We claim that momentum is conserved, yet most moving objects eventu9mz2d 4adbc 48r-yewqally slow down and stop. Explazbq2a94 dym crw e84-din.

When a person jumps from a tree to the ground, what happ wh9/cm**j/uuk winy 6ens to the momentum of the person upon striki*wjy*cwuuh9 6 m/in/kng the ground?

When you release an inflated but untied balloon, why does it flyzn 1 yy 0;ambm p+dh/ z88h--6zzzfmmn across the room?fay;m8dn- 0mh +m-nmz hz1zb/6pzyz8

It is said that in ancient times a rich man with a bag of gold coi x iov/s(nqe+7ns froze to death while q(sx/7v+oeni 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 a *+ jdl9gf /jusguu4i7nd is essentially in a vacuum? uu9/47lj *is dugjgf+

According to Eq. 7–5, the longer the impact time of an impulse, the smallevwz2k04,a6ph+ 5,h b1vw+f*ux txohstka f/br 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, which are intended to inflate during an automobile collision and reduce the possibility of frawzbaxff so5/ 62hv,uxt*1hp vt+k0+ka h 4,wbcture or death.

Cars used to be built as rigid as possible to withstand eojoczt0 0.v,mgd/ va-:go. rcollisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of th j: tgo oe0rg-vz.cv0,am/do. is new design?

Why can a batter hit a pitched baseball further than a ball tossed in the ai llr mhjep)vz)ezgq8*3/7a88)ymta f r by thev )qel l7a ymfhm3)t8je z*88)raz/gp batter?

Is it possible for an object to receive a largerlyz;v/ ,l ccc0 impulse from a small force than from a large l/c,0vczcy; l force? Explain.

A light object and a heavy object have the same kinetic energf: 54tys e:s.8--ezfcto w prey. Which has the greater momentu f sectr8-:wye 4.fet5s p:zo-m? Explain.

Describe a collision in which all)hcci8 x n6 ab)4ztz)d:dy1ff kinetic energy is lost.

At a hydroelectric power plant, water is di5 5ckv,/hnxm77 kt tx,n) fkszl*vca t20son -rected at high speed against turbine blades onnss*7tkm-n2 xk5zc7/)nvc otxh 5, k,0fvl at 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 rebounds?

A squash ball hits aae dm8zzy )zxd x+-e1a. i+lx. wall at a 45 $^{\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 m/2z. eh ., /ibwhz:pg8sqyucsteel plate (fixed to the Earth), from which it rebounds at very nearly its originhu/w/z. csz e8b:g.2p, qih myal speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load i4s:c2zwbl1i en your arms?

Why is the CM of a 1-m lengt om5*tf8 q6qkhh of pipe at its mid-point, whereas this is not true for your arm om fot8* kh56qqr leg?

Show on a diagram how your CM shifts when you change from a lying position to a w l3.r8tt etxqvggu8 l6x.k)-v xy r5am/9a5z sy- q z.v m5a et6.)u5lk x 8v3/t8xaglg9rwtrxitting position.

If only an external force can change the: s vfd8ux-r5t )/ppiz momentum of the center of mass of an object, how can the internal force of an enginef8pt5d -u /r:vzixp s) accelerate a car?

A rocket following a parabolic ;o3xq*foivrel,9q .u.th k8 rpath through the air suddenly explodes into many pieces. What can you say about the motion of this system of pie qxrhur.v8* 93f.le t;o,oiqkces?

  What is the magnitude of the momentum of a 28-g sparrow flying with)3*ek uidor-*so 6 tnm a speed of 8.4 msdt- i3u *ek*omrn 6o)/s    $kg\;m/s$

  A constant friction force of 25o:9ev+ b b4ogmft 2.he N acts on a 65-kg skier for 20 s. What is the skier’s change in velocity?9b.+:o ef2hve 4tgobm    m/s

  A 0.145-kg baseball zlnepi9 m 0m-i5ztgz; buiv;g9ati.7b : 0a/g pitched at 39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time between bat n p .ab-z0ut5 ii9 0ag;eg/lv9izt7zibmm;g: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 horim- ;4gbow x21 rwkvtgj2 h0t6uzontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initiallytrk12wt4ojw06-v 2bm hgxg u; 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 po-xvunm4 nk(; q;3hmcvh18 w on a rocket, given that the propelling gases are expelled at a rate of 1500kg/1; 4;v( k8xw hcumonn3-qhv mps 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 a25z+gdq4 yltj pparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, wz52jt+qy gd4lhat was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad c. hz je3ixqu(:ar travels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will b:3ju qx ie.(zhe the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second bg -a(a oh o-i/*ojqii:oxcar at rest. The two stick together and move off qoi g-hia:i jao(o*-/ with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds caaq naor0w o54w(2-y +,ztmkuu n whip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare k tquazr52o(ynmo-ua4w+ ,0 wto 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 consb:g sa;qy m86mtant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the trackym qs ;86bag:ms, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits a/dwn6ro b vu*-n alpha particle in the direction of its velocity, and to *rv/ 6bunwd-he remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 2oowk)9ir0n* pa7/6i a.ik h ui5 ar-cj30m/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m9a.wojo/ )6 5uc -rnp ki*aa7hr i0iki/s If the block is stationary 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 speed pk1l+7nh0eag 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 veloci)bfz: h+41h8vfbf.hk - wazdjbnr2f7 ty of 115m/s To alter its course by 35.0 8fnw4b 1hhkfdar )f.zb: +7jfh-v2bz$^{\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 atb*/ bqc*jdq6h a speed of 45m/s The golf club was in contqhd*6j /* bqcbact 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 nai miqnv:;1e 6(uwqmt)j,d :tayq yz5q2l at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What aiq )w zeuq2nd5, qyqt:v:tjm1y6m;( 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 2ima9-wmznz4 7wy+i l/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 in1fe;xe9 fqy;vk v8 rv8 charge of the crashworthiness of new automobile models. Cars are tested by sma ff1qv9 v 8yvk;r;ex8eshing 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 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 easf(sunr9z; q;ut and is stopped in 0.75 s by a herfnus uq(z;; 9ad-on tackle by a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennisp,r4m hervo4 04d l +,bxv1tos ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a functionb4xo ,,rdme4r4slvov0h t + 1p 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 thm0dio 9 ptccp *in5/t;;/ jpsje 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 bcp; 5 o/0jp ;tdsip */ijn9tmcreaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of collidesk8.8tpwg s ;ubh0zdi, head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and directg,8 .uip;8t shw bk0dzion 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 5ht18 jr.9s nv/etgb,)mrtf *s hf9 vohead-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly fgbh5m *rost frt8n19e)vt9h/j s, v.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 equa 3huel9(;8fajp*w /pbx -ceigl 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 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 d3lhgp wu( e f-exib8p9/a j*c;irection. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s2b c6h3p:mcrmqn3l + p collides head-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 l+rm mblnp: c6h33pcq2 et 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 spee0sgyw4qopzyenoa -84 ;3+s xdd of 8.5m/s collides head-on and elastically with another ba;w3es-+ a0oy84ny s4g pdoqx zll initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an am6-f 7. a8sfh:p; hafuaqsi bg.usement park 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,b-hu.8hiaa;apf6 7fs q gfs.: 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 w2,- bj;ca6 pew.6/u 6mgaknuwin; sekith a second ball initially at rest. The second ball moves off with half the original speed of the first bau-wemk n6,k ibcj/.6w2ganp su;; 6eall.
(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-a+ /dqyje *r yeygq v-ba4;(o frictionless 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 incline moving horiz4dbeeqo(a+y r; j*/-y- vqygaontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an objeb ns 8 ..o;bvkk(:6 ciar. g0+kcoiruuct 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 res5,jy9hho r6c7jvv0dh ults in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twi7j5h,y9r6 0jvhhco vdce 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 traveliuc,iq(0tu p2g ng 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 vertu2i(,c pqgut 0ical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the(udcz3dqh a,0c m+sb fskt,6bn0 1a 3p fraction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into tw82j s 5duho ;/wk*vvhgo pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in5gd;8h2jkh*w vusvo / the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rea.xaf3b cr72kdo1 nzr:r end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two carsr7bcna1f 32 ox.kdr:z 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 of 1.205nm*:r onr 3ii)oq8xdjc4lj6 m. Approximately how many rebounds will c m6orx* 3ii4jn )qd5ojrn:8l the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is 6)hiklycjvw - 2,d;0e0s1hkcuu/8i ytfv 2gythe coefficient of regvkcf ue/6 yhiyhd8w2j ; su0v2 0i)-c ,y1tlkstitution, 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 t tcsa*4vjz*m,k/ xispj zsas, 2; 7l1cwo pieces, one with three times the mass of the other. A depression is made in both facesxa/lsp,z ,4ctij * avzss7 j1m ;s*ck2 of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker 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 collid* oblom:f29ski c:k7jes head-on with a 10.0-kg object:c m*k7 2lkofo9 si:bj 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, an electron, and4pr61u/hf b j:mf idg)8n.le sl*g7ke a neutrino. The electron and n /41gepml*6fbid. gjukeh f78:rsl )n eutrino 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 mas ;:rta ny:ftm+8 fcfs6s $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of ernfm9())y 83mts 4c4rr.kse/ qbg hn rqual mass, each having initial speed the two move off together with speed v/3 What was the angle between tnr38r nmghk 9rf4mc4qse)).(s/ytbrheir initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and m: o(dm*nthu4at:l co;7 vh s3ueet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? lo tno: *7u3dau h scm;(t:4vhdirection 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 cf: u/yqtp;1 ho eot+gvjx3 0;oollision with another atom at rest f 0o1voeth;:qx ou/ +;3yjptg. After 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

  A neon atom (m=20u) makes a perlp 0h75 xp5eu ;+oxqdgfectly elastic collision with another atom at rest. After the impact, the neon atom trave0ex;plo 55u+xhgd7pq ls 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 systenw7nv*:w l pyt+d( :wrm shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg wrnd7(*ww :y:p vtnl +mass.    m

  The distance between a carbon atom ( gvygc+zz9*+gf0t *re$m_{\mathrm{C}}=12\mathrm{u}$) 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 ,ll d,j+o7h eih8i2 tiof the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume th l loet7 i,iihj2+d8h,at each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 i9 xw xs mdw*5hp+9hjqi1u66qg d6m3r m, 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 the loaded feisip+9mu5xh96j r6d wh*6xwg3dmqq1 rryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides tx ze-r4 /*zzdhl;v.spf97 l z/4tvb x$l_0$,$2l_0$, 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 ca+3h8jp4huz k(aec j, qses 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 the crane operator can pick up the load without tjk 8zuh, (+c4heaj3qpipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole ofv mmzh)x,/w +lq d55ow 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 cenlvw d,5xzmq 5)wm+/ ohter of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as thos lj+3 l6cum*wzct/;(axctjd ,e in Table 7–1, and calculate the mass of; au/cj6d,wj+ tcmtx(*llz 3c one of your legs.    kg

  Determine the CM of an outstretched arm using Table *(t phe *pqzultpx)2s2xub . +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 bent5a c4c:m+6demagwx h n12eiwoxtua 5i4 am:*7 at a right angle. Assume that the person is 155 cm a:ag 5na+ei:c76odi*mw hext24mw a1xmc5 u4 tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position sugwk lg-h ber 7e. ,z0l s,,n8pyaqw1b6ch that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how w, kelhsa-pebw,b,.1zr80 q6 ylg 7ngfar 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 and Moon 6wyllj xrfg l8( 4 fv1,joz)y)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-,y pj587 :yra1yzqvbdank1, uz /oaw-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 cylindrical :9pc4lf w(i kthead 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 pt(4 9ifklcw: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 kg)npq c).tleoo*4;gi +p 1 akfb 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. *tci)gl + )o.popanefb 1k4q; 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–d ynxk.q5kw p scq/t *,ti0xo,.2,iou 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, are in the air and station+ )4 bu c-rmdj2upx/ltiuy.;gary with respect to the ground. A passenger ;ucb ilrdu um4-2/y+jpgtx. ), 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 pitc l2tt4vmp/ h +,qy(qh..mbuhd7b f-zkhed horizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during tv-u (.dm.4ml+ 7p bq tyq 2,khhzhftb/he contact.    $^{\circ} $

  A rocket of mass m traver9h+hpfewbr4j 3 gq*3 ling 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 wit5liurh+xuc)xg.f , j2 h the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in wlicj5, h)u+xxufg r. 2hich the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) aici- p xb;-iuwnjt)+8cquires a speed of 2.5m/s by pushing off with his legs from an 18i x; + ucp8b)jn-i-wit00-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 kgy0 jhes-s3--k2ik yit , are initially at rest in outer space. They then push each other apart. How far apart are they when the lightek-j - s ky2e-si3thiy0r astronaut has moved 12 m?    m

  A ball of mass m makes a head-ik( 5a g26ymknon elastic collision with a second ball (at rest) and reb2ymkn6 5 agi(kounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case i2e;n- ln5rd5m38dhr bgtym(3 mie5st nvolving 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 cra5ym8d2tg 5(m3enrdb;m- tlh r is35ne shed 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 9n:mc8w -ro*yx l8 te*mc jy+ra 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 h9l+y o8:m-mwcnx ye*tjc8r *r eight on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest directly ab;cxr3 p (b sql),ltlcvdyg9-.;jh pa)ove it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded ch p;.yadb;,)sl jgvqx9lc3 (rt )p-lin it?    m

  A 25-g bullet strikes and becomes embe vp:xe a2o-paye l ;9bav5iu.-dded in a 1.35-kg block of wood placed on a horizontal surface just in fronvpaax;ube -o ip5a9-e. 2v y:lt 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 and the other of mass 60 rmcs n1 ,ur2z.mj8tm1kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting 8mjr11zmr,.cnm 2 uts 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 was a ;a d4l6n+uzl49kvejvbout $ 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 by an explosf/t-lhgd4bc ,rg;r:n ion. One fragment acquires twice the kinetic energy of the other. What is the ratio ofg ;ch/t4 l:-fr,gdrb n their masses?   

  The force on a bullet i2kqltsv egi3tw. )6qi7 /mf d(s given 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 masses4tse-o(whutb q(ye; t +siua*ec,5 g4 $m_A$ = 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 inca prxpq46l)boq 9v.+ +o /lo2 f:jrz77ob dsnto an alpha particle and a smaller nucleus. What will be the speed of this recoiling d.j9+ xfo/2prn)lcp+a6o4r7b oqqvs:bo lz7 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 target) is jlo.n r43ql7 7uj5n41sgp dl3wjqn*l 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. mg7-n)zl)jw;3*a tt5 i qfyax2kg 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), wham .n;s-1czf8p(gl5 q6hmps a +ovrbg +, .zbrwt is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide witg ,p-bwh8sfn z15z6mav.(p;gobr r.lmsq+c+ h M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure57l8 mdjaa 7b 034jj; kvel46gu hopyv 7–47 shows the planet Saturn moving in the negau4 0e lbjh8jl4yo67v3g7d vpka ;mj5 ative 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