We claim that momentum is conserved, yet most moving objou/i - c:a2x cqu::ms7epkz/fects eventually slow down and stop. Explk :cmq /xu cu iafo-:sz2/7ep:ain.

When a person jumps from a tree to the ground, what happens to the moxz(b( o zi 6;t*cdn7somentum of the person upiz x( n6zco7*db ;s(oton striking the ground?

When you release an inflated but;lwxohr 8;xo8k1f(ol untied balloon, why does it fly across the room?8h;orf( 8olxw x1; lok

It is said that in ancient eusob4b 6 z;eqa1v+.mao4 a)ld g+ca; times a rich man with a bag of gold coins froze to deat)ad; 6cab ee 1 ablu; .gavs4o+z+mqo4h 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 wstv m7 cqep7j oi6+36(6tzh behen it is far out in space and is essentially in a vaeesp7zij vco3+ h(qm 7t6b t66cuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller theqc/szcf .gab-epb06q43b d; h force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acq0bspcz be/a.4;c -d6fqhg b3 ts. 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 v2a lqd3bncl7cn )2 o 3e7-k*bql4k:yfzz(s drigid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What 2l2qe3z ddy ck3akn7b qz: lc) -l(vnfo4s*b7is the advantage of this new design?

Why can a batter hit a pitched baseball futv2ap ssz93w/2l xg 9urther than a ball tossed in the air by the battert3u 9l wssxpag /9zv22?

Is it possible for an objectb8 rlinu2it/: to receive a larger impulse from a small force than from a large force? Ex rnl8i:btu 2/iplain.

A light object and a heavy object have the sam7ptu/y*5y7loc )ek kfe kinetic energy. Which has the greater pkyolfyku77t )*ce/5momentum? Explain.

Describe a collision in which all kinetic energy is lost.)g iw;j(/u(tar9 om rybtb3 *q

At a hydroelectric power plant, water is directed at high 4kx: oz3hak h0m4e z-kspeed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water reboun3z 4mhe- xkoa4 :kzhk0ds?

A squash ball hits a wall at a 45dzc:2. tdp2i s $^{\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 duoxn4lt rt4x+p*e 8h4 2f6zcto the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer pa z8crne24t 6x fl+ot44 pd*uhxrt (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward nt9wx 4iml-crh 230xlwhen carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this 88x(+vil g7 n+yx-sq ozfje9yis not true for youf+8o9zy jy87x+e (v g isqxln-r arm or leg?

Show on a diagram how n p)7y(6g.tqqih0ynryour CM shifts when you change from a lying position to a sitting posig (60r7h. piytyq nqn)tion.

If only an external force can change thku+4; vn/dktyug o:z )6pkl2xe momentum of the center of mass of an object, x4lykgkvudp+2o 6u t/ ) ;nz:khow can the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air s1 lq5 /ca;zmaduddenly explodes into many pqz c;adma5 1l/ieces. What can you say about the motion of this system of pieces?

  What is the magnitude ofunb)zde v5x4 vr z-95q the momentum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier.pbcob/e ( -yx for 20 s. What is the skier’s chanebb.y-poc x/(ge in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizonttt zs.6qj xy:)n 8rv0uxj;9 naal line drive straight baan0 .);:r svj uty9n6z8q xxtjck 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 horizontally with a speed of 10asd.fro scd( 0k(a70 c m/s Fig. below Calculate th s sc o(rdfak70(0d.ace velocity of the 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 rocket, given that the propelling gases are expsnzje o sze yk67zb;(+46q jx5e)/t ynelled at a rate4exse6jky5qb;t 6zzjs) 7 (nyo nz/+e 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+.cpo hnhvsg4 ,wx wd9)af (a68clo8p 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 alone on alevel frictin:uu s*h w*sb3onless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What wilh3*: uw *bsnsul be the car’s new speed?    m/s

  A 9300-kg boxcar traveling2aubb+ 0xn8pmy.i a* j 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 offu)k.3d fw 5mxk c4mq9 100km/h If the air strikes a person at the rate of 40kg/s per square kfwmxmu3.k qcd95f)4meter 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 railrov8(k* g oh9h)m .fqpunad car coasts along with a constant speed of 8.6m/s on a level track.oq9mh)(kfp. hv* 8un g 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 420m/s emits an alpha pe3 qp 8c2(2 arc qpwpkb*m(:dvarticle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass *rwdqbkpvpeca23 8: c(pm2 (qof 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-knku 7 u;zmi 96hvf.8iwg block of wood and emerges cleanly at 170m/s If the block is stai;zu v9w6 kmf7n h8iu.tionary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a sped o 5hyse pol0axwns ej)1r23p3 /7xl,ed 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 + zhvl1 75x4pjq w+rs8yorqt) in outer space with a velocity of 115m/s To alter its course47 tv)8rxj+ +qz wyosprlqh51 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 oui3td1k-/j4kvssy 5,5 j ajmfff the tee at a speed of 45m/s The golf clu 1,jks 5us4fmj5av- /d j3iyktb was in contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes to rest in a4c/ ci/c4c axsh9m f4w time interval of 8.0 ms. (a) What is th/i9fx4 scm4 hc4 w/ccae 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 strikrr)5fzd/+ fs ;znz9 qmes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthiness r o ,f36s+peptof 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 p,36 p+rof etsof 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 runningpoqt kzd ,*imw4) (5z ly/jv6o at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due weo ,lt6 o54p )z j(i/qkwdymz*vst. 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) points in the, z (tepd4d( lpf4uj8u +x direction and is given by the graph of Fig. 7–33 as a u,(tu(efp4z jpdl 8d4function 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 without breaking thgk+1 0uwwglu/f/ m-j7 aiy : oknfyp94e 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 seated position (that is, in breaking/4:wwa guf7 -mgk1il+u/knyof0yj p 9 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 k16 ; .bnjb( 0ok-qvfw4m nqfrug moving east (+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 andbqo6 n q(1um r.kf;fnj4bw0-v direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a hx(d,32gwuvjculj 2d dgle/5 , ead-on collision with a 0.900-kg puck in5lvuc3ddxg,d2/ug2 (,e j jlwitially 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-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 undqan w;q;lzrd6fmx7e f)q:h5 1ergo 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; ex7q 5 zlqr hamf:d;nfwq61), what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis bagx1+r2x tg. mrz9.qcgll, moving with a speed of 2.5m/s collides head-on with a 0.0m+t92g 1z q rgg.rx.cx90-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-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that ispq0ya/7 oar2 sxylv*9 moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate*x9 qv2/saay0roly 7 p
(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 par bu2ck */yhd/f.gvm,f k 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 ydvkm b ,*fufc h/2/g.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 elasti29wj)htnt q:1v/ v kchc head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of the firsj1vkh9t )q tvchn/:w 2t 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 frictionq5md; kr. q.fpb,yxol,6lzt/bi( xg4less incline 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 the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the ld.(6qxb;b 4,qlimr /xyzgf.p k,t5oincline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an objezig4s (1)n xppct 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 heigh(wt-a+)-vzcq 61icryg( z bqdt h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swin 61z-aq-c v+dzr (c()qby twgig 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 hud rsel-r*39hvrk6u+mns97 traveling 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum*nr76 v 3hhmlsr9-ru deusk9+ swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic enndgz6fm 0 3l:wergy 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, on0der,8figrv1tp zmn1r p69 9d ouwd 0,e of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kiem98rg,1ndz w9 d fdup06r1,vp 0itronetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped at ay lo,8hn3 tbyuh8kx/zf-: .2ngwk p2e red light. The bumpers lock, the brakes are locked, and the two kzwh823:yg 8 f2b ,ykt -unox/ plh.necars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height on*jcdjl+1c7vq)l vxf 8 dxea,,:3mpm f 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its em fx)xl q cdm,ce3navjdj8,p7: vl *1+nergy?   

A measure of inelasticity in a head-onyz7+0:n6iujjj 5s-m jf 8 pijg collision of two objects is the coefficient of restitutii j06+5uf7j j pyj8mgn- s:zjion, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, ;koaxp,nh 57s one with three times the mass of the other. A depression is made in both faces of the cut, so that a fh,;s 7npax5koirecracker 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 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 injzmg,.z.; z kx the +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s,;x zzg.j. zmk 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 nucleu9w;doit9yr xoec fcw s 2)x)do5d 8(3ds, an electron, and a neutrino. The electron and neutrin93eddc8d5wwx9i)f o(r)2yoodct xs;o 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 mass r )u*os g*((d0tq-.l innffyn$m_\mathrm{A}=0.400$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 objecgl t0 do0y//pkn)2z )y0fbcyi ts of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between the)y/ fnc0yyktol)b0/ 2ip zg0dir initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at rig- z ab0ujh +kx4-lhzs7ht angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the colli7b z-ukjxa4 h+zsl0-hsion, 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, 6oab3zcyiyeuws7, yz(zu)8 perfectly elastic collision with another atom at rest. After the impact, the neon atom travels ayiubwazz,8sc yz(o6 3 u7, y)eway at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision with a+m+8l gimt ,ftnother atom at rest. Afterltm fg+t, m8+i the impact, the 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 in .vjuiw+ , ; 4bb qhem*a-unu-/lzs9me Fig. 7–38. Specify rel*jvnuslm qe;b-.9i ,bazw - m+uh4ue /ative to the left-hand 1.00-kg mass.    m

  The distance between a carbon atom (;z53 y r3yofea$m_{\mathrm{C}}=12\mathrm{u}$) 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 fart7..nkd qn*halea u2 ;o1x-e zn1ork5 from the front of the car will the CM be when two people sitr;z. nqdkt7o.auk2 l5 aen-1*oe1xhn 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 wh qnky4-f*t(u/yz/q7 shd) k/ n ptr.* rq:pzm, of mass 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 tpqw:/t 7 4 h.s)kprzyk/fdhn-quy * nz/r(qt* he loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides yytu3q 6ck z7+$l_0$,$2l_0$, 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) palleb8 qv94i kv p:dd2ost*t has a load 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 horizonbtpis2od89qv4 k:d v*tal 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 radius 2R has a cir 7n mjbjaaqgsu -8) on f,o1 po0tqo6n8:0kc9qcular 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? [Hing:)a0oj9o68 fnc1 -qp, oqn78 t uknoq0asjmbt: Try subtraction.]   R

  Assume that your proporti-x7vkt3,wbrus o1k g 7ikxwu;4e *-hh ons are the same as those in Table 7–1, and calculate the mass of one xt7bk ,*wxh7eo4uk-w s;v h- irk3g1uof your legs.    kg

  Determine the CM of an outstretc2-s/s 6kai hrh-qj5uahed 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 txr6 ywvi o2;:hv,n,c:vr ,kj phe position of the CM of an arm bent at a right angle. Assume that the pr2 n ci;h:vxj,pk6vrvwo ,:, yerson is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position s d2rk o+od6(asuch that his arms and legs are hanging vertically, and his tkdoado rs26(+runk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth s,;ml/lda vk7him 6d 5and 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+zw4f vbut .oy5f2y: u 80-kg man stand 10.0 m 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 cylindricalr/a0xvveqcl +7zu*z 70,,b;d w zc q,luujs)t 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 thiw xvc7) e,dt vu,zqa0s, /rq7+l zlcb *jz;0uus 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 headfarb 1 e//jux6 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 ma/b/jeaur f6 x1llet 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 E.9 - s10em6xdytrm atzxample 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 goo,*ip,9x a,y ie kasd)ndola, of mass M, are in the air and stationary with respect to the ground. A passenger, of mao* kxa,p)i, syeda9, iss m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is popped st5pi(;y .aj7vi -ca eozraight up to a height of 55.6 m. If the contact time is 1.4 ms,(-.peycaj7oia5v iz ; calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travel ,gsw o0gs,c4aing 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 corner pocket shot shown in Fig. fafr4impre+5-mzg fr +)0h o17–43. Relative5rh r-ra1)if4gff+z pe +mm0o dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by push5uvg:ti;mix,whn:ywmn9 : d(ing off with hiy:v::g wuxi (mdwh ;9,nntm5is legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are initially at res4*e6 joqch-esm .xeh 1(owamen 7p.q1t in outer se(sqoe n61x7. ha jwomq -.he4*1mpecpace. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elasrz ;)o p ayalo (kt6mm,tc)gd :7r(9zvtic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original 7lco(( kamt9: o)a;vmy,6t pzrdzr g)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 coq/o+a tbb1.8pffk) e qurt case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of 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 wha18tbqq +p/fb f. e)koeels 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 flbi.g qba k),:b2ws gvw48m 2aj:+lbwright 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 mv.kl,gg2bb w is a)jwa:b28rq4:w+b 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood ag ljf-* )n2vkat rest directly above it. If the bullet has a mass of 29.0 g and a speed o*kng-vjla f2)f 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strike 46( *n8o.azuhlfhoyn s and 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 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 theualnhzn o6hfy .*o4( 8 bullet?    m/s

  Two people, one of mass 75 kg and 39 aj)dyfrzdkt*r *- ngs:+ mqthe 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 9:- j+*r)f k*td3rygmnzdqasother, 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 abocfi 3velmvmwg ozyq,):0+2w bytv9(*ut $ 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 fragmente , 1l9a-h4enzqtswr:cvl; q) s by an explosion. One fragment acquires tnt-4qz eq :1c;v l,a9sl)hwrewice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the for 4(t8j)+wj8ybvzwlb) nws;o cmula 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 og)d:udmy idwwz / b-6./2xw s$m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha partj2;tkpovk*8dn bl3 ip(so 4k3icle and a smaller nucleus. Wp3ko2 pit 4 o*ks8kjdnbv(3l ;hat 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 tag(pjvb81 x7 zistoksui 9/z03rget) is fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slidehl 4uvgyx nh9+(5i 5vms 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 k.oo(zrzpykn1:1;hl0 f4 c dimass m if it is to rebound from M, slide up the incliyz:okd . o 1(zi;fh1c nlr0p4kne, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slinguq,*i a 4p09svoxxw0+a xs oo8shot effect. Figure 7–47 shows the planet Saturn moving in the nvxu sx9oa 0+s4q*i8p0a, xwooegative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s