We claim that momentu+m73 :2y sq 01f5wueeubt s8 umri0lu-cxwbq9m is conserved, yet most moving objects eventually slow down an uu5qsemb:tw28 3-bl7es0muxycwf90+qr u 1id stop. Explain.

When a person jumps from a tree to the ground, what happens .kbhl yt3ymo1; qx,;2o 3rqyiw2, qmyto the momentum of the person uy ,3;y2mk3i2.my,y x 1olq ;bhorwqqtpon striking the ground?

When you release an inflated but untied baldw*, ejxxs 7;/-t uuswloon, why does it fly across the room7te ;xdu- js*w/ s,xwu?

It is said that in ancient tids qucyv7 ar*b0l5(tc(x+ yo4mes a rich man with a bag of gold coins 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 miserly? yy( 4u+d5v0q c*b7xtlsrcao(

How can a rocket change direction when it is far out in spu qsw)m rw0)8zi ),m.rs :bwtaace and is essentially in a rwsi w.b mu8t) 0mws:rqaz)),vacuum?

According to Eq. 7–5, s ;rn mbxxoig ;ee5(2z mbp zhgay8x36k9:z*7the longer the impact time of an impulse, the smaller the fz7(s x:;oenp kgxmzh5a* b3izygxe 6 rm;8b92orce 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 reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand feyvz+rmk- ;;(vrg/re 7ef6 qcollisions. Today, though, cars ar;r m( f r7eq g;-f+re6vv/kzyee designed to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further tha vtgt)hc5 -1osn a ball tossed in the air by the batter vh1s)-ct5 otg?

Is it possible for an object to receive a larger impulse from bp rd0qx86gc fb0(a+sa small force than from a large f + 8r cbfxa0dpgb6(s0qorce? Explain.

A light object and a heavy object ,ojkb)b g9rh) have the same kinetic energy. Which has the gre))r, jbb9h okgater momentum? Explain.

Describe a collision in which all kineticjajsje1+:yrw0afc:h )o m+/ b energy is lost.

At a hydroelectric power plant, water is dieaw +g0)uk o7 uiq09fqrected at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designe) io wu0a+7qe9u k0gqfd so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits aclr qm)( eu: rw2wef84 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 dropped f3; -ysmi cr:tc.er1rgrom 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 g-yr3mt1.cs:ci; rerthe ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carryingg +zueyava/s83( ze8e - tqwp* a heavy load in your arms?

Why is the CM of a 1-m length of pipe uggkhqt5 qh 3/9g2y *18ho.dof3uzr o p s9m(pat its mid-point, whereas this is not true for your arm or le9 sktquozhq2(odghy91.go5 pr*3f3p umg / 8hg?

Show on a diagram how your Cc0dx4o xqg kgdlf( 7a:,,sv-x M shifts when you change from a lying position to a sitt od 4 -(cg :xq0,ag7vdl,xkfxsing position.

If only an external force can change the momentum of the center ow *wws1r+9j) ymrk tek qg;:4xf mass of an object, how can the internal force of j tm: grq 9+w4xy)* wkek1ws;ran engine accelerate a car?

A rocket following a paro8hc*w uvc7n++qt wb- abolic path through the air suddenly explodes into many +uqw7-whcb n+cvt o8*pieces. What can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a rnhk 6kzs8-/zspeed of 8.4 h8s6 n rk/kzz-m/s    $kg\;m/s$

  A constant friction fo* pq6xv*2q +h3ghzijp rce of 25 N acts on a 65-kg skier for 20 s. What is the sk+ 2*hxzi3p vq ghq*6jpier’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive tka-co)1:nbistraight back toward the pitcherb-n:k taico1) 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 thr t rh98vrs*ztzbq1t;0 ,/rloyows a 6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming yzq ,1r0rs tol;z */thv98btr 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 that the propgo 5(fjvupet )ce zsm2j65q3vk2k1 n1elling gases are expelled at a rate ofu5 m pej)tjvfegkq 2sk53zo(6112c v n 1500kg/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 breakaway for a touchdowntrfaud-.a+bei1 h-/ 7lur ap ) is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s infla-ba pt/ ru .+d-)7uhi1 aer the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevhz8e dsq)/k/;:xi hf *s j4ntkel frictionless track with a constant spee/tqkn : d)z8hssxi/h ke4j;f *d 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 15m/s sav.1imi5k ;b rtrikes a second boxcar at rest. The two stick together and move ; i1b .imrvak5off with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speeds of 1qpd8+ 1tjk9q8 nh z v lgqphwoo.qt.c,g2/1w)00km/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 person is 1.50 m high and 9.. ttw8nh8q/+wjgk q , dglp)2o1 hzqcvq po10.50 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 consta4l4 w n;du(nzpnt speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of wl;pn(d4u n4 z3.5kg/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 p: .:lw*jg(p3a vky mp9w +wic(fkhx o2article 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 origipw:mhkwg(+l o(ykw :af2.j9 pi3 *vxcnal 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 prdv 0sz//kiky ;js s ab(:8u.menetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block.k0 zss ju;bvirk/y8s/ ( :mad 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 a spe. g:+ yu+nrhvyed 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 oute+dl-/fx g1 c 5kli.wcexb9c 0pr space with a velocity of 115m/s To alter b lw i 9c+xpxeg.d/5clc1k-f0its 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 bz tqse0auk-chhsd67:06s: s at a speed of 45m/s The golf club was indzt- 6q: ashu:skcs0bh07s6 e contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity oftg6qi:2pt zz ys8z:z77 j.7h jauj)zv 8.5m/s and comes to rest in a tim 8t: z7izh7tj:zvzuj6 p7jqgsy). za 2e interval of 8.0 ms. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.qo 0b; yiwm0d, xp:5gu06kg and speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthiness of new autom7/r/ 8d almnkmobile models. Cars are testedmrk l/ a7/mnd8 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 and is stopped in 0.7 b42bfpi4 dw0fto.:g c5 s by a head-on tackle by a tackler running due west. C b:cw.o 2b40d gf4ifptalculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points in thb7pu3s5l45x3+jj1w yc q dwule +x direction and is given by the graph of Fig. 7–33 as a function of time. 1x w l3jyj457bdcu + wl5puq3sUse 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 breakinuk(z66a qsj q2g the lower leg bone of either leg? Ignore air resistance and assume the C uq2j6s kzaq(6M 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 g.ng+-s 1dfpd k)bd1wmoving east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly k-dpsbw.1d)gfdg +n 1elastic, 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, 9.m;sp gzy)/y.dyxoe moving east with 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 w) .z;ysx9 gmyyd/p .oeill be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elk,k08hmz * u5m 2.l+n7id eziq ho(zkx;c2mbzastic 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 theib zk m2c7luhm5;qh2 *8, ze0+( ziokmxdnzi. kr 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 offjb0puuk4 s0/ 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis sj 0k4pubfu /0ball, 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 wit :i2rzjbyto z2( a0,jbm o:z5eh a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bouncesb j zz,5 bry: jz(0aeio2:2mot 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 amusema.* wek ;std/hent park ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences /w;*. hd ekatsin passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a secondksww7sw bv4n 55rkzx+9 z tp0; ball initially at rest. The second ball moves off with half the original speed of the fwz47 r w5tv05szn9;kxb+ks wp irst 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 cui41v y,b: hephbe slides down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom tyiv,:1p4h beh hat is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of masok32xp8o:iq+8 .w: umrbsdw ds 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, -gufzsb2n -2e5at, 8gqp)7wx d-oi icprojectile 1 results in a maximum height h of the pendulum equal to 2xi7) 5sq-wcdeg8 2-, o g-fiuz2bnpat.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 buries itself in a 3.6-kg penr 5unvgy w)tjrj. s+4/dulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine th)u+5jrgynj t4vswr/.e vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetk8s/ 3 o+bp6pta ri+ cjtxib:*ic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into two pieces, ongepzg5d; : /f3ug+afu kr7j kuu e0(v8e of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each p/gp v f7f;k8ruka3:uz+u eg jedu5(0giece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collidj9 91;5n virw fu:olh muc:dxyg2u)d6es 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 speed of the spr2;o:6dmfhwd)uicyn1:5ulj9g x 9u vorts 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 rxql ug 1bsh6,t41z*laebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of i1 ,hat6x1l s*glz4bquts energy?   

A measure of inelasticity in a headuqu l-npv3;eag /d z/(-on collision of two objects is the coefficient of restitution, dzlvg(n 3e/u/ uaqp-; 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 scw04h xnp*,y into two pieces, one with three times 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 w *4, cph0nxsythe 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 hej;moa lt uq9/0ad-on with a 10.0-kg 0lj 9;umotaq/ object moving in the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an electr o4 p j*.qhtv34cg8pzuon, and a neutrino. The electron and neutrinq3cozg4.* 4v uppt 8jho 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 maysa:c ,(05s/ t/f4 zyx jzergxss $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision zjx-.1 (i: v(xbaxtxqbetween two objects of equal mass, each having initial speed the two move off tq-jazi.xbx:( x1 t(vxogether with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move f l;yn vw 7m- ;,p0g8rfm*px sltfd5.mat 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 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 0;.7p,w td8m*f mm npxgfy;5rvslf-land what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with another atom at r- t6axfwxzn6 +est. After the impact, the neon at x6wtxf-a 6nz+om travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision with another ato w0p*tjj8le)+y4zb xh* 6ab xhm at rest. After the impact, the neon atom travels away at a 5hpbj6e8ay zl bxwt)*40 *xjh+ 5.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown em)w oc 2ig4tobff /9e/y z+q:in Fig. 7–38. Specify relative to the left-hand 1. 2 bfit:e)feg/yqom4c/wo9 z+00-kg mass.    m

  The distance betweenm4 z3-t5(o r2ezpr-gdz,rc tb a 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 iaitbc27u k4r;ikzuvw 4yjtx078 .ea2 s 2.50 m behind the front of the car. How far from the front of the car will the704xt4ik e8 .j7uazkw yic t;2ubr2av 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 mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 680:+gu e4 a3 fro::qfzgh0 kg, is used as a ferryboat. If three cars, each of ma3qz+a geh4 rofgu :f::ss 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 sidekj8mvxs h )z sg 4u(x5rj p4q;ov(-w3os $l_0$,$2l_0$, 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 tomato paste (see Fig.b)t0qco9hc+/. ly q wo 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 bwo 0c/loqt).+9q cyh up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular pt zabx ov,3f./late of radius 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.x. aot ,zvf/3b 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your prop6.qpi q2bn+5u3fvltc3ra:hsm7 ad /p ortions are the same as those in Table 7–1, and calculate t dh. / 5ba:pn3+f7q vpq6lu2tr3i acmshe mass of one of your legs.    kg

  Determine the CM of an outstretched arm using Tablenx br(:amwe5 t44n4 vy 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 CMla78ti4qanj g w 1g.+*t6rflcqpz.7f of an arm bent at a right angle. Assume that the person is 155 cm tall.z+.qatp jwrnl q7f.7t 84fg1 ig6*lac $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is imcd:zrf3migz h/0 ,, cn a position such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use3dr/cfzgi c 0:m,,hzm Table 7–1.

The masses of the Each9srwf0jyu9 4cj r-) ikgz9 8rth 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 aparx,0czr (ixae3h .c y9gt on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a u vfy)s4del2u-niform cylindrical 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 2s-)efv lduy4 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 head of mass 2.00 kg and a diameter1 ,i .g9swsesl 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 ,i1el9.s gsw sm, 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 (Firwwh37o, x ib.g. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and st 7ulenqu ;f9rc: (cqh7ationary with respect to the ground. A passennul 97 cc;rhqq(eu7:fger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizonr uin,qmdso d) :*k:v-tally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calvm k,i-us :)*:ond qrdculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling wn:4 p40gahf7 xr5wvej ith 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 pozr kat1(7ka3g cket shot shown in Fig. 7–43. Relative dimensikz13r7a (akt gons are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including spabm8 bmr4eb *m(z)8 x:3cpujv lce suit) acquires a speed of 2.5m/s by pushing off wit8lmbz cv 3b:84r*j xm be)pmu(h his legs from 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 6 **i1cdg 8qxnfusud.0 0 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut ha *sg .0cinudx8u1*f dqs moved 12 m?    m

  A ball of mass m makes a head-on elastic collision w2 bl;s8lxz*ajst x8x+ith a second ball (at rest) and j lxzxa x;sb 8+*tsl82rebounds in the opposite direction with a speed equal to one-fourth its original speed. 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 av/( 9+ izbs7fg+xif p fy8:6/ibcuqg m court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of masf iyqb( /+/s8xbvf9+iigpu6g mzf7: cs 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 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 qz3h+8mbtv 03 f;rqsbof a 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. If all collisions are perfectly elastic, what is the boun z+qsbtq;30bmv3 8hf rce 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 k*9/rzp (s5fevj ilh1wood at rest directly above (iz psv*l5 9jre/kh1fit. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg 7972wwro l( wgm5 mfm)zbap(j 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. 9w 72bo 5frjmgz(wm m(7pal)w25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowboatf957milk0 pr sbo;2o ym2ah, 1lr eu0v of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends as9l0,mouy 5pe; bmkv 21 0r2of7ihlr of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abrdh :e x)o7b+9q)hhtqout $ 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 framq)jg+ )wwtcs7c8z8 b gments by an explosion. One fragment aczmtwj c)q7c88b+)wsgquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bulletd02qstu6 2ty r 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 masses ;iz +9c0ys8- .uw,e by;xeqd(fofeg s $m_A$ = 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 restap ddjx)u/: )mxo rt,*ra(g3t decays radioactively into an alpha particle and a smaller nucleus. What will be the speed of thi p)3ra rg(mu:dt/ta,oxd *)jx s 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 (clay6mlqxfc* 0wl, target) 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 slides dojd(fn 66kij8 own 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 on mass m if it isrnri9i,po;wof s+7 5 m8k,o av to rebound from M, slide up the incline, po os+naivf;5r8i k mr,,7ow9stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn movino7 x k6itd ,0zngk4*zzg izidto 7 n6xk4z*0z ,gkn the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s