisionah .uf1l: hl-khzyf;k (x/k; t with another atom at rest. Afterxf: ;;k1( f-l/ktkal.zhyhuh 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

  A neon atom (m=20u) makes a perfectly elastic collision with anoth02oaik 8tgr m8er atom at rest. After the impact, the neon atom travels away at a 2rmi8g 8o0atk 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 showncasltzu2z 202 in Fig. 7–38. Specify relatiaszt022cz2 lu ve to the left-hand 1.00-kg mass.    m

  The distance between a carboncl ec.2f u.+p.);nirocri ) ws 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. How farwo o e5m9h5:jobko01xa0k s:z 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 peopo9kex10k aw o50job5h:s:zomle 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 6800av zc;48ctag+5 r5*m gs zf.ve 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 ferrygf4 ;msz 8e5.g+v5ar t ca*czvboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides mc g4;c6nr0,as b*o bj$l_0$,$2l_0$, 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 h -jq:p7yhvb 8was a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find 7 qv8wyj:p-b hthe 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 hole of radius R cuk jf7;yt+/ xrut 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 fuk ;ty+7/xjrthe center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as t0)c) c8 ivgipdhose in Table 7–1, and calculate the mass of one of your)i)dp0ci 8 cgv legs.    kg

  Determine the CM of an outstretched a zdy onw )iu-/1uj5prnsor:/.rm 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 pomi.f8t t q+0wfsition of the CM of an arm bent at a right angle. Assume that.+m twtff 0q8i the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a52tcx u8o8ntntja 04n 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 this CM be outsn nat n858joxt4 0uct2ide the body? Use Table 7–1.

The masses of the Eart2omjo15h :iw g5djwm-h 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 fricto(aa,-2mi1w zchm hs 5ionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diamete:d( ,2mh(rrz: dy tbcyr 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 toss,( b(m2ch: tyydrd: rzed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical herk.l gf9.py(r c*) 2z fjsl(wnad 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 trajectp.k *jgsrnwfzly9flr( ) 2. (cory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29), rq mt) hxo(mavg232k*8 i;5f /pdhzit$m_{II}$=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 masstwfke: ge)fc* 2l00 vr M, are in the air and stationary with respect to the ground. A passenger, of 0g0elfkf v2:c*tw) er mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitch oxe*l3tn 6tp.ed horizontally at strikes a bat and is popped straight xtp3. leont6* up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travell:j. u 363yi txucm2ck :1pzmeing 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 face ,kdz:)ktv(n(snpx 1c d with the corner pocket shot 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 s1nkct:kd ((vz) ,npx ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/v/1v.d wbx no4s by pushing off with his legs xdv.1obw v/4nfrom 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*y:el-xyshe*mo hp:+ 80 kg, are initially at rest in outer space. They then push each other apart. How far apa:-:py oyh* hleem+xs *rt are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-v,qkh*y77 nof on elastic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What i,qy n vkhf7o7*s the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving an automobil t)t oyvxmqt644sm(q4e 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 roa(q4 t44 mxtt)6yvmqsod was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concqrgl :vei.e88rete 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 bogl reevq8 :8i.unce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg b x*,3) jyerp vrkqn7x3ii;zavs4 m :x/lock of wood at rest directly above it. If the bullet has a masxqev/kix,374mr3 ipa )v x ;*j:y nzsrs 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 any*74zrjme3chk2 3vzy d becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distyz7ke3y3hrzv 4*c j m2ance 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 thewkm1v zo41 *p4ta eforh0bp7lx5k* )3:o eyw o other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchazy:*o 4fltp 5b*exw wk1 oap) m01oe r7vkoh43nge 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 about 7k58j v nt+3 d2odfvie$ 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 explosion. O(/hr, fikrxb8 ne fragment acquires twice the kinetic energy of the other. What is the8rf(x kbhr/i , ratio of their masses?   

  The force on a bullet-;)mub1hk)6eky klrc8 hhx c ( 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 masses5.jqzocd. wenz ;tqmu1 /q9*k $m_A$ = 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 res0tv1lwj4 pni+ (v w5zvt decays radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha z0l+wj(tp wv1i 4vv n5particle 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 avl wbucakpqlq7.m4 b8v;1m s:gd hm 5yq,,z4.t 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 slides0zsq9i6l*jcg down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit weer :q gi,ykiqu*guj:1cq 1 3e/1,ut on mass m if it is to rebound g*1qt k: u /guj,qei yewc,1:31uqerifrom 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 slings26w1k b;lf03luqv fi chot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6lfi0kf3cu2 ql6v1w;b km/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