We claim that momentum is conserved, yet movh u mj-w/j43dst moving objects eventually slow down and stop. Exw ud-j 3j4/vhmplain.

When a person jumps from a tree to the ground, cs hgk-h 3t2.wwhat happens to the momentum of the 2g ctswh.k3h-person upon striking the ground?

When you release an inflated but untied balloon,zolbz c 21ppox5c/l:( why does it fly across the room5clolz2/cboxz p1 :(p ?

It is said that in ancient times a rich man with a bag of gold klh(2kxo mp);e* b,r fcoins 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 donex;e*b2)l (kr pmh, kof to save himself had he not been so miserly?

How can a rocket change direction when it is far out iazh-/lpz :4smw s9*z6nnwcd-hg:- e in space and is essentially in a vacuu:whp-z -da-9h *wsicesgl:znzm/n6 4m?

According to Eq. 7–5y8p2 xnn,c e,:rsgz;,k-) ;yokwnbl p, the longer 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:gx;,y,-yekn)c ;wks 2,zpn8ro bpn l, 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 coa0uk9 l dz1z0ekav)+rllisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. Whaz+ukkv0z 901a ad)elrt is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ballbw6 2m vuv9u:d tossed in the air by the batterbu vuv2w69md :?

Is it possible for an object to receive a larger impulse from a small b7 c)ser/y8fq-8i6 ;r se+cubeohxt7 force than from a large forebi 7 7ur t;qxrs)ye 6s8-/of+ebc8 hcce? Explain.

A light object and a heavy object have the same kinetic energy. Which hru *52tc* vm;edhveomm)e c/* as the greater momentuedcvme**/u*5r;m ) moc vt2h em? Explain.

Describe a collision m a/vee ;s1u3oin which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against t f8ycsvunu.pd8/7l j7urbine blades on an axle that turns an electric generator. For maximum power generatsly/dn.87v ju7c 8f puion, 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 453wmd nn9 3im1 ii r*cpk:b.z-u $^{\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 (fixed to the Erobjty8 ,r zg.k0-nz9 arth), from which it rebounds at very nearly its original speed. (a) Is the momentum oztj,- 0 gk8yb .or9nzrf 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 whenvtnb v+6z4guen/v/o k,c. *hs carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas thir4u,tnxa s 6p1s is not true for your arm ou sx1par 46tn,r leg?

Show on a diagram how your CM shiftemar:/47ry;f ic ww3cs when you change from a lying position to a sitting positi :4yf / c;mr73aerwcwion.

If only an external force can chang qh)s8js* uct(e the momentum of the center of mass of an object, how can the internal force of an engine a8 j) s*(hutqscccelerate a car?

A rocket following a parabolic path through wqsb:bp0w3q xi3 6s *nthe air suddenly explodes into many pieces. Wh3q:3bsqip s x 60wn*bwat can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed of r8wd o (:8edh(k;d(gz.c jfu8 kwjfu3p;e3bp$8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s8 of1m8*wo a1 ( 3zs/hutmimzb. What is the skier’s change in veh*t1f/3 8um booi1mzs 8mza(wlocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horiqbv nf2*y.5 pvzontal line drive straight back toward the pitcher at 52m/s If the contact time betwe pf2nbvq.5 yv*en 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 horizontally with a speed of 10 jj)du pf2x, x-m/s Fig. below Calculate the velocity of thef2xpj x), jd-u boat immediately 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 magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rock:-aho66fg; p wdnj(qwo) v0.ap u k+suet, given that the propelling gases are expelled at u6+fow:;pha wvns0ja . )- o6pqdu(kga rate 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 movingx xe ,.iio)wq5 at $4.1 \; m/s$ 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 a e0re:idfwu-4(,k9mw:7 uqp hk0 ka rlqpp,5ylone on alevel frictionless track with a constant speqfa,4m::r kw 0-qrpp k5(07uiy wk h,lupede 9ed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travel yiv l/n(*x2t83 uo,jrr7.xi1 kyb ilving 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 If the 7hpe. 4/pin1o61 2ga ,bmefvjz deg t5air strikes a person at the rate of 40kg/s zet,a4 f 21o6g. 5/dj gep1vpmnb7h ieper square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of 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 (evk74k tn1ij d7s2s nof 8.6m/s on a level track. Snow begins to f4 1ed7invj 2sst7 nk(kall 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 420m/s emits an alpha particle in t/r y p(mmny5-/dqv / rky4dss-e (sbr/he 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/rdnpse/- y s/4v5 rs (m/mdk yqb-r(y 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 em)nt7cuizn1bs: + -y;0me etv derges cleanly at 170m/s If the block is stationary on a frictionless surface :+1 tu b7;dy)-cn 0 nvtzesmiewhen hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveli+hbn5pu9 ya-4 8u xkoing 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 with a v q*4ylm7: :h)h1zcxkc .sfbsuelocity of 115m/s To alter its cours yl1)z .u*s 4q :sbxhm7:fcckhe 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 45m/s The golfd5, y5,5+s aaewtyjh -5u wibl club was in contact with ty,ad5 5jlbwy+-u5sa 5whei ,the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.56wtie95 ekmj;m/s and comes to rest in a time interval of 8.0 ms. (a) What is the imp j6temwk9;5eiulse 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. mn9tm-0 kc,m6e inacr1 b+;be06kg 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 crashworthino mlpa1*w93 emess 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 w1m* lp9em3a oof 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 a gm)-s fz rc*d5j6:ruv head-on tackle by a tackler running dd*fr:zur5j6 cv mg -s)ue 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 actinyuo+) 5anxb -vg on a tennis ball (mass 0.060 kg) points in the +x directix-+u yv5b)o anon and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-4;1njuvcdw vdxu;ef) f7jh.a1ji1p 1kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a disa v jn f .dfuujpw;)h4xde;7i1c1j1v1 tance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving easys6w)-zodgj7 t (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440w7) y6-gdzo sj-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 o/7c xn scl;9c1pxehww422snw3 ,w dltf 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg2cs 4l;w1nswe/x p 9cdc h2,wn x3wlt7 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 o n-ut h6mjvjv/d 9b13hf equal mass undergo a perfectly 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/v9mhd vb1 jnht6uj -3 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 witvb(;j-8 zeri y j/*)kjbo. ntyh a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s ;-oetr nv)jy /(jik. b y8*bzjAssuming 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 colliwfm0fy:pg: ktz-2o 3 ydes head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate f: :wz2yfmo-3yp k0gt
(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 para8 *xyuldze97k 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 passenger mass8da9u xyzl *7e. 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 headb1yl7td1s5lttj : 0j jl*b-jeyov.l 2-on collision with a second ball init1 jj *0ed . to:v- 71yt2ljsljylbl5btially 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 slides down a frictionless incline as shown in n9 866ah 4lefb lm2pazhzq ot0 o7q21bFig. 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 the table is 90 cba on0z9a8m672fohtz41 6qq2h elbl pm 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 objl-3w r16a+ nrkd0t0hh jxkn4aect 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 dfa)2pg26fh n. q;z9dxb t he01 results in a maximum height h of the pendulum xh2fa.dt;en6f q)bh p d029gzequal 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 travel5ovaumeb46jd1 ad9 4 i8fbih6ing 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s h6abbi fm16j8da4id9 5v4o eudisplacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula fm5;jy2a + bq94,s2prqffy bznev li 62or 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, initiallybyff,o z+lhx eff;2 s sg2* m/+v:vnlk1yq,m 0 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 much kinetic energy did each pf sqfm,lzgb/1f: y ,+fl0hevm n;so2*+y2 kvxiece 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 2300-kg SUV stopped at a re4t4w 8d n2sywed light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the sp8ny4te2w 4sd weed 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 reboun p,y6tiyz ;d,ods to a height of 1.20 m. Approximately how many rebound ,o yz,pdyi6t;s will the ball make before losing 90% of its energy?   

A measure of inelastiwnzxim 86so, h i00+1z7w tqwfcity in a head-on collision of two objects is the coefficient of restitution, e, def6,08xz1wim tw7zwsoh+ 0fiq nined 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,joah 8 hm7da4p+p 9 yisktx0-0 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 is set on a rough-surfaced table, and the fuse is lit. When the firecrad7pp-jx+ ta8 as0ko9myi40hhcker 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 directnedf )*63ljx vion at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass if: fed)vjxl3 n6*
(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 -g5(kuh(ey)ybqhc n2 decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emittednk25 hyhquey ) -cb((g 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 mahggef- nrq/7r i43-zzss $m_\mathrm{A}=0.400$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 g1 ed4)/+t uq7i82nhm cbwgdfiph:mh 73y-q l collision between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their inw u:g)q3beidht8m7-m y+ 2phic/7q4dgfnhl 1itial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles agfq4cz 34(hdcnd meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving todz443(h c gfqc 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 collision with anoi. gh(q.nkz. ether atom at rest. After the impact, the hn..zkq(g .ie 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

  A neon atom (m=20u) makes a perfectly elaz7tnpz gd w++4stic collision with another atom at rest. After the impact, t gt+4 zz+pwdn7he 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 the three-mass system shown iksqjityk,m ( 2 dj259an Fig. 7–38. Specify relative to thea9ds ,m 5ik2qjy( 2ktj left-hand 1.00-kg mass.    m

  The distance between a carbon ah+(.o kf sp xez)(:nlw4gy5rctom ($m_{\mathrm{C}}=12\mathrm{u}$) 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. How fary yz8cs bt vkljp34y-j 57o:)w 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 kctjy-z7) bp s 4:53ylv8ywjo? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of wwf nj2 8v;.ummass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of v;m.w8wjfn 2 uthe loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides z6q qwdndq,kio*4vf*3f ac3 2$l_0$,$2l_0$, 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 lo g zaq2qk4p6/wad of identical cases of tomato 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 thgkq2/p 6qzwa4e crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of r 8m/9n+(cweri;rk qlwadius 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? [Hin9rrn8i w;qec/+wmkl ( t: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, hzx f d7pg1ypwthj*7u912; ri4 qsn 6land calculate the mass of one of your4l76gnhxzrtf1qud * i9p; wp7 h21yjs legs.    kg

  Determine the CM of an outstretched arm using 7yh ;u)qrm idx9 xrw,:Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the pdk o1-3j*9ayg syn2j2wpd*ssosition of the CM of an arm bent at a right angle. Assume that the person is 155 cm tall1j3k9da yos* 2y* 2jdsn sw-gp. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his a tch94jdf/ s;p9eo60 zjn y/eirms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outsidjsf6z/ ec09j9yo p/4ed i ;htne the body? Use Table 7–1.

The masses of the Earth and Moon are s 5jqb m8,qz4a/glrv, ,aeg(n$5.98\times10^{24}$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 fri h6 sop++quy/uxfv*8ictionless 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 ani1:3;u(mw:.z rkd;eqrngm v ed 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 :3z(r1;eer w. :mnm q;uvidgkmallet 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 kg and a diameml9c 1 7j 1wi2bkasg9mter 0i1s71bk wj2 c9gm a9lm.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 follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29), co00hr11en li $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in tlkgle*/9mhi + he air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed meas9*+eil hkl/m gured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at5 dj6g- hm6s9 6it1bli a-xzkp strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4-b gp6aisz166 -h5 xkt9 imldj ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling w.q u i*i )vxbtrw+ff,0ith speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown in Fig. 7–43+zt9xa ) mhmq r3*dxmey-bq +,. Relative dimensions are also shown. Should the player be worried abou- mqqzx mteh),m3bday9x++r* t 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 1ej:o*p(kd/kk o;mdp pushing off with his legs from an 1800-kg space capsup(do*/ pdkj:kme1ok; le.
(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, avej+t;:cb8 l dre initially at rest in outer space. They then push each other apart. How far apart +8ljb:cdte ;vare they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a j72hdns;ch+3 d kqc kh9h2ow8second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. Wh qcd d8+j32 2hownk7ksh;9hch at 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 yjq k 1e h(+0z;x7bhpfautomobile accident. The accident khp 70 1bejyzx ;f(q+hinvolved 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 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 totalahtag x y2a/di 0em1s:2/z,k m vertical height 4.00 m. The ball hits four times on the way down, eacia2hkdxg/es :2aztam/y m,10 h 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 into a 1.40-k nqri r(u2f9ue 1c,ksl i+zf,2 u15inxg block of wood at rest directly above it. If the bullet has a m,si1e,k lf u n2ci(fxzuuin1r2 5rq+9 ass 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 and63fu4vh5 ib v7ien0: diew97 osans2o becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and t65n v37 u snie4 7h wivdbs2:09afooiehe 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 of mass 60 kg, sit in a ro +ocw2+md6 gwawboat of mass 80 kg. With the boat initiadoc+w2wa m6 g+lly 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 move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass wa-4)02om t iu6qi kvzhiu09 iogs about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is sud) t1)sv tf(mqedenly broken apart into two fragments by an explosion. One fragment acquires twice the sq)et)mf(1 vtkinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is give nq7-; 2r ; f)tyq(y7npxmvyxfn by the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses 4 x hq4i3wfc:j$m_A$ = 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 x9.2-vs:bsn: ey m;vrdj3rctdt z/w , and a smallerdrdmv/e2yw3jvrsnb:.9ztc s- :x ,; t nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay tarqox. 7ui2k*dt:jd cc :1r +calget) 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=2.27iz;e2u7pt(ful.sa kkg 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 limit on mass m if it is to reboundqg3.anp jg-l7 from M, slide up the inclineqn3ga-.7jl p g, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slguyi1wh5*4b8t c q8 *caspal hr2)8qe ingshot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed 84tl*a8c uscph12rq 5 ey igb)wa*8qh(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