We claim that momentum is conserved, yet most moving wo6d e (uh )wjz20at6bobjects eventually slow down and stop. Explai)6ewb( oj 6h2dzatwu0n.

When a person jumps from3rv/ k qd.ecl7 a tree to the ground, what happens to the momentum of the person upon strikikc./3dvqe7 l rng the ground?

When you release an inflated but untied balloon, why does it fly a398pvz2vkd cw cross the room9 k2pd3wzvc v8?

It is said that in ancient times a rich man with a bm2to s/t;gwz: q0 za)xag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push h) gsw/0 ozz:xqttm2 a;imself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction wjrt idm*79 wj8hen it is far out in space and is essentially in a vacuum jd8jr9im wt*7?

According to Eq. 7–5, the longer the impact time of an impulse4.n zf mji-lt8 8umn(l, 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 to inflate during an automobile collision and r4 tj8.nm iu(8-mfznlleduce the possibility of fracture or death.

Cars used to be built as co ;x,*ks je176b abmfrigid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the asox7;a6b1,ecf j bk*mdvantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed i)4 d3bl yzw)mopn 0i5on the air by the ba ibz)n opml3 w4)05doytter?

Is it possible for an object to receive a larger i q)szl5mz *53g a q)jl0f)xv97 qdyhznmpulse from a small force than from a large force? Ex59)*3nlhqm zz yvz qa0)gj l)7sx5dfqplain.

A light object and a heavy ob;f) j+qq5gaqt9j mycnvx 773tject have the same kinetic energy. Which has the greatert3v)n ;9 q+g y7axjq57fjmctq momentum? Explain.

Describe a collision in which all kinetic energy is losta2b+vwsa 1:4 n jyed5t.

At a hydroelectric power plant, water is directed at high speed agai tbo cl26x77cm57kqr wnst 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 to7x 5 lt km767cocrqw2b a dead stop, or so that the water rebounds?

A squash ball hits a 57* ghxs js(t4r/qoopwall 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 dropped from aue, 2 z;m6mizx -;*ngzmx7dww 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 part (b) for a piece of putty that falls and*xw w mzim 7z xmez6u;dn-;g,2 sticks to the steel plate.

Why do you tend to lean backward whwbt a9e b-ybrn93r ;8wen carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas ts2m-,+yfba vt his is not true for your arm or leymfav+,b-2 st g?

Show on a diagram how your CM shifts when you change from ox kmk7f),mp- p8wo6f*6ag tma lying position to a si6 ptwfofkx a86po7mmk,gm-*) tting position.

If only an external force c8d,g.vg1 fsbfdamc 7mu/ 2*:9xxw njcan change the momentum of the center of mass of an object, how cm wd f1fu/ax8.2ggvbjndcm: 9 7 *scx,an the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly o5 4rk*l/kw)yvej shw7.p.x yexplodes into many pieces. What can you say about thewv /jlxy5 .yhk7sr k*4w. op)e motion of this system of pieces?

  What is the magnitude of the k7/mh n h*o/w(ysl- dhmomentum of a 28-g sparrow flying with a speed of 8.4 m/w- m/*kshln/ydho7h (s    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg uy41k6lvm;d)ka q8v1f1d a3 : hahgriskier for 20 s. What is the skier’s change in vel)3:81d vfyu4 kak1rhva1a i; qg m6hldocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal liu6q(1f( ovlg( q8prum3j* ev kne drive straight back toward the pitcher at 52m/s If the contact time betweenueq36m8uv lrfgop1q((v k( * j 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 rhvo+lcf-t,0 v1ceog jcg6; +kdc0m(a 6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately afte0e61+oc ;tmf(+0 coh,-crv l d jgvgkcr, 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 resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that2 px+5ooyfsb7( n) ixf the propelling gases are expelled at a rate of 1 +)ins fo7o5 2f(xpbyx500kg/s 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/s on an apparent brea .hv-yfzcs(7b g,pp i:kaway for a touchdown is tackled from behind. When he was tackled by an 85-kv :yc,zp(p- . shibgf7g cornerback running at 5.5m/s in the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone op8z8b(i 15 6jhof fofyn alevel frictionless track with a constaj6fyibfzh5 1o8 o p8(fnt speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at dbs0pfy g*8v715m/s strikes a second boxcar at rest. The two stick together and move off with a speyfg*p 07 bs8vded of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speeds of 100km/h If thx:snod -9uils 5a1 6aoy:ny8ie air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of frn y8lo u1oaii6 a:y95ds: -nxsiction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of 8.6m/rr/5 akq(8ve ts on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg//ae(t8 rq5kvr min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially mg2i.yf7k4ns (iwzqy,0tj-om 2 ,e rq moving at 420m/s emits an alpha particle in the direction of its vg2 0nq2oqsy,zyem.4kt fwi irj m-7,(elocity, 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 particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s peneluty2; a m-lj:) pv,d zcu(w4ctrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it mcuv; (,myd2: p) llc 4awztuj-ove after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at az4o.j9lh8pix n0nwp , speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a xd4/m xypf+ r,velocity of 115m/s To alter itsr4xxypf m ,/d+ 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 kgz9 9ugc0xqn y- is hit off the tee at a speed of 45m/s The golf club was in contact with the x -9 n9z0guyqcball 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 gyy + .kj0;u *eos,zvy8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse*.o+y; ug v0jk,ezys y 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 shvfwx4svw -k5rhm6:2o/saz1 dij j: :+ h ye9a 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 crashworthis+ or t+7pgek1ness 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 e+1or+k t7psgof impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in 0. ;i1tr:66 ,yd3swff j ruc0xsk75 s by a head-onssctfkr wjx0r:,i;u3y6 fd61 tackle 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 kg) poji,h7- 2xw j,:ci mt7qhv(ex pints in the +x direction and is given by the graei h ,wmjq7xijptx2 , vc7(h:-ph 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 the lo:jspu1 de 0e,ower 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 b eu ed0j,ps:o1reaking 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 ea9 )q b4rx8.heq newjr,st (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg bal9w4rq) e rb,qe.n8hjxl, 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 wit)b saucgle9om )2:yf- h 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 collig:ce)oy2ml-)f9 abu ssion?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 pllx3th vqw 3v; /:nq6rerfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite dirqwv: ;lv6r 33qhxn/lt ection. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides hejews )l +vv6x eeg:: k-dx1:ahad-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 represent the 0.090-kg ball.)v)+ :ev lwgeed 6xasj1k: :xh-v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed m q:+n ryi ftd)eh kro+s:)06m7czc e5of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bouncehr: ckc+ s oym:i)e+ f6 nz5q)d7mer0ts 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 amusems1 iz9kj.x0dgz4zapt*0u:fqowm ,: d ent park ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg ant904d.koup,mgdzi *js: 1a:z x w0qzfd 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 elvp3sx fw-dp53te ;dn/ astic head-on collision with a second ball initially at rest. The second ball moves off with half the original spee/ -vt5sfd3p;xw3 epnd d 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 +huhy0 +p6r)tnsgw(frmhxzp 8 ) ,m5qfrictionless 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 chqx,6+hyh0t grzn5mw )p sm+8r pf)u (m 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 ofi0v.)bm alwph4sv7pj 82k2d/gxhi. j an 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, pr*krtxfm2o .-ub5t xs5ojectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes theur*s f- 2mo k.xtbx5t5 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/sqky 4 7gkiugpyj-43-/2iqdi t buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and ho2d py ijq-tu 3q-iygkg47i /k4rizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fractibqrb r0rljp-w yy;znvgm 7+ xk 3.ah7)j/n; 8eon 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, int;4r qq; bvwv6lp:)mpoo two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion6olbvp ;v w ;:r4qm)qp, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides intod n.uyngt)4iwxe 5;j9 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 frictioyex igud9nj)5 ;.4 twnn 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 frxq ik2dd-+z/r+ 0;;efcv zciq om a height of 1.50 m and rebounds to a height of 1.20 m. Approxi+zed/;crqq x-cd k0i if+zv;2mately how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a1jd)3wa fs)zn nst :v0 head-on collision of two objects is the coefficiea:nwfdtsn1js 3 )z0v)nt of restitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the mass of the ot;axxud+q:w3 zsc8 42pacu3 awher. A depression is made in both faces of the cut, so that a firecracker can be placed in it q4 dpawx3:c2 3a+uux awzc;s8 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 movjqxc9.a* dv g3ing in the +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each9a 3qcx*.dgjv mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an electron, andv yna;5b(cph2e)i(z oy93sy f zn4g:a a neutrino. Tp9b ;v2cne)yhsz( 5f a: zg 34y(ayinohe 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 mass9myevm 1h,uz:3ppl-h2 ka5dh :ok t8q $m_\mathrm{A}=0.400$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 colliska,dc/ e-ja r,ion between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial directcaj,kdr ,ae/- ions?    $^{\circ} $

  Two billiard balls of equal mass move at right angnx /3l8is2cwpd2;r vt;w qw x;les 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 After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction ofri; xlvwt8s q2 x2;w3p dw/nc; 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 wiwh (/w 8r-f0daeqg3;16h vnf z;gqjpe2qaz2c th another atom at rest. After the impact, the neon atom travels awaf6pqcf gr ( /awend;3-2e1q0h8hv zzqgw2j a;y 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 ata4pdxf r j;(qmsz l(ak)a 9;kjw. 78s perfectly elastic collision with another atom at rest. After the impact, the neon atom travels away at a 55.6 krx (dpzqa;7kt8m4aj.w; (s) s9aflj $^{\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 mas6oam eadx:gt ;54wb) ls of the three-mass system shown in Fig. 7–38. Specify relative to the left-hand 1.00-k 6mae goldt;)b:5awx4 g mass.    m

  The distance between a q,qz d+kr66ct xgx;wdd 42i/k 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 1050l5 j t-h 8.eo4w te9t0zpzta;g-kg car is 2.50 m behind the front of the car. How far from the front of the car will the CM be when two people sit in thz9l -wjg5;t hp04z.8 etto etae front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg(bb: e 9ku9ffg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, an9fgb9ufb ek: (d SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides :t4k;2gd bfso o7ae9 i 8n0mmh$l_0$,$2l_0$, 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 of tomatoixari.-v7s4v vyr;jj; djr ; s6n 9gd2 paste (see Fig. 7–40), each of sjri;jrd2-iagy 6x 9d4;sj; vv7nv.rwhich 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 radi.i2; wwhynd6 cus 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of thc;. dw26yn whie plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calci .ofg ma;*/rculate the mass of* cig./farm; o one of your legs.    kg

  Determine the CM of an outstretchuxjdi:ppw61 t;l *nc)ed 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 arm bent at a right a86* w/yh c1oe uhyjn2flu9 qr6ngle. Assume that the person is 155 cm tall. 981q2 fec lw*nj66h yuyu rho/$X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is 3hf3zzi-0yoo yivxshs7 gce.;:62zfk r *. mein a position such that his arms and legs are hanging vertically, and his trunk and head are horizontal, z. x : o.hmz kycefvi-e36syhr30sf27go *zi;calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon are(z:, w njo6o 4e*yn.hnmkk(mvd5un 8ls w+)qo $5.98\times10^{24}$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 frictionq4;c9ds3 jv 1pqo ia -:wfp5h *ujm(ogless 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 dia6wj3t0dlye-vr5;j f smeter 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 abov6yr5-; 0vwt jj3eds lfe the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical ds m) y fvmq sa2axef0yhl2u4(1 h:t*)head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0. fx tl1 4hmuhy2)a (q2fsyd)aes0m:*v500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fzd0 pq/,- 4purcamut 54l.lexig. 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 itsh-xyq1qtj.ry b b+ 9-h gondola, of mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope w+ yh -rxjq19-thy.qbbith 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 pitched hxgh,1 ci0 e1cgu)ewkc* jn-- corizontally at strikes a bat and is popped straight up to a height of 55.6 m. I 0hci - j1e*-1kcg,ne gux)ccwf the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling wit/q/ nftc p8xgp,q -dtt :ibm(3h 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 d; k2/, .l2qsodmcnajshown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in2ndda .lsm j; 2oc/,qk which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (aml44asn9 f,wincluding space suit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-kg space capslsf,4a a 9m4wnule.
(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 69*hgh(w6unso9y*: e gpb a4vl0 kg and the other 80 kg, are initially at rest in outer space. They then pu:64gl h yg9*v(s wh9pnab oe*ush each 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 ball (azx: zony6-9oo:o*lma .js3 ;bva v a6ot rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the massa lv;oso6z6 mzx yno v.oaj9b3o- :a:* 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 3ya0vq/kwb1 : 4bsyozinvolving 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 baby v4 qwso :z0/k3y1the 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 aw7ax f5sc/r13l-gs lmb4xyu s*8xb- m flight 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. *u b4 fl8ssr-ml swx-bg5a3 /xy71mcxIf all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest disgo m 6k;rhq:3s99hh*1o2 mffq/y lc jrectly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how mhq639s *lhc1yq2 rooffjs :km/gh;9 high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becoqjxsf -/cl53g mes 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 to rest, what was the muzzle qg/xf-35ls cj speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a row4zjakkku ljq 4i2 4na1 2*oqcfy53. jhboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what dirj14i2k l5 nqoakaj cfjzh.uk 4q*4y23ection 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 wasbv0w22t;.odtl1w mi g about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments by an explol -lnxf -uh,,fmjt)e*zhp c4 .sion. One fragment acquires twice the kinetic energy of the other. What is the fch ue-*fm4znx h ),,j-lltp.ratio of their masses?   

  The force on a bullet is given by the formula F = 580wu t6)6f.bk:c dpnagc:7 d3wq -( $1.8 \times10^{ 5}$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 ud*2;g/ etdou $m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an mh :; kyndlm(xxv-7y.alpha particle and a smaller nucleus. What will d-yyn 7ml(:x;.k mvxhbe 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 tarlzc-wrtq8x)a9zu- (z get) is fired at 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 slidesm)p7 ;dzvn7rq 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 ofbag-u.o)hh os*:3b limit on mass m if it is to rebound from M, slide uf u oh.gb-ha3ob:os)*p the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet S0g-m c3 +eoauraturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Satura0o rgm3ce- +un 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