We claim that momentum is conserved, yet most moving objects eventually sd0at fvcu09ox sy90c .low down and stop. Exfyot dus0c0 .9xc 0v9aplain.

When a person jumps from a tree to the ground, what happens to the mqdow 9m6/ uq y 71a;6fnq;yijqomentum of the person upon strikm6; fqiqja;o16wdqn 7 yq/9uying the ground?

When you release an inflatets p.*v zm iuawz1r(ndby )je9 13y+e0d but untied balloon, why does it fly across the room?(d1t*)sa +n 3uyiy 901p ezz.wrvje bm

It is said that in ancient times a rich man with a bag of gold coins 5/hls(i)g zfh2 z*mtng0p.rhtlk. 6wfroze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What cotth 50.zplhkzl ( ngiw2*.g)h ms/fr6uld he have done to save himself had he not been so miserly?

How can a rocket change -e3mvijscgm ph. 7t+ 0 uaf-0zdirection when it is far out in space and is essentially in a ejs 0 ch.3z-m+-pg a0 tiumf7vvacuum?

According to Eq. 7–5, the lomxc vk) n7ev:g th5ly(a(xw0.nger the impact time of an impulse, the smaller the force can be for txc t5lvg( en (k7x:m)a.vwyh0he 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 collisions. Today, thg 29x jj+4qb8:uvqcqrough, cars are designed to have “crumple zones” that collapse upon impact. Wh4 r u+j qqq:gbc9j82vxat is the advantage of this new design?

Why can a batter hit a pitched baseball further thanh h(04mc ylr9rdy;r e, a ball tossed in the air by the batter?lrryy,c h(e09;r4 dhm

Is it possible for an objecm) 55pd cn1gqmt to receive a larger impulse from a small force than p 5d5)cq1n gmmfrom a large force? Explain.

A light object and a heavy object have thi(q;6:cu - q s)ujrui ;qvc9qde same kinetic energy. Which has the greater momentum? E:v - qcuicqrsj6();;qiq9u udxplain.

Describe a collision in which all kine8l((9zol 4iy )1szn6nhvhix1qfvv3v c ww:, jtic energy is lost.

At a hydroelectric power plant, water is directed at high speed against turbine;vl8mmw ,d5(ct b :rpz blades on an axle that turns an electric generator. For maximuz 5wprmbt :c;,lv8(dmm 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 walf6ikl +b*9qlhk5 r;u4ic7*5izkhrkj l at a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a han2n;ed0xr47 aw*a q6efy+xm vrd 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 pa7we;d *02vnrn xy4fa6m x q+eart 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 wy 4lm p+bpx8 qjuj o;4v+y4x;when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is not tru2:ss2vznd 7 lwe for youlw s2dnvs:7z2 r arm or leg?

Show on a diagram how your gy3j 8)ui)dggCM shifts when you change from a lying position to a ggy )8i3j)g dusitting position.

If only an external force can change the momentum of the center o23qlhby e /.fk o+wvl1f mass of an object, qkfh.y2e v1 lb+wo 3l/how can the internal force of an engine accelerate a car?

A rocket following a parabolic path through the adeeus o8o -bli g3 3uk5u--l8air suddenly explodes into many pieces. What can you say about the motion of this ske8lg-5a s-od oul33bui-eu8 ystem of pieces?

  What is the magnitude of the momentum of azc2 / 7mlnnzv xsh30c)+ r2qw2i sbo)z 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts okk:dp) f 2wh0i ).bamrn a 65-kg skier for 20 s. What is the skier’s chbm2 wfkdh0.)a ripk:) ange in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit c y3jih3;ra +bgvy+j+e 7: kewon a horizontal line drive straight back 3 : eai;kerwj yv73jyh+bg+ c+toward the pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out e71 p)m2 pdt;;53ikuxe nzzfdhorizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, asskempd37)u zxef;t5 npd1i 2;zuming 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 magnitude of the velocity of the boat is    m/s

  Calculate the force exert2fpq6umb/twas lydrq93p /6+ ed on a rocket, given that the propelling gases are expelled at a ratr/b6ayp d+t m9fqp/3s6 wl2u qe of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving aa2r ulp;+pz:6xet4 l/d oz4nnt $4.1 \; m/s$ 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 cardy9a8-xahijez;4 dk0 travels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s nexeh-90; k8da dzja4y iw speed?    m/s

  A 9300-kg boxcar traveling l6,zv-y6 eh,upilx k8 iiq52t 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 horizontally at speeds of 100km/h -yu ld):x9pv nIf 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 per-dy9nv:p ) lxuson. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constantme*jpn- g9g7 y speed of 8.6m/s on a level gp*jn y-m9 ge7track. Snow begins to fall vertically and 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 initially moving at 420ox0npw ddb2 t0k5 4ik*m/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 thexkw40t o25ibkp0 ndd* 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 penetrates a 2.0-kg block of wood and muj)3 k3y1-go.zmuyz emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does )kzm3-31uym j uo y.zgit move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a spe)s0hpd*u+ja ul:l h k 9fhr):ded 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 ma,/92loyeet gl3b lk2lss 3180 kg is traveling in outer space with a velocity of 115m/s To alter its c2ge9,2ektlll3 ly/ b oourse 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 theaupxw1: m:o4n -8jusy tee at a speed of 45m/s The golf club was in contact ps8xujumo4:- n1wa y: 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 0abr+.pdz04,ym 4 fu+drnzb1 a-icm*iumtz+ nail at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the+fu zi*4zz0ri m0ta+m-by, rbn1ad+4dp .muc nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass mvj0g l 8w,wp2n, cw*om=0.06kg 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 crashwo:z+zn8jwx h 3mr ;9smz.pvyt ,rthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A ne:3jz tzr,n9wvx 8 pyz. ;hms+mw 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 0.75 s by agv4 .w -)0jug rglcjd( ov9i-s head-on tackle by a ta-9sjc (gr o)-iugd vv wj40lg.ckler 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 (ikippw3p2x:0.060 kg) points in the +x direction and is given by the graph ofp 23pxpii kw:( 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 withoumhzns(e/m6u2xjv) m3tb i.- 1w i+ baat breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance o(a36 ve nm+2wja bm)/thz1 -sixub.imf 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) wi+ajj)f (04.y)zu vkrgupfp y4th a speed of collides head-on with a 0.220-kg ball at rest. If the collision ig r a)04juy.(+v4 pkpfy) jfzus perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s hascmlb hda-c;arrih*n ,hf ;9 42kh2+))cvlc uy a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collis-cuhhhrllh4*y2 mi; ac)a c f9 r+2n;,) vkbcdion, 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 perfect 6go )p5hb3pobly 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 ap )hpo6 b5o3gbt 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s cx- nf/ma k)sxeuj:2e 3ollides head-on with a 0.090-kg 32:k)u-f nee/xaj sxmball 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'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s ck hs)fd ) /,4bodyux,wollides head-on and el 4,)),uhdfxk/s oywb dastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park riav*2k, r9qm o, 8caegrde 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 passengegr2oa98 *, crqe,vma kr 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 a.kcml(j,. eaa 5t-rnln elastic head-on collision with a second ball initiallyj.tr a e ma.l,c5(-nlk at rest. The second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slidesacpw5*a lnc.ghx a+9.2z9 gb b down a frictionless incline as shown in Fig. 7–35, ..g5ca9*zwhx +2blpaca 9bgn 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: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of mvvyc j 7 c0qx:r 3erg6wcb/)q;ass 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, projeecy g5)r0h)ox ctile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A secor)c)g5 0 hyoxend 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 itselfpo 25ut3 dg7v)v;f9qcyw3;lz4h p zrg in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in ano4 hv)rp;zc5wdp 37ft3luzg 92 ;yqg v arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula vlt hu ;cqx3k*/9kus1ixt 0 8.pmdm,ifor the fraction 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, into two pieces o: f xdmkd,2klh,2j0d, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did eofdmd22:,h l,kj kdx0 ach 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 collides3vk+k . 9umurma,jffh+3-oo2*k snrg 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, c vo. u*h2gfkr mkok- ,ma+ f9js3unr3+alculates 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 height of 1.20 mzxxy 0twv1skl 2tnl0z,26 yd3. Approximately how many rebounds will the ball make before losing 90% of its ek263,v0210ztl z ydxl xsnwty nergy?   

A measure of inelasticity in a head-on collision of two objects is the coeffic;ca s8c6n7f2 +af /dy;ote jqqient of restitution, e, dne8casqf foaqcy6+j;/2 7 ;t 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 ;ea0zyvb ta 6*uz2cp7times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explo 6u;0t27 *aezb vcypazdes, 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 r4ou66l6b hsy 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 eay46oush6b 6lrch 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 ele(,unrc gwip+) oil( (rctron, and a neutrino. The electron and neutrino iw(ncior )ru, l p(g(+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 massuh8w )d- i6und/uwm;l $m_\mathrm{A}=0.400$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 objez d;eh1e/db+x 1ytp 9ects of equal mass, each having initial speed xd/tdype ;z 11+h b9eethe two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the o :jh li,jd 6;ti/u;0d rvfsk,urigin 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 and ws,0d ;jf;:i6,rk/ utiu dvlh jhat 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 y.ldh*6mjr4 d8voc wva r,b1ce+cfi -/,g su 3rest. After the impact, the neon atom travels away at adfa6vrwcm-3sub*+ ieo 4 ,.y h j8,rdg cvl1c/ 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 perfet le2dna9)6o px a(l.vctly elastic collision with another atom at rest. After the impact, )axt69dalpo en(l v. 2the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of w/v5t(ny+ e .2arqawathe three-mass system shown in Fig. 7–38. Specify relaw.yae narva q t(+5/w2tive to the left-hand 1.00-kg mass.    m

  The distance between a carbb . jvyhn:s59gon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of the car.k;sau qk w v0a leh;.3m7d+s+ umz*h2g How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? As*.ehu vdhwu;a7 sg+mkl2k+m s 3aq0z ;sume 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 u1 ab8hkbl glz bu61/5used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, anb8b1/bhak u 5zul 16lgd SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sideuv1bci.h +k ;os $l_0$,$2l_0$, 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 identiylv5. ijq4ei -gr h+5ical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center 4e5qijh i5+-vrg i.yl 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 28ajr+jfl. ol 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 offo.l lr+ 2jj8a the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are thec( z s2z,jaiz+ same as those in Table 7–1, and calculate the mass of +zscz(, zia2 jone of your legs.    kg

  Determine the CM of an outstre a0/ yqoc gi5nyjfq;(+s*e 2kbtched 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 th;1y0 1f a kwdsa8q rlx3ts-zd*e position of the CM of an arm bent at a right angle. Assume that the person is 155 cm tafzsdts-l10 a q;y 8a1x3kr *wdll. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hangin )x 90 h83ubfojhmn6rpg vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will onm3hjr 6)f9bu p0x h8be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon z-v+y4(ojta oare $5.98\times10^{24}$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 apar,j6tcyfdmpxzx10m.8 n*qek 2 t 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 uniform cylindrical head of mass 2.00 kg and a ,dd vfl2((lvddiameter 0.0800 m mounted on a uniform cylindrical handle of mald(d,(2v fdlvss 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a u .vjee m0o9 fl)1g,ubnabl y71niform 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 air, how far above the bottom of the handlmfylol1).,1bgjuv a9 0eneb7e is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Exampe q5:m9rwb ui4le 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 gonrvn*9*w8hn .0zvz zbm dola, 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 with speed measured with rezv rh nv8*zz*nwm09b.spect 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 pitw/i8zk sy g,xv)r -,osched horizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the bal, , i)wssxyr-/ko vzg8l during the contact.    $^{\circ} $

  A rocket of mass m tre99e f5h ena3xr3* mgktq,xx+aveling with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corescp3gffl0t e(m v/:x3;-vlener pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue b epffsm3/3cvleve l-0tx;(: gall will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit)qx3r38eeigsfvu5( 1 w acquires a speed of 2.5m/s by pushing off with his legs from avs5(qi 8egx 1rwf3u3en 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are initially at rest in 9mzjghj 7iw(82 .qq:i:6wyigtvxhuv;a)4rvouter space. They then push each other apart. How far apart are tv2g4 j8rv) ;6a z:(qqm.j itwihu7hvyw:g9 x ihey when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elasti6t c)lsv;vd6o 1w6i6 4v zbaiic collision with a second ball (at rest) and rebounds in tz)4acvs; vt61iwd b l6io6i6v he 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 a court case involving a5tqlul5s*f(nm v o/zoc72mh 4n automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. T5onf*v t hqos7zm/ clm425(luhe 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 of a flight w;iu.cvj g5v3 qw c7ks/ xd2, o,rsw9pof concrete steps of total vertical height 4.00 m. The; wqj k2pu.csd,s,wx wr97c o5vigv3 / ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically ineomu8j i7ok 7clkd2; 1to a 1.40-kg block of wood at rest directly above it. If t7u2m8 oekik7 d1 j;lcohe 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 ibu .) 1djaz7)p0ie(dja ;lucln 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 jujldea) b(a z01;)7diluc p. 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(ihzp9 :4xstvn/ fa*r, 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 /vt(iaz4n *fxs:9r ph 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 about mim xuosk8 7o1:ya5jgn .rl-6$ 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 suddenmqs;:wi- 8,lt.l nzbcly broken apart into two fragments by an explosion. One fragment acquqlb.:,tnlzsic8m w - ;ires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula Foqaw-k /n.bo9 = 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 zva:w)c5qqry) id)jd j :5 5zo$m_A$ = 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 alpha particle and a sme 8uansq )y9sc/5vbz-2kj.b br5w qe2 aller nucleus. What will be theaqj 2bk8rys)-e2./zq ve55bs cbu9wn 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 targ;sha 9ia-bv3k ) ,8tx;tgnzs ixqc1o8et) 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=2.2k be;)lf+h netyvtl2a6+ f +g7qg slides 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 limirvix3 v 5v 3t1bpd7zpdo)8 al4t on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide with M agaa)x7vd4v v p8pibdt1z lr35o 3in?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effe7 zj1zk,9ngu7ekoz 58qv hx4lct. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is 78l97vj4 zzon k ezx,q5kguh1 $5.69 \times10^{ 26}$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