We claim that momentum is conserved, yet most movity4*w6nu g1v tq86; vryr;cs lng objects eventually slow down andutgrr c6sn;lwy6 * ;v4tvq8y 1 stop. Explain.

When a person jumps from a tree to the groundxy +zv0/gwgo /q25dio, what happens to the momentum of thg+0gq/dy2wi5 ovo/x z e person upon striking the ground?

When you release an inflated but t/ hkvl-e38ts untied balloon, why does it fly across the room-k/8 tvshtle 3?

It is said that in ancient times a rich man with a bag of gold co2 zcmom r8enqy u/j jjep6,3uh-8xk :-ins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miser, 2 mj:upk qoy6zxej-/88er-mj hn uc3ly?

How can a rocket change direction when it is far out in space and isntbd2w5k 95 4q*thhoykhup kk:26n *f essentially in a vacuum 5k* 5nk2fd2htwqt6o khkyub4* n9:ph?

According to Eq. 7–5, the longer p4 +-t7yf uz*whuxmz :7pqi8t 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 are intended wmy pp7*f-u 7:tz4th8 u+ixzqto inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand coll00 )kutae1a)qqy a)r yisions. Today, though, cars are designed to have “crumple zones” thar 10k tuyq0))e)qa yaat collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball gqu/ u scfls:tkyw 908hpg -lnlo:e4c* vi*)8further than a ball tossed in the air by thyh )n 88s* ck ls/fvlw:c*0lieout 9ggp:qu -4e batter?

Is it possible for an o. x q r5gvoyftv-,4h0zbject to receive a larger impulse from a small force than from hqtvfrg04 5v-yz,.xo a large force? Explain.

A light object and a hgsl(m 33c0m dqeavy object have the same kinetic energy. Which has the greater mom mdqc0 (g3l3msentum? Explain.

Describe a collision in which all kino29pfkf d , gc3nxr02oetic energy is lost.

At a hydroelectric power plant, water is directed atf+wj8g4 xdby 8b 6k*mrrbd. 7t 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 dead stop, or so that rygxbk+4. 68ddj8rtwb7* bmfthe water rebounds?

A squash ball hits a3whv +3zirodb8dp4 v1 wall at a 45 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is droppnekgeh3 0v6l5 vt 0j7qed from a height h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer k0nej5ehq6t3gv0 7l vpart (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load60c 0snlu;r:x qeum.z in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas te/q + dbm0pzeplk-o(x3-kl1 lhis is not true for your arm ork-dq-z0( 1l pkx 3 eelpobml+/ leg?

Show on a diagram how your CM shifts when you change from js)* )b(vjhrg frph0-a lying position to a sr )j-s(rg*v hfhb)j0p itting position.

If only an external force can change/fm : mzp;t -g0uv0uhm the momentum of the center of mass of an object, how can;zpu/m:t m-0hv g0m fu the internal force of an engine accelerate a car?

A rocket following a parabolic path through t slz 4*+ 3tqffa.tu(xahe air suddenly explodes into many pieces. What can you say about the moxf ts3a qzf+at .(*4ultion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed .e ,b5lupwua cf84f0vof 8.4 m/s p5fwbu4 c u ,la.v8fe0    $kg\;m/s$

  A constant friction for; 981s h ylomz3muz*asce of 25 N acts on a 65-kg skier for 20 s. What is the skier’s change in ve9s*sz;a z 3m1 lyhmuo8locity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit onlulr,s:63tdyo :zs f(.k 1nwr a horizontal line drive straight back toward the pitcher at rf ursz:wtk,16 o.nsl d (3y:l52m/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;fi 4un9sek 60lj p,nx 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. 0f j4uike; 96x,sn pnlThe mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocketm k.ev6ti*:p : qwbwd,, given that the propelling gases are expelled at a rate of 1500kg/s 6kw p.dt*:iwv,m eb:q with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/sqq96 ;m gk j/9abzpxo* on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual speed immediately afbjakzmx9po q6;9*/g qter the tackle?    m/s

  A 12,600-kg railroad car travels alon2d g ver0f xrs53 bgs634ovu)ge on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the c 0rbs5v42ds gg3 uv6e3fr)ogxar’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar at rest. The twg,gitlyn64 8io stick together and move off with a speed of 6m/s What is the mass of the li8giy 6ng4t,second car?    m/s

  During a Chicago storm 0z dnsr33fa(xw8q3 dn, winds can whip horizontally at speeds of 100km/h If the air strikes a per rs0dnx awd3n 3z3f8q(son 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 :j,ae+;joe zmn0x y 2hec2zw9along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and 0cw,oez :2m29hjajex yen+ ;zfills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha parti6:)zq+ o 9dfo tfk;1uj7iz sxfcle 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,t+fqj:7k;fzo6z9 u x d so1i)f what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg blebwill)4n. y8 kfe2:fock of wood and emerges cleanly a.24l8 e f:ibl n)ykefwt 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at-3p 8;4c 7xttmn ropzo 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 is6jmk2ut8quuy 2 47c;qty. fos traveling in outer space with a velocity of 115m/s To sfqmu6qj8;u4u72 o t.t2cy ykalter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the td2c9g u/yvarr .xvm1 3ee at a speed of 45m/s The golf club was in contact with the u /ar1 3 xy9gvv.2mcdrball 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 comes to rest in a tfasjai l//-ju3 4 qm5fime interval of 8.0 ms. (a) What is the impulsefsfai/q5a uj 4-jm l/3 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 s8 g(6ybom gd*rpeed 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 crashworthiness16 hej2bhh,m lgwj:g89 or c6r 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 time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by lr6 j12 wg:mhocgehr9 8bj6h,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./xc*r2l9f7m vzi74zf y tuns and is stopped in 0.75 s by a head-on ta /n7t9zmz4r u2fslv7*xi yf.cckle 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 tenni) xtnh()asx9is ball (mass 0.060 kg) points in the +x direction and is given by thenixs)ah (x9)t graph 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 breaking thdt *z 3kmrwqvw/2b), ke 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 breaking the fall). Assume the bremdwq*vk3, twk/b r )z2aking 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 r*yt8j2rpfh.yy 45,oq j r5adkg moving east (+x direction) with a speed of collides head-on with a 0.220-kg ball at jr4,ar8ojh*rfp 5 dqty2 yy 5.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 speed of 3m/s has a head-on collipr:.86ale/v x 9kvjok sion 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, and let B represent the 9ekjao6p.xvrk v 8 :l/0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equa)iz :n9 mz:cf+rddxw; l mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’sw9zmr+:nf: i;) dzcdx 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 gmo8- f7m2 mpa.9ljvi, moving with a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming ma vo97pi fm.g8j-m l2a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-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 colli8 qlg3kjpkx)8 des head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward wit l83k gx8j)pqkh 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 approachesp,kqd-3 pis47kwb zm b1*7tny the other directly 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. 4,qmy zdppb* ib13w tk7-nsk7 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 mqp 4v hub)uy/x 0q-4y9:cfmea/ol en*akes an elastic head-on collision with a second ball initially at rest. The second ball mobl c)y4*qh:ex0 qf/4enyauv/u-p 9omves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionl ak9/( *aslhhress incline as shown in Fig. 7–35, and elastically strikes another cubehrha (/sk*9al at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an objecti+ /okg 4vf(xp 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 results in a maximjrs,9)uv5 ztd pi,k+yum height h of the pendulum equal to 2.6 cm. A 59y) pkv,,zir j t+dsusecond projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg pendulum: pp kxq, lj;9jt *jj,bm;z epb+4lpb. hanging on a 2.8-m-long string, which makes the pendulum swing upwarpb9 ;, bj. jm :bjlp;epltj4+xz,q*pkd 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 tqn(v -k ;3ztf/z,i/ jf egqn5energy 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 resc2d 8 q f-yz.cw.bfcw*t, into two pieces, one of..zfqcw wc-dby8c * 2f 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 represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car colliy,e4m6b (ehb2 riq xr 95huhm8des 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 tires and road is 0.80, calculates the speeq i964x5eb8 rhre (hyuh2b,mmd 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 r(chmj syh7p *i/9(*v oxv:do eebounds to a height of 1.20 m. Approximately how many rebounds will *9*(oejhvy(c vhxi somp:7d/the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the coefficitva,o7o0*p wgent of restitution, e,v a7o,*0 ptwgo 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 timcac+pgkk ;-9 rp sg5g+m5 m8rves the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks kvg58 m-rkpa+gr ;+c p9csmg5separate 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 direcp48f7 zroi t.ption at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s z7trifp . 8p4oFind 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, ands 4q 7e2l3uak electron, and a neutrino. The electron and neutrino are emitted at right angles and hqdul2as 73k e4ave momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of mas inv+v 2/b5rgzs $m_\mathrm{A}=0.400$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 a-gsniy+q8t 2cq:t:z collision between two objects of equal mass, each havinqy:+tcg2-8 s nitq :zag initial speed the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass m6id rmk/9lww /7(vq poove 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 right along the x axis with speed 3.7m/s (lpwk /d7woqim6 /r9 vAfter the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with another atom w(gf7 lw0r7 -8vhan(smngj -n at rest. After the img(nm 8w7f(n a jhsv7wn-gr0l -pact, 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 + aj;3cdn7wl b.i/iqt lse9y7elastic collision with another atom at rest. After the impact, the neon atom travels awinl/;7 +tjc9 e.db 3 iawy7lsqay 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-b uwi 1-:+ueoodek0o4mass system shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg maew+1 uo b0ed:uo -oki4ss.    m

  The distance between b7l(c5gy i.yra 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 th(lvxn adpyz.p463oq q) ko r14: )qrtee 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 has a x(a6 r4o) npyvlqke4dq) zq3to .r 1p:mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of m z7w 1;-qt6pxkcu h1wpass 6800 kg, is used as a ferryboat. If thp17h;6xu wtqz 1k pcw-ree cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidevj (wwwx+1m+u s $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases on 75 l;h,xjl/2d vcfsmf tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up /v,xf5n;m7 c2 lhdjslthe load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular h2vy ;5 rbu)/lc g-hcgaole of radius R cut out of it. The center of the smgyc h5 ulrag2c b;)-v/aller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as th/ y-u5o9dlvu pose in Table 7–1, and calculate the mas9yv5-d puoul/s of one of your legs.    kg

  Determine the CM of an outstretche k,im 3nh*yy3tj2:yxsd 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 od- ,g sldy)ti)v0)u5yz2l p)ufq0 atkf an arm bent at a right angle. Assume that the person is pf )ky qu5 2 )i)stt)aludy-d,0vzl0g155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a positijts h t6a/p.-mon 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 outs-ptatjh/.6s mide the body? Use Table 7–1.

The masses of the Earth and Moon 2(cv junadh u364 o,hwf2zpla5zu;/ j 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 fri 94zc 5tqatp.dctionless 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 ge b4h y uy/s,*1wonkx;le (a/mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kusey; *e/wlh/4,(n1 ok gby xag and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindricy. .q rvka-z*hal 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 v.r zk.*yqah -that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Exampljahu0,5hekh3 (u d z-le 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are indx4b6) syzgl, the 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 (r64)lz yx, sbgdelative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at saf(fw yqw, mp)b,n7j7 qxlc(/trikes a bat and is popped straight up to a hewx)(fw,q/c,(qf 7ylbp7m nj aight 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 trl wf dz9(k.d(paveling 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 corno h3 +2kpp j3sbxem5 ;irsc+c-er 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 ball s;cs+op r5h2b ecp3 k+3-xjmiwill also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5 hcmer6 c xmjctl(n 1/51h*x+gm/s by pushing off with his legs from x/mc11eg h r5xj+6*l(nm tcchan 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, ar;sfgrt ( t;q3ee initially at rest in outer space. They then push each tt;q;s g3(rfe other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ballb tllp8h l/b5( (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed.tbl(bl5p h8/l What is 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 conv0 tk a sy3c+., qjnb034btdpb(s*apurt 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, car A slid 18 m while car B slid 30 m. The coefficient of kinetic t s+a n 0sqd4v,3(0p.tb ca pbjn*byk3friction 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 zy6ru8p3lm+te hkfqqw5-.l r n *:mf4zzk f50 of concrete steps of total vertical height 4ztz hq5 l krwuk8n56mp* ffly+:03m qf r.-4ze.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 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 o( ylfyym u7p)j5m2wo0f wood at rest directly above it. If the bullet has a mass of 29.0 g anyl(7 2ymjw)o 0fu y5mpd a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and be:(k, :dnzplwk: bxiz2rw4ds* comes 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 distance of 9.5 m before it comes t2l*x4kd,d:kz:nwriw ( zpb s :o rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass xh-ks. ;-e i 9fejlbb+ kg9u,f75 kg and the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people,9fihe j x +,bf.g bs9;lkkue-- 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 w na1hhcuv),l6 as about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into tx p dw whmtlqh9e286:4wo fragments by an explosion. One fragment acquires twice the kinetic ehwtwm8ep:h42 9 d xlq6nergy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 580-( .xtvpnc51cw:y z.gn; $1.8 \times10^{ 5}$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 masses0/:d ee1 ijf /srv 2 ,+fluyqdq:eee0v $m_A$ = 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 radioc; q u -e8u m5rsqp1gu,oahd36svo.m *actively into an alpha particle and a smal;d.a mcp18vumq,geu5qo6 -s ush* ro3ler nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired atc0onmprn 4h:,(x /: wa ehyc.c 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 arap6qb661jxw 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 on mass m if it is .*i4)a1siqc,wnyw e8pr si:bto rebound from M, slide up the incline, stop, slide down the incline, and collide with M age4scr, w1wb*)i a i .8iqnp:syain?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn moving ijf-j*8emu 9j t*02p y,udbknhn the negative x direction at its orbital spjhbj,k- n8ef*dj2 y0*p mutu9eed (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