We claim that momentum is conserved, yet most moving objects eventually slow8n++3 o)upb9ib+lyc bxqata 7 down and q3lnap ca ti7+b +u9b8x) yob+stop. Explain.

When a person jumps from a tree to the ground, what happens to the mom.w wmg3 xvssyh 3i 34r5jjiv)(entum of the person upon stri jy(.j gs4353)vv xi whmsrwi3king the ground?

When you release an inflated but untied balloon, why does itgubyj 76em:fev tyzty-. 1h9: fly across the room?ym6huve9e y jf:y1.tb zt 7-g:

It is said that in ancient timep4uezvz. to5, s a rich man with a bag of gold coins froze to death while stranded on a frozen lake. o zpte4u, .5vzBecause the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and 2uk+ l3 cemywlyd. 2hg6li 2a7fblm)ob:n -e/ is essentially in a vac+/:nllw b2g6ayfl oby)ku d m7e.c-il2h3e m2uum?

According to Eq. 7–5, the longer the impact time of an impulse, the smz .c-2n2obazg bgn7z :e2gi6valler 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 nzgb 2ibgv 7 agoz6c2.-:en2 zto inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to ; ) nk1)98tpm: dzuyo,zy.raafb;hziwithstand collisions. Today, though, cars are designed to ny)fua1pt;km9dh z o,a yr z;z8i.b:)have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a bb.g-b uhk0f jst89k(f all tossed in the air by the battb (utf8s.g-0k hjkb9 fer?

Is it possible for an object to receive a laq,v xafdg0ub xl, )d0;rger impulse from a small force than from a largex);,l0g d fuaq x0d,vb force? Explain.

A light object and a heavy ytgbrg hm-mhr06x235 object have the same kinetic energy. Which has the greag2hg b3-mm6y5x trr h0ter momentum? Explain.

Describe a collision in which all kinetic ener iu7oglq4p es-)sh0*lgy is lost.

At a hydroelectric power plant, water is directed at high speed c0w.b9*f.w aryma9s qagainst 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*b 9wf. rsw.c y9m0aqa so that the water rebounds?

A squash ball hits a wall aez5 sdc ql4z)8p fd8v/t a 45 $^{\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 dropp-puqn k6um yi9c5 am644 ytuy6ed from a height h onto 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, during what parts of the pro6-nuy4i uy9k pyt5 6mcu 6aqm4cess 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 hea +u6mhg6r+cn f:j p68rq/s tazvy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas mmx+og* e, sj7this is not true for your arm *e+ x7g j,momsor leg?

Show on a diagram how your CM shbu+gkxt7iu ifc-.gg* 8ps (r7 ifts when you change from a lying position to a sigf *c.+gx7 u8btr- (pi ukgs7itting position.

If only an external force can change the moment1jd7xb45tnr-w o *4licjw v4h um of the center of mass of an object, how can the internal fi rco l*bnwd jj44- w7xht41v5orce of an engine accelerate a car?

A rocket following a parabolic path through dhswu+73t 6h0gpj hi3lj1v;j the air suddenly explodes into many pieces. What can you hu j3j hp7lw0+h;gs1 jt36dv isay about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28aj, bb2on02ci -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 for 20 s. What is the sk5fed7p-b *+d-s mmkx z*z .hctier’s change in velocityc7edf.5*pmb* ktdh-zm-s+xz?    m/s

  A 0.145-kg baseball pitched af;w2ryl8gp+0) qj bvo t 39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52mb+2 lp)8j y; f0ovqrwg/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 unkmk8c99r ,iout horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the cnrk998iu,km 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,u j:rwe;:s4 av given that the propelling gases are expelled at a rate ofuj;a:rwv e 4:s $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving at096 lxjf e)vs,xta0z./y pqra $4.1 \; m/s$ 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 frictionless track with a ce57xv ry yh(/uonstant speed of 18m/s A 5350-kg load,initially at rest, is dropped(u hvry5x7/ye onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling akt5e v2b4xs.e j ahvmf4 )mt3d,7qsa2 t $15 \; m/s$ 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 speedvf- 4hlk8fc ltm,i/b1s of 100km/h If the air strikes a person at the rate of 40kg/s per squarehmki l t1 4/bvffcl8,- meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along-t4a h j6xla)zqvob 35 with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car aq- 53 bh oz4xa6)vljtat 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 init md o(h1hwz+qk)6-iktially moving at 420m/s emits an alpha particle in the direction of its v i1t(d 6kwqo)zk+hmh-elocity, 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 emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and 3xp(e8yx gz 6kemerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, hkgpx8y6z 3e (xow fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at +-u tffqi.q3u8j: zeh a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a velocity of 17 yg h6;dh/4id;,ue-o w okqdf15m/s To alter its course b6hhd4/eod; yo gf, -w ;iu7qdky 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a s+ e p j;v-greqslgk8;5pygw2 a/xn 4c5peed of 45m/s The golf club was in contact with +v2gr/aewq;p4ny j5ck g-85xlepsg ;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 ofax2ecgyos+ 4 / 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nail?2+ syg4oxc/ ea    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes a wall a5/f e)8xl zijcqn1 m;ut 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 crash,i5b2 04 7i mfk 9/ n,vw2mryrlmwbqquworthiness of new automobile models. Cars are tested by sm5/2,k4m imqq0yw9brr7,lv f u2bin wmashing 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 att dpe 4.(so /rl;xkdg) 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due 4tlse rxd/( p.k)do;gwest. 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 kgl3yam*11)* flo6wti 9 kan czb) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate nt9mal *awzi3k)6lc1fb o*y1
(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 5*6vsr sfzp uz;m4(5rwnbm .a75-kg person jump 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 . zuvfmar bm56*s z4nr p;s(5warea) 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 collit dis6x664ek/+:wr;ljn u+d rz v5ouh des head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball,wrdu+x e; :u+k 4jd6hs ilz56r/6vnot 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/xr1wr(( hplrh9jv /h ,s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the rhh/jr (w9v, lxhp(1r 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elast;wp zi/dul3 da:w2* bpic 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 repr2l buw3i*;w/ zp:pdadesent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collihjw 6 wwh5re,z-;nrq9(,pw p ides 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 e wrp ih(6w5wz,r;pqnhj-9 ,ewach 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 0.229w nx: zw(ju*n hp5lz:0 kg that is moving with a speed of 8.5m/s collides head-on and elastically with anowhzpj xu (lw:n9*n:z 5ther ball 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 amusement park2xpb i-7v5 a -l*dafha ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car Adaavf2px h7 -ai-bl*5 has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a second ballmhz0x(p6 i)-01 vap2b ad(1b e ggkduc initially at rest. The second gkah2d(x-z6 v)uadb1(pgbi0p c e10m ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incli ik)j(tug y/b81vi dwy7bry60ne as shown in Fig. 7–35, and elastically strikes anv)ug(y ij70/d w6br 1ki ty8byother 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 horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of mass u-*+u vknn*dh3xc 6yum$_A$ 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,r1;l vz (6gmqun;bvfx*1 q6xh projectile 1 results in a maximum height h of the pendulu;1nq6v(m bx z g6vu*h 1qxlf;rm equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in- ftawbik ak, 1rqi9006k4ok w a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swikt90i aq6akf-b,1wwr ki 4 0okng 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 enerny)rl9 ( 2.9/i jzb jxnbsju5ngy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosionp*g0p5x*tz bb etcelph(.9y 2 breaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J wertbx*eptb*pe0(l. zph c25gy 9e released in 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 rear end of a 2300-kg Slzyp,lm-r.:8njt j i6 UV stopped at a red light. The bumpers lock, the brakes ar8m-.jirp lln,jzt6y : e locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the 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 ox:ixtepcly8 7 1p:l/ af 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing18e c7/ yail pxx::ptl 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects isym/: t s*qajn9+ ra4lxgen /i- the coefficient of restitution, e, definegy*n irax jl/+ s-t:4qm/en a9d 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 times the mass of the s2bn:*;epn6c ukaon ;other. A depression is made in both faces of the cut, so that a firecracker can be pb;*a nuk oc:s2 epn6n;laced 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 atmuxishpd-btmf* ,u y xpw:+w ;x4 25f9 5.5m/s collides head-on with a 10.0-kg object moving in the -x *4:pxbu5 m;+ds9iu ,p-x ftyxmw2w f hdirection 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 nucleu11 7i wnn yk(l719lllsad3hvjs at rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emittednil7 1kwah3yv sll97jn 1l1d ( 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 masz;f d3 *l4hr +rznh:;3utj,qnv s*arw s $m_\mathrm{A}=0.400$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 equal mass, eachjrm9au: 48 jjmhmkj59 having initial speed the two move or9a85u 9mjj 4j:k hjmmff together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal a4lq8/ vhekjv wmmm87q;52vkmass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumeq4k5he8vlw2 k78/m am; vm qjvd elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with anoth7b1cbopv74c) h x j0uqo uy/:ber atom at rest. After the impact, the neon atom to:/cju ) x4bvpbh7quobc 0y 17ravels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision witab-hyddi5*f;b de2n 1h another atom at rest. After the impact, the neonidnfy e*1 db-5da2h ;b 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 Fig. 7–38. Spec3 pa03c.br crwtp7-p 8(mcq zdify relative to the left-hand 1.00-kgqmc8p- t7pw0(c z3r d.pa3brc mass.    m

  The distance between aqoyhx7* w8 z:w carbon 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 x/o1s*rb y w.1dhyi5 5r6rvdwis 2.50 m behind the front of 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? Assu*ry1 sr 5d vr/165bxidh.ywwome 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 as a lygn96 *h 83le ezaaq9ferryboat. If three cars, each of n9hl yla*aze9g8e36 qmass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides rm2 tt(l.) gyun8 auz;u7go1h $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of tomato paste (see Fi z1b bag.xwr,,z1oy h5g. 7–40), each of which is a cube of length l. Find the center of gravity in theh1wbrg 1 .bxz o,y,z5a horizontal 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 circulajdpoo.ec8d5nb 6 .g/mr 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 cent.depbdojcn6 g85. /omer of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 9wxnm*r*6 thh/p9f) m*zl awpd )ox3a7–1, and calculate the mass of one of your legs. *pd)nt rhz*axm*9x ww39/6a pm lf) oh   kg

  Determine the CM of an outstretched arm usivmapbudorpc :/:t80)s*l0nz ng Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM )pr rvjx8( 9qo aenr:2of an arm bent at a right angle. Assume that the person iov x qrj) 89r:(rp2eans 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a posid yb9)qn,5 p2anq e+j5ksj7iition such that his arms and legs are hanging vertically, and 5,i5 eap+n7sy bjq2nj9 )idkqhis trunk 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 Earth86zhq xr yfbwt7nca(+7, o gj5 and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart ipso 02a/ouz 8on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diameter0p pg bh5q/q-f 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 mallet is tossed, spinning, into the air, how far qhbq 0-p/pf g5above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a di+r4otn 3dqv/+ kk5kmt ameter 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 mkd+kq5 to/3 k4mtvn+rallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29), s,dq i;d45lu19uh;mhcr1 wta $m_{II}$=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 stationary with fd9/59nnhr:rg8nq qu respect to the ground. A passenger, of mass m, then climbs out and slides down a rgnnn8 uf: r9/9d5h qrqope 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 horizontanvwdk(b rd:hugjv45 /,gntb25c- xv7 d7k3prlly at strikes a bat and is popped straight up b/w5burvp3 krv:vxn 4 7 2t- (,k5ndj7ghdcgdto a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m tra 2 (ij bh5pl(kce2qe0e saki8k.y c,8,li:sgvveling 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 F4w+wof (1nc7m ih,oeeig. 7–43. Relative dimensions are also shown. Should the1ewf n7,ohoeim4+w( c 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 2.5md5 5aa /o-outw/s by pushing off with his legs from 5aatwoo 5ud- /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 initiw mogh1 jo v9*8zi-ddj5y s*k;ally at rest in outer space. They then push each other apart. How far apart are they when the ligy*1;khgo d m-5d*v8zwj9 s ojihter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collisio rerejqsg1+71n with a second ball (at rest) and rebosqj1+eg7rr1e unds 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 witnesm furaf)t7: nlk)y. *yb0bs q 0ara0uy/mef0 1s in a court 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*s0 yab yuf0mlqtra)0 u7 1akf:0r/.fbmne y ) 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 3ujl ui-*3 b sa1*ovbiof 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 steiiujb*lv b u33-*aso1p 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 at rest directly aboqpr ycsiul208 :r j(j+ve it. If the bullet has a mass of 29rriqs(pyc0+j lju2: 8.0 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 1vb 0s7ri yf1hl:x0y :k.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 bef0ix1by v7rfhl ky:s0:ore it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of masf t-geui.i -)qs 75 kg and the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchant ife -u)-qi.gge 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 abou3o v lz:dwjy)*0 ,w7xa-dgxsjt $ 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 fragmentsodcqhgkotccu,,b7d t8 wy- vsg 12yq 1t2( 0;o by an explosion. One fragment acquires twice the kinetic energy of th,tg(2 tbd 7o0sq 21ucygy18tcc-o,dwo; qv k he other. What is the ratio of their masses?   

  The force on a bullet is given by the formula Fqy8.n*c4ze hk:xqt m- = 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 ita+ j m42 .5ar.tf8fvkbdaj9;ki z x;$m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha particle and a smai.j+ (d j+a+jodrvas:52qnak ller nucleus. What will be the speed of this recoiling nucleuq k.aa2(rv 5na:+s djdojj+i+s 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 at an angle o-j)9sb (sd1ra/qklffxd/n lk/ 0 ( g cvjqq,s(f 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.0eb6q+u b oc93r $^{\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), whattlrk9 e (jf l *(/ixpp+q3qj;l 8 6ziqm;5vdem is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, an fm5(l eqq8*edp3v9( kx j qrim;zip/j+l6;lt d collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows+1)yz /0 lywpuv(imus crbp*)8e7zqx the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The ma8*1)0pzbz7w/ucirqeup( ) x vm +ylys ss 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