We claim that momentum is conserved, yxa .nlao/5mcryx, 3lo2,9tddet most moving objects eventually slow down and stop. Explao cldl mdxa.3t5a/xn,o2ry, 9in.

When a person jumps from a tree tung+t a z-ha-l+ hx/:qo the ground, what happens to the momentum of the person upon strilz/ ngu-h+ h at-x+:aqking the ground?

When you release an inflated but untied balloon .638vsvodaji1e3rf s , why does it fly across the room3fisdvv 6.s a81orej3?

It is said that in ancient time:hmaj +u xw*a2s 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 misex*j 2hau+: mawrly?

How can a rocket change diwssjo+.ti 7 4g .m+ftlrection when it is far out in space and is essentially in a vl +7tsjt 4.+fm.wis ogacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller the g 4 o8k0gd2)bgjd2ldp force can be for the same momentum change, and hence th lg) dd204d2bjgk8og pe 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 collaa g(lk(c/, pqisions. Today, though, cars are designed to have “crumple ca/,(gqa(lpk zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further-o;wpqfq7wcj3 :a 4i -4nk szr than a ball tossed in the air by k;q-iwjc74 nrap qw4 z3sf:- othe batter?

Is it possible for an object to receive a largt 1agxp65y ydx3g)x.ler impulse from a small force than from a large fpt d15 xly ax3.6)xggyorce? Explain.

A light object and a heavy object have the sa(dja+/9+khx,r v t jfvme kinetic energy. Which has the greater momentum? hfrx/dat,vj+k 9+v(j Explain.

Describe a collision inoa;zu++i0/b 8k 3x.v twnx mgx which all kinetic energy is lost.

At a hydroelectric power plant, water is directetja xzhs8y4x q r+3a*3d at high speed against turbine blades on an axle thsj h yx*qrata zx348+3at 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 the water rebounds?

A squash ball hits a wall at a 43 8 pdpf6c+tyq5 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixb32drds2(jai ed to the Earth), from which it rebounds at very nearly its origi2jbr32sd a (idnal 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 sticks to the steel plate.

Why do you tend to lean backward when carrrbb f 95xz05lah5e0+ nt,i/m7ilph bt ying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas th.if4a4 arjp*o is is not true 4p.j*aora4if for your arm or leg?

Show on a diagram how your CM shifts when you chys0: zdolq3ahh8- e2f ange from a lying position to a sitting p:h yl-fzdoes3 02qh8 aosition.

If only an external force can change the momentum of the center of mass of an obsb*zx h* w.)egject, how can the internal force of an e*gb)sh *x ezw.ngine accelerate a car?

A rocket following a parabolic patti12 e cjwr6v-h through the air suddenly explodes into many pe - jwvctir261ieces. What can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow f w.l0bt-h)lh b6oiv w.lying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N ac; :s w3ova bw7ytum9k;ts on a 65-kg skier for 20 s. What is the skier’:sy a;3m7bwvk9uto; w s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit o1xqmv(5 oy voab4ma:c .wd17tn a horizontal line drive straight back toward the pitcher at 52m/s If the contact time betwet cy4 vxad1ob .o:m7qv5(1 wmaen 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-kp szxi,hb;dzi6 63c n)tz/ i0lqij5f 4g package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass ofit4z;i sb zxd,q )cni/66p05j h z3lfi the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, giv,*le9 si7idtv en that the propelling gases are expelled at a rate o9s7tev,il* di f $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving athvc :: u+ xp3ev-l ejvhj/5a*a8up,r y $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless track with a constj w4fcn2he2 n5ant speed of 18m/s w2h4 ncn52ej fA 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 travem rdk9nctpa700j;( xj f1xsf,ling at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizon4lsp npgum1g c43zi3(tally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Comparl c4m3p3pzgnug(4s1ie to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of 8.6m/s on j 8) mwt6g x;5-aggwpla level track. Snow begins to fall vertically aaxg)p-mj;wl w8gt5 g 6nd fills 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 initial.c 1)p7pz bax xb5t0v *kgd9wlly moving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have.t91pp *xla5 w vzcg)bbx0k7d when it is emitted?    m/s

  A 23-g bullet traveling 230vp 86 (vhe7kaem/s penetrates 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 move af87vveah e6k(p ter the bullet emerges?    m/s

  A 975-kg two-stage rocket isdz:f)*h5) 0c +tis7igfxwkld traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is travelircr jx36ulzaz n9 m a:5gb(zcf ed8/).ng in outer space with a velocity of 115m/s To alz6u .g5cfelandzb8)r(:a/ mx9jz rc 3 ter 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 tee at a sp- pw;.cb5 8 e/ey3fasrindu+reed of 45m/s The golf club was in contact with+;b5 rd.-aey3u8 nc ir/efpw s 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 naip*8 mtr9bu8kb)i64ug2n dbq+ pgjwk.l at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What ) w pirnb*m2 u4p6+8 kug.jd9btkqb8g is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes a wal 3do-r(ux)xlchet3 ;el-w m l1+e(gfxl 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 zzwa1dgq:p1-k6 q,sayt,p;l crashworthiness 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 broughtqwgp a;q6s1:z l, kzp-da,t1 y 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 east4-bz.l(ag ()h zo7uua nkptb8 and is stopped in 0.75 s by a head-on tackle by a tackler running btn lbz(o8u)(zkpa4.uh g7a -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 0.0+f mm6ea)uk (b1vs4iw8q 2aowk6 t.xf 60 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methoxbk+6m6fa2q)4 ka(.mwof 1svuw e8 itds 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 break(k bb/24 3uxkqcboope0 :i4c wgf2wu3 ing the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m frbpwoqeg 4 :xiw/3o2ubb2u 3c04kkfc( om the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of collideos) j1y./+f b 5ipjhyys head-on with a 0.220-kg ball at rest. If the collision is perfectlys/ ijfohj.yy 1b)py5+ 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 collrkk-m y2 6lb0cision with a 0.900-kg puck initially at rest.2-mcryl0k6 kb Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elasti 01-ibsw3 .j)ai jq-v/qbg kgrc head-on collision. If one ball’s initial speed was 2m/s aniq.bsvjra)g k qb0/- 1gw- 3jid the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.-lrymtsavbovm( i4,*x 2k::a5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1 v-vak( ::t2xlmao *m s4b,yir.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'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a spe4t ly7 pia)xx0ed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bouncex7axp4i )t0lys backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement p6ts9iirk:fzwu o*e - +ark 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 in passus9te wriki+z :o*f-6enger 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 c3-yv+d6s *scm4mw 7me zof e/4gmhg:wollision with a second ball initially at rest. The second ball moves off with half the original speed of thef:dwewm hg o673+ym4 msvcs4e/g*m -z first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as shown in Fig. 7ut 5r3 jo+.mtkys; (zij i/h imh.0nr1–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Bo .th0(nyokz.;rj 5/ t +1iirmhm s3ujith leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of mas nupe*p*jf 4elp( v5p wj4d;:ps 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 e d(hgl4t2*r fl)w+fw+ wjq-a1 results in a maximum height h of the pq a *- (dffejtg)llwr+2h4ww+endulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s byihr4b( 84i4+;-5y ba ncmut*h apv8 zd z8lphuries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an p84t(dmhzv 4cli ayb-b +5 ur8ph8a;iyzn*h4 arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fradv9b/3l hh w 3f4hu8:z.c pqomction 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, intoh. qrkjn:st0k hf8. r* two pieces, one of which has 1.5 times the mass of the other. If 7500 J were releasedh .sht*jqr0r kn. k:f8 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 collides into the rear end of a 2302jr 6e:j-gju 8:;semrp:p svn 0-kg SUV stopped at a red light. The bumpers lock, the bramv-;:2j p npguserj6:js:8 e rkes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a heiggu/wdx4-n)/ /1lj l kb155hazy:7w pnvi vqrght of 1.20 m. Approximatinwlq:wk)p1ba 5/ - vgxh1j /dn/z7gyru 4 5vlely how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelastic lt*u.mk0- lo: re4mdcity in a head-on collision of two objects is the coefficient of restitution, e, definrdk-t 0lm :4.cluo*meed 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 pieces2 c27p6,+dbsl:r0cae f,ipa b joewz,, 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 the block reassembled. The reassembled block a6ce2fc: bs w,,r p+ lad0oip,27 bjzeis 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/sh.*m- n g;s 9pf)j7f0xvss: xgrfgi+ s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mafn -97jhm0 s*fs sfr;xgg .spv )ig+x:ss 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 ao h06cqbirnm, 20gx1at rest decays into a second nucleus, an electron, and a neutrinqcxhn0 6om 0gb1ri,a2 o. The 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 m)3 axn *uu/wqrass $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of j2ho/4ov eabfkdo dfys(:263/ l6nl f equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial di346onf l/kj (/ b eldhoaf22vfoy6:sdrections?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and f +k rtw6nwb7t85c) pyxur*6kmeet 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 axisyu k)+t6k c6n8*tf7r pwbrx5w (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 aq 3 sgd6,/ vn(hxt+j+u) hclngt rest. After the impact, the neon atom travels away att,l)gjh 3g+cdh uv6s(nq/nx + 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 collxk d4e8+ )fw zwhodrxbo3:7 qd.v;0izision with another atom at rest. After the impact, the neon atom travels a)bx wzd;37 : z+.dx dwqoe4rh0ikfov8 way 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-mass system sh 1:qg/elaxop3qpi de/00p:pckwo 3nj 7p;d(pown in Fig. 7–38. Specify rel 7 :n0p;iejoppog q:/3 a/x w3e(p0pl q1pkddcative to the left-hand 1.00-kg mass.    m

  The distance between a carbilvue,pi6(((e0 vbb.j dw:z lz0o w0e0z p2gqon 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 behi v v;zclyy:a7r.ky x4:nd the front of the 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 pe. y:rvxa cvy4 z;7yk:lople 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, is used d; )mtuflwnf0 fz17*aas a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loadu)tfd f1 fzal;07wnm*ed ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidestt7pczx t 5:0e $l_0$,$2l_0$, 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 loakra m ci8.:ioif64 a3fd of identical cases of tomato paste (see Fig. 7–40o 8:kri6ca4m. a3 ffii), 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 the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of foxz+e/j2t4 pradius 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 the plate? [Hint: Try subt/+eop2tx f4jz raction.]   R

  Assume that your proportions are the same as ffao )ld*2)vl3 mue r-those in Table 7–1, and calculate the mass of one of your l*loa fu)lmrv )efd-32egs.    kg

  Determine the CM of an outst0u9fq zka*2 s;enos: rretched 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 ri1d v0a 6tbj/hught angle. Assume that the person is 155 cm taj6b uh 01vt/adll. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is inwhow-d) x-m. fffp l14 a position such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate h fwm.)w-df-x1 p4ol fhow 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 Earqr-. x3bb.q 2lrhr+mutg*hx n7fz 2;f f gqo2+th and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on frictna7h 9hqd(3wpb89c e vionless 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 mh)+f -y1l asp+yvgrg;ass 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. -ly;vhyg g s+pf1a+ )r7–42. 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 cylindricb2(s q/gn4z uaal head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will folu4gn/a sqb2 z(low a parabolic trajectory?    d    d

  (a) Suppose that in Examp w:)+p1.pd nxnj lln2wle 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 masd+ dcb(h02n cici a-l8s 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 with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does thhdacd i02 8-(i bn+ccle balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horepu4 *4/tj,k;b8 j kq qlgul1uizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calcul/jeb;u4 1ku t *k,l8lqguj qp4ate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with s z9qa 5yqo i:lmc2 3//zqo08vcsa :g)xlrcx 6upeed $v_0$ 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 b0xzdwca1.q(r6tpb 4 faced with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about0 b. 14bqr(6wpcdxt az this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by pu(yq2c w 3ypf.-q u0knxb:j8 pishing off i -y cw2ku3pp nb8j0yfq.:q (xwith 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 9e zu4q)5- ljlsqes/u t4c w3ymass 60 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. 5euqw4ue lqsy/9c)t4jl 3-zsHow 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 az/-y 1)yiioey3 qk xb896yq *n7qhv ai second ball (at rest) and rebounds in the opahqi ebq q yy-6n )89xkiyi3zyov1*7 /posite 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 a court cu*q75) ;afb zy ;fsyocase 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 caryfcy a)ou 7z;*b;q 5fs 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 of a flight of concrete steps of total verzxfv wtfq t5t lj6m,p .i39f7.tical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a,tm.ftw fzfj t p56lvi.39 x7q 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 of wood at rest directly abwwjqr ii57(pd 8p3xc x16gwh* ove it. 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 xx* pc hr p(7w 3wwig81dq6i5jit?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood s 7pc4 3npvj7tplaced on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block anj7tp v4csnp73d 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 speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other h8akbpaqpx 61s+ m7 3cof mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from eack618m+ap3ah7 xcqbp s h 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 aui.nr 5z5k3mn ;p )h in1/vf *q+rwlnsbout $ 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 ap5ha5xn rz3d7lart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the o5h 5lazr7x3 dnther. What is the ratio of their masses?   

  The force on a bullet is given tt;p:);vlgek8qgv2f 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 massesyg f+/5zbaf u /bf06hl $m_A$ = 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 radif 6jzj(4 r5)mmc-u+z qb2j hyxoactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alphj5-b+cjjqx u r2ymz6m( 4 fzh)a particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at fq i ,wwj2.v9(ole a6pnhx7r3uz-ft4an 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 doweg(qt:gl.75odb0rk bfa)z o ,n 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 u/:10oq i0j0qdp:(z ukknic*qy p :vnd pper limit on mass m if it is to rebound from M, sl0 1ok nui:ppvijd/y:q:0 z(*0c dqnqkide up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot m i1ryz/i t)a*effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital sp z1taymi* ri/)eed (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