We claim that momentum is conservedq1 kl-zyvpsz9ek7+y lt83fkd8/d6 e t , yet most moving objects eventually slow down and stop. Es d7 q16e v+k8pkfl/8ty93e ylk ztd-zxplain.

When a person jumps from a tree to the ground, what happens to the momentu(i)o bo)pxeb;-dz9u qm of the person upon striking the groupi;(eo )bd-q )xo9z bund?

When you release an inflated but untied b3bg b ;*0r i:svsm8 obf2vrkj.alloon, why does it fly across the room23vmb *rb 8if.j;gsk0o r sv:b?

It is said that in anciun72 d, mcf. ows*ojn1ent times a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionles2.*,du wjf 1nm osco7ns, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and *+j.k/tin oe- buq0jo is essentially in a vacuum?tj q joki*.b/-+0uoe n

According to Eq. 7–5, the longer the impact time of an impulse, th;9vr9+ zrehuohd; 5s l* qdk(he 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 basi du v9h*;sroqeh+l(; hd9z rk5s, 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 rigi-+j9o dqeqdbl(m /vu)d as possible to withstand collisions. Today, though, cars are designed to have “crumple zon ue)b( 9d+j /qolvdm-qes” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tosg(haap. (np 9e*.o rybsed in the air by the batter?b p9a.e*h.rp ony(g(a

Is it possible for an object to receive a larger impulse from a small fa crr0t7rt ,)x y psf3ak227igorce than from02xgsri,2apkyf tta r)7r c7 3 a large force? Explain.

A light object and a heavy object have the same kinetic energy. x2 xp4x1dxlj 5-y1ca lWhich has the greater momentum? Explc11lxyx25l dj4xapx- ain.

Describe a collision in w he9v:/4rvmg f48 g3/wfwzejphich all kinetic energy is lost.

At a hydroelectric p wse2leh4r7d q-5r)a 5 y9u1wmigh/ tiower plant, water is directed at high speed against turbine blades on an axle that turns an electric gen514e/tw)ih957w-qsu iarrg yem h dl2 erator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a 4h(dwpdls+j/ 0x z(t),lx b ze-5 $^{\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 o)j2ut1oem3u9 8p pn(ree a:d pnto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, d)o 8unj (pe2rpe9d p:3m1eu aturing 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 i1nr9+ r ;eddyl3 e/x2udcey 9zn your arms?

Why is the CM of a 1-m length of pipe o9*wsvj 47+n j oe3t0lpgfly9at its mid-point, whereas this is not true for you0ynsj * fp+j9o9lvw3gtoel 74 r arm or leg?

Show on a diagram how your CM shifts when you chz) s1xs, (ha3l.tzsnhange from a lying position to a sitting positiont1h)(, ssz3hxas zl. n.

If only an external force can change the momentum of the center of mass of an p,g6jmy8r y rr :i 41.neb9k x.emey0robject, how can the internal force of an engine accelerate a ckxr r8:m06rebeyr p mg ynji4y..e19, ar?

A rocket following a parabolic path through the air suddenly explod79-k0dq9 r(fsvhz +5 nguywu hes into many pieces. What can you sayg5n (-z7hrqdywkuh90s+v uf9 about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with q2q8o:x 0v*9zrg c91 vxez7l3sgzcgoa speed of 8.4 m/ qgz :9v9o8gczgqx1 v*2ozelx0csr37 s    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What iswx5 )xv2lv ts( the skier’s cha52)xxw ( tvslvnge in velocity?    m/s

  A 0.145-kg baseball pitched at 394fg;bf)( zlpt m/s is hit on a horizontal line drive straight back toward the pitcherl(ft pfbg)z;4 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 1xh;aur;uv d bavs, i39.dup:/ 0 m/s Fig. below Calculate the 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 vedp9rda:u av;3i,/suu x .;bv hlocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propellin,tq (c jmd.jli16snh) g gases are expelled at a rate of 1500kg/s with ast(iqjcm)nj1ldh. , 6 speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/u 62 oqki r/phy7*ck;es on an apparent breakaway for a touchdown is tackled from behind. When he was tackledu2*p;orc ykh ke 67/qi by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad tpg q1 be)kptp)g2 /wyo6uk2: car travels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is 1pb /og p k e2)qk)wt:6gpuyt2dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15k k)jedn -)oknt)g 0y9m/s strikes a second boxcar at rest. The two stick together and m ktd eon)y)- gn)k9jk0ove off with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontallyn qf *ud;csz- zd:m;2f 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 o;duqmsn* 2:z-d ;cfzff 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 of 8.6m/s oj jpq5qribz1gp49hd-tg,sr0;i8+h i n a level track. Snow begins to fall vertically and fills5pi80,rgii4 djj1qth+r s gq9z -; bph 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 mobextbe4 -3id1,z3xu19xmzbpving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is em19xubb 3tdxb -zexz41, eimp3itted?    m/s

  A 23-g bullet traveling 2301 w5lftm210/jnths8n iv d3 7 n0glvxrm/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary onv 8tns i1vn2gxr/mfjt ldh71 35nw0l0 a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is travelinj 6c:5;wdf sp,cypk: ng 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 wi lxc+x1g oi1x x/ga0pj5, 1pxnth a velocity of 115x 5j xp + 1xa110glin,xox/pgcm/s To alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is higgz kwt.( 92yit off the tee at a speed of 45m/s The golf club was in contact with the y.g2 zg (tk9wiball 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 a timoxd blyz4088zh +d7bu e interval of 8.0 ms. (az7u zy8b+dd04o8 hlx b) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed vun(t2qjm10 (7 njpm rg=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 xnojy jr94y77az0av2 the crashworthiness of new automobile models. Cars are tested by smashing them into f jvyya49oa7xrn7z 2j0ixed, 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 east anlt9j.o zinor e8w. w*9d is stopped in 0.75 s by a head-on*9z .rtowliw9 nj8oe. 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 tennis ball (mass 0.t m nr(d+ 1w-urcxzx; 52rsz,i060 kg) points in the +x direction and is given byxir;,c2r5mzsxz 1(u-+nt dr w 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-kg person tm+lisj, je9a8ud- +pjump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bai- muspt+ 8j9d,l+j eone 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 ejhya/ xh j/.0bast (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. Ib ha/xh0y/.j jf the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a sp6bmq92bfp vrved 6 k5 y4s3q8ieed of 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 directiosb49y imvqq3d k5p2f v 66reb8n 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 nj/2nx6m:qrst +r 9bgvt53 hlequal 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 a2 :n6+ vgrrj lbmxn/5t9t qsh3t 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis bai-:kc p,jx0qipsi 1b)ll, moving with 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 Assuming a perfectly elastic collision, what are the speed and directio1ji)c q piki-, sx:pb0n 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 coll:d7 2+f.a2dfdkoj bswides head-on and elastically with another ball initially at rest. Afterward 2d7+o .f:sf bddawj2 kthe incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elasticallrpml o*.x183c3y 6c6g sqazxk y as one approaches the other directly from the rear (Fig. 7–34). Car A has a1x36k3ql ao z6scm .ygrxc8*p mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makekglgk( :z; c;-cgkv36bxfb9j s an elastic head-on collision with a second ball initi3cxzjvk 6-gg: bklb;f9(c;gkally 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 tfw;:3y9wx b q a6bfh0frictionless incline as shown in Fig. 7–35, and elastically strikes another cube :0fwbxq3hw;a6y bt 9fat the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an objecg6y of7.;r b4qrch x9zt 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, projecti fels)o0r;hemqy 9;; ole 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high,q)oyhfr9;om;e l e;0s $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg xleph ,,v vpx20) 3a)wg23ni7gqnljkpendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an)0qx ,e3xv 2p2j7gv3l w an)nplik,gh 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 energy 57 l;ebz4o h5w. w vpcv7dump6lost, $(\Delta\mathrm{KE/KE})$ 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 two9f/ee4 fe ke(z 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 piece acquire? (Let A represent the heavier particle, and B repfe4/9zek (fe eresent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the r+ ahuzp bl x/o3q/kz +36*ewrkear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid fork/ 6w qx+h+ eoplazu3k3r/*bzward 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 heighuc5tk7hgdoq9., 7bpj qv8,ot t of 1.50 m and rebounds to a height of 1.20 m. Approximately ho8gukphdq, o t5j .bqtcv779o,w many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the co4ms 2i bdrq6o0efficient of restitution, e, def 20o6 qdibs4mrined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three n ,/rl9ox;+r;xcalak 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 firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each blc n9,alrkx +;r ol/a;xock travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-d0a3m46:t/sbio bwim on with a 10.0-kg objecttb /b m6ai0w3dms4i: o 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, andi 5ybz0a3 ohy(jr n.ji2n05cg a neutrino. n.(2gizn 0 03orh5c jy 5abijyThe electron and neutrino 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 ma n8gs-c 3hgvc6ss $m_\mathrm{A}=0.400$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 betm zi qg ,0chd48f+est+ z*,dhctnyv,* ween two objects of equal mass, each having initial speed the g+ h* ,tyqz*szc imvc4dhf+t,,nd80etwo move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right an rw:c /d 7,hdw:j8gyesgles 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 segdyr:: w,s8/ 7jhd cwpeed 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 pedtw v /ib:vc:6rfectly elastic collision with another atom at rest. After the impact, the neon atom travels away atv/ :6twbc i:vd 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) mizu16(nmb ov5* rmj mahj,+2vakes a perfectly elastic collision with another atom at rest. After the impact, the neon ato*2nrui j( hv6mmm ba,o5+1zjvm travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–3b 9r0meh6o 77q q.0yv*nyvnat8. Specify relative to the .hqab*7 rovn70q nt9y06 eymvleft-hand 1.00-kg mass.    m

  The distance between a carboh47,l lu1s wur ufond2 p9ums )7y81ntn atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of the car. H -4msuanx2a/ossu830t 4 gdkiow 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 /o-s k ag2ud sint4m0u84s3ax people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used . b -uosry;7pu:(q twtas a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determiuo:u (.-qr p7;sbwtyt ne the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides p 4gyccoi34w k :q0.sy$l_0$,$2l_0$, 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 )v nfz7mgwc9,l g/n0hload 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 the crane operator can pick up the load without tipp/g vmg7z09)f, cw nlhning it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a tyhew, wgfn4fl* 1f(cqhz, *b.i1) h*jo3dwzcircular 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 positiodb*,wyzw ,*tfhnj1fzweh3l (fgc) *.qi1h 4on of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions 1b j3trlm+ uni0 8 czvlk3u2m vd,-bn -+apqk,are the same as those in Table 7–1, and calculate the masrkv+c ,jm b- nvlq3a-u1+k u38,2mbt dli0zn ps of one of your legs.    kg

  Determine the CM of an outstretched arm usib gt9q rc4b*(xng Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of thn kkb oenn) y+i*/n/a:nm3s1 n6hr4cqe CM of an arm bent at a right angle. Assume that the person is 155 cm tallb3 ni )qh *nyk1 e+/4k:rnn ncnmoa6/s. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hltb+x ox(; z6oanging vertically, and his trunk and head are horizontal, calculate how far belolx+ tb6zo o(x;w 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 .xf8slfpj +6o5tr 4bxare $5.98\times10^{24}$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 frictiq (uu9+jcbm:eiopv: ue(d* o0 onless 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 uni)sglm *r5 wv.e n0ox7de 4ds45lzsz/nform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical hando0d5n ewsz)sx l4vs7 en5rdz/m .4g*lle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.0-6nd g/fn9nex p*/ n8vb 7hxvp0 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of vhf*/n bge- xx 6n n8vp7nd/p9mass 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 Examxoz y10(n++emt c hj/xlv30 svple 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 gondola, of mass M, ar1vtr( o-i*aabq3c o:ne in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth*ioc aq(b3v 1rn: o-at) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is pop7gonwe;z 6+qwped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average on;gw e 7w6+zqforce on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speede 78eyo*qxi i8yxkp o6i+/i 7s $v_0$ 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 f9mjbb, +*pfo raced with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worriedpb9*brm+ j,fo about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including spac*2qjrfvdl;a t(93r l le suit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-3 lvt(l2ad ; *l9fqjrrkg 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 +dfzf61e6a ds 60 kg and the other 80 kg, are initially at rest in ouf e+fadz1s66d ter space. 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 elql g)y5 af,yu),9c hyzastic collision with a second ball (at rest) and rebounds in the opposite direction with a sp,5yz )u,ag)cyl yqf h9eed 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 courj o sw47/txcfg tfmu7/1xc4n *yu;)rrt 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 c7t/j1 w4 ;nu /ux)*srtgorc yxfm74fcrashed 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 step3ps 0hf1kqs q1pvo3 1ds 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 heisqsp1 3o1 vf3 0hd1kpqght 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 direck//fzw,qnb t) tly above it. If the bullet has a mass of 29n ,f/bqwtk /z).0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block opw783bhikz 7-bzwu9 5g t, zekf 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 t7ug -be zz3wk5w 9p7hb i,zk8the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 610;t3uw4w0 *pke 3 qwrifw7fy auq:dp 0 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will m fe:170wf;uaqp u0q3kt4i3*y ww rdpwove    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass wasaw/:k gwi;q3h 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 sudr5+bwm7 / wycfdenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the+cb/r57ym wfw ratio of their masses?   

  The force on a bullet is given by the formula F rt8 gsd3i2ul pslc7*; = 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 k y pc24lpid.4$m_A$ = 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 radioactivel r;d7 ;juv,qi hry1+)jkvj4e iy into an alpha particle and a smaller nucleus. What will be the sp i7 1y)ejrvukq4,hrjd v+ij;;eed 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 target) is fired ad3.qm +2 ;gbt i0wubyzt 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 sli9dsm0ir .w+yrdes 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 uppero3wtbr o2ad;s 7rc,uol)d 50i- r v(lf limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide withroo23lv s(c 7 f rb-;walo50u) id,drt M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows wavpea8-d 4r7 the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The ma aadwrv7p-e 84ss 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