We claim that momentum is conserved, yet mostw 8/*nku1k8*vcdhon l,kbq0su xq :8g moving objects eventually slow down and stop. Explain.nx 8 *wgku8qs ,/qdvck u80*b:l1hno k

When a person jumps from a tree to the ground, whvms-k:a+9v;d dwn -prat happens to the momentum of the person upon sw nm-9 dvpk;rv-da: +striking the ground?

When you release an inflated but untied balloovm n1u4by20jfzz 3 s-dn, why does it fly across the room?2m4dv f n1ys 03bjzu-z

It is said that in ancienuthpcd8d 0)a .t times a rich man with a bag of gold coins froze to de d .c8u0)hadtpath 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?

How can a rocket change direction when it is far out in space and is aye; zg /y( foxa8ob+0essentially in a vafgb/; zaea+0 y yo8o(xcuum?

According to Eq. 7–5, the 0/xot sb9 dj.hlonger the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, whico/s d x.bt0hj9h 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 collis.)l a-3a i9dxpdke,cqions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of thi.-a9cx d,ea3q) plki ds new design?

Why can a batter hit a pitched baseball further than a ball tossed in the hus/4mhp /e f2nu; ushzj)41n air by the /umnh 4s u/sn12hfzup4; eh)jbatter?

Is it possible for an object to receive a larger,/6u;kh tmlbm tq5t8u impulse from a small force than from a large force? Explaiumh8ltk tt ,b/;m 65uqn.

A light object and a heae+5c/a ed1jjcg8 6hdv vy object have the same kinetic energy. Which has the greater momentuh8ajc6e+15jev/ g cddm? Explain.

Describe a collision in which a3mn-hg ual 1vj qo8-i*l q7/i/mux l/fll kinetic energy is lost.

At a hydroelectric power plant, water is directe2yag8y0ogk ,wd at high speed against turbine blades on an axle that turns an electr ak,w g2o0y8ygic 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 u /rvum xv/sup k(ov0.ya7+e945 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixeddzli.ji0 6dy t8z)c6u to the Earth), from which it rebounds at very nearly its original speed. (a) ic6uityz d06 dzl8j).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 carrying a heav:k)cmtk-d r;rul c9;yy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-poqc.a 9 f1fan5g qna)w6int, whereas this is not true for yourn1qf5c6 )a.9 nawagq f arm or leg?

Show on a diagram how your CM shifts when you change fromj,h 5 w3mwfdp) a lying position to a sitting positio5,dw f3j pwhm)n.

If only an external force can change thi ,gjxy3 y:y-ne momentum of the center of mass of an object, how can the internal force of an g,ji3x y:n-yy engine accelerate a car?

A rocket following a parabolic path through nf39 1inrv (0cr(/ pfnmncv ,rthe air suddenly explodes into many pieces. What can you say about the motion n,fn/0(ir pn 1(3 r9mccrf vnvof this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying wic pildvk)-(c: th a speed of 8.4 m/s )cdci (vl-p:k    $kg\;m/s$

  A constant friction force ol(3oz3liv bxet1r45o, i zz.bf 25 N acts on a 65-kg skier for 20 s. What is the skier’s c z.1eiio5txb brlzo3v3,l z4( hange in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit oce8pz38*e eb:2 limlun a horizontal line drive straight back toward the8l:*lzic3m ep 82uebe 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 horizontalwi,tdbm0(-;)ans r ije*tr l5ly with a speed of 10 m/s Fig. below Calculate the velocity of the boat immewd* ;5bt e-irl)(t0nm asj,ri diately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given tz ol8gvqok lxki; xj5k;7 3;:that the propelling gases are expeljx; klkovo; gi;: kqx5l7t8 3zled at a rate of 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 foru+rwgo8wt /0eut 2:an9z 6ftd a touchdown is tackled from behind. When hefu +8/ua9 wntott2 :6gerdz0w was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictionless t uthrx:o2+mdsex -9qi )h2:r e2eoan9rack with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What wer9x )d2ohqrha2u+ es:2 e:im9tno x -ill be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a secondt tei3a 3w23ig +bpwho*m+g r6de 7z:d boxcar at rest. The two stick together an3ab i*r6te27md+gpzi h ow+33tdg:wed move off with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally mny*b 93k3 n3sjv.m m3iiz* suat 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 thezj3 . bm3snm *yku93s iv3ni*m 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 coastse7u uz/x 3ns .nd8t3uj along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically an8x d 3tz3nu7/u.jn uesd 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 420mk,yexw ahnkzc0. 7 8f8/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,a8hewcyf kn0 zx8. k7 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 w3-obyh-m5rre ood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?-5 rye orb-h3m    m/s

  A 975-kg two-stage rocket is traveli3kzz:;e9r*n tt(9f hz m nf4wtng 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 traveling in outer space wcjhqr-. z9n8z:v*teuu 7lw5l ith a velocity of 115m/s To l8 5. j7huerz* v q:nl-uwz9tcalter 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 speed of elawqnfx5*p1 qg 6y .3 u17yx,j2xobt45m/s The golf club was in contact with the balayp1wo5.fy6bx q 2gejxl,*x17 un 3 qtl for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5kq e5c9n aar;5m/s and comes to rest in a time interval of 8e r5qk aa95c;n.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=0.06kg and speed v=25m/s strikes a wall at g z4z 2:trnqhru90.v oa 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 k5wazh4g4 yz4new 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 bz 4y544 ghawzkrought 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;qykt9 g*phde:l c4e 7 stopped in 0.75 s by a head-on tackle by a tackler running due wqd4c;eyt 97g:h lk ep*est. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) pointsyry x;po a2:6vr, :e(pe, bjei in the +x direction and is given by the graph of Fig. 7–ebpa;ver,:,( ex r:jo yp62yi33 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 w,r /pb (;xc*vxjoef.g ithout breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the o ,bgpv f.xjc*e r/(;xseated 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 (u*xpjo ;s3 6q smg8;bq+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direu*6jpxq;gb3s m8;s q oction 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 hea9a8gk kjo fbp s(p2(.dd-on collision with a 0.900-kg puck initially at rest. Assuming a per p(dgkp. jo2b9s(8kf afectly 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 perferci,uy-vywh sdqy) 9j.e -(1ectly 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 afj 1yey-.,ve iq( - w9h)dsurycter 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 2.5m/s collides headqz ca*-lh txa4 .y1av1-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090*azl4hxt 1ay1qv a.c- -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 c,cr vi a i0qykc32ys fs;:8su3ollides head-on and elastically with another ball initially asi8rckqu3va0 c 3si yf;:,sy2 t 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 ride collide elastically as one apprfy ty7s3+/7jep t z0h8;akfpjoaches the other directly frkpt+ 7 3;pfjtye aj/z7hf0sy8om the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision withha9 0 oxf7o*lu a second ball initially at rest. The second ball movf* lhxu 0o7a9oes off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incliy 4rl0inm+bw* ne as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and thei 0wyblm*nr4+ 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 o a:j3sl )brct)bject of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a maximum 8vwnyjm04 vgh l43o(f height h of the pendulum equal to 2.6 cm. A hmyl4(vj ognw804 vf3second 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 i9r2b ave3(2ha rmep62c)x8hh- livs otself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulu9phl (-ov8b e2s hm)riv3xr2 a6cea2hm’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of ki0eem*r rw+tb*netic 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 an8 s(md-ndf*svy;7zjo object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how m8vz dsf nod7;y-* m(jsuch 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 rears7ji7z ;wde3t 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.e73w ij7s dtz;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:b.o w+te zu0v of 1.50 m and rebounds to a height of 1.20 m. Apb+uo. :tvwez 0proximately how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the co p4*mnv or8hq.gdbv99efficient of restitution, e, dhpq9d v*b o9mv8r.ng4efined 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*ywq k010bhh2t xq7vj,9eb*kra l:ta7 aj,wr 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 the block reassey aqjk rb* tah ww0 27,1t*7rh,jqvx:ek09albmbled. 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 copjwdrfmiwxu 81)c(6qn)(x- jllides head-on with a 10.0-kg objep(xnmixr jwf6 1)-w) u(j8cdqct 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, utn,q2 l z2rde+q o),pan electron, and a neutrino. The electron and neutrino are emitted at right,,q)o ertd + 2nlpq2uz 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 masm 3 w3*,i a8wbpkl)jans $m_\mathrm{A}=0.400$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 axhmksc*/ i:luf6 ..fcgq6gtc4 sr 37two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the a*4/c h lg.63fcsu. g6ica7t fsxqmrk:ngle between their initial directions?    $^{\circ} $

  Two billiard balls of k4,i ssno:c (mequal mass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B i:nsi o,cksm(4 s 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 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 collissauzfj+ .cqb ,ln /jk rg10/e/ion with another atom at rest. After the impact, the nesek,/.q+ 1f//jcln0ruag zbjon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makesi95lzboh dged.3 ,mlons: .3m6, zzp v a perfectly elastic collision with another atom at rest. After the impact, the neon at35b ,s:zmlizdzp eodlhv 3.m n9.6 ,goom 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 the three-mass system shown in Fig. 7–38. Sb( py/1i3ef ;ork fgd*pecify relative to the left-hand 1.00-kg m k(f1/bef* dpiy3 r;goass.    m

  The distance between a carbo0l46yrhvky xr xe m7z*d/hgpu4o-,.m n 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 tx x-*6nny*qak he front of the car. How far from the fx*knq6*y-xna ront of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is uselml 63o7inxd+za4+jad as a ferryboat. If three cars, each of mass 1200 kg, occupy its N+ni oxma j7a6 z+l3l4dE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side3la+nc5s d p0r, ehe1k +t,xsws $l_0$,$2l_0$, 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 zy5 oe,kdxj-i+ ih*l-paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the l5 *x-d,ylikhoz +e-jioad without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cut 7 hnvdsh(7w; sout of it. The center of the smsv7w;hh7 nsd(aller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those q k m5kwq, dse8997yxiin Table 7–1, and calculate the maqd895mkq9skwyx,i7 e ss of one of your legs.    kg

  Determine the CM of an outstretched arm a-ju*y-l jk7gusing 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 rgh7 sb bb19yi3ight angle. Assu7 b39bhsib yg1me that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms an3(jdwezlxmt r) 82gj,d legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be.j (wj 3telg2x )8mzrd, Will this CM be outside the body? Use Table 7–1.

The masses of the Earbh.ezv /3 dcj0th 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 ; 7p.jbwb bp.rm apart 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 diamet+ zn a5i*8k3r(pjsc yter 0.0800 m mounted *( 3kz+tnarcpys j58ion 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 follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kz t 1 svaht5h305lywb6bps.8ng and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.50yn8hb0lp ht 631z5.s vtas5wb0 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7guz .2y9rvcn ;–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, are40(o.pucxh:n +g dl4 tuqqgs/ in the air and stationary with respect to the ground. A passenlu g 4qnc ux+4(0/potg :qs.hdger, 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 pozt u sd9 6jv1t*rcr+8itched 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 9rs1vjud6zo+ tt r c*8on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with spbd8ey q5het f*cro37j; 8v*theed $v_0$ 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 fzp39- skq)hzn5/kb j4r xjd;q aced with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also showhn 4-d z q;/35k q)rjsjkbpzx9n. 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 space suit) acq n7is3kb,9 a55 mlzcvhuires a speed of 2.5m/s by pushing off with his legs from an 1800-kg space capsuci9b 5s nval hm53k7,zle.
(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 sye1i vw)rhy :g6g3ws6s4 z82g . yvfpand the other 80 kg, are initially at rest in outer space. They then push each other apart.gh3ey66v41r :.yf8wwgys 2i sv)gps z How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (ai370vwma -a ayk0uv0yt rest) and rebounds in the oa0k03yya v wiavm -7u0pposite 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 an automobivf e*( iq4ahch;kd8 g)le accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collisi;48f hqi kac*dhe)v g(on, 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 offlcx90 vr *enu8vd02e;n 3liw( pcel2g the top of 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 bounce height oncc(ene0 ng3 urp;89 w d0elv2li2*lvx the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of w/n f:vni/ -odkood at rest directly above vnfk-o dni/ /: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 it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kiyy.c n7txi0 0g block of wood placed on a horizont0xi0n7c iyy. tal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg;koz 1m82qmlp and the other of 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 each other, now exchange seats. How far and in what direction will the boat m2; ml8ko1qpzmove? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abk1rbry -3wkb137adb 7cfu:ih out $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments b 73jyf3y+r x.n5ko srvy an explosion. One fragment acquires twice the kinetic energy of the other. njfk7o 3x.y5v3s +yrrWhat is the ratio of their masses?   

  The force on a bullet is ,o zpvou1,hlknqxr5++aq4 8 zgiven 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 massespdi ijm7w zxdioe2te3 ijw os(0f1+);, -v)pp $m_A$ = 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 ibeix,:m( 0pjuqxw,(i:ap5mq1i wa4 anto an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particl qmew xxujp5iip 0:,ab,q1:w4 ama((ie 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) ijdq9 j we *6k 714,2oltxy2luk hh4ohqs 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 down a s+sl(rdf 7i ,qqy+rqcgv* *r730.0 $^{\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 mux 4u8c(b aua6idve7bh2gk;, if it is to reboundkhuvucau64( 2 a8ige d b7,;xb from M, slide 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 effect. Figure 7–47 show,db7ytzuk 8g7s the planet Saturn moving in the negative x direction agzy7k,8du t7bt 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