We claim that momentum is conserved, yet most mo92g gkldomk .2ls37kt*aa 3 hyving objects eventually slow down and stop. Explain. *to2k2kd slka73 gmla.3hg9 y

When a person jumps from a tree to t,b4)o8 kn0dj2 jbk hnkhe ground, what happens to the momentum of the person upon strikid hn k4noj8j,)bbk20k ng the ground?

When you release an inflated but untied balloon, why doe.*;t cu7 oxhmd1qg,oo s it fly across the roomq x;m.t17o,goo udh *c?

It is said that in ancient times a rich man with a bag of gold coins frojew doa *l01eu+ *ud 5ox:9b*wr0vu5vrmlm2kze to death while stranded on a frozen lake. Because the ice was frictionelrjd:ue 1*m m* akdvb2 9w0o5*wl+xu r0uov 5less, 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 is essentially)b9 ietsf1 64sutg( jhyi+o8y in a vactjosg i4 yf hty iu+9e61()b8suum?

According to Eq. 7–5, the longer the impact tye2 mo25 -/0ri5wmag qs t7k 0yjczx/hime of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of z-027 g ymokjqax r25hm5/e0w yci/tsthe 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 fracture or death.

Cars used to be built as rigid as possible to withh* /xcwkx8 kjbzxc4xkh (jw+3+ t9ac, stand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon i xaz ( bw/9h xw48* kthcxjk3,c+kxjc+mpact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further thfww*uyae 6 )i4qb4( :wobk7g ban a ball tossed in the air by the battfau k(44bibwy*: wqw)7b g6oeer?

Is it possible for an objeci+md *ctkz3 mc1z c(o7t to receive a larger impulse from a small force than from a large force? Exc 1mco+*7cid tkm(zz3plain.

A light object and a heavy object have the same kinetic energy. Whicmu2u+l r.-szf;dk 0rjd(ez x* h has the greater momentum? Explaiu kr 2-d*e(u lf+.m;jd0zzsr xn.

Describe a collision in wh h5de,,z ae4knich all kinetic energy is lost.

At a hydroelectric power plant,ibxytql4*d +bc fl/9 ) water is directed at high speed against turbine blades on an axle that tu t*y)fclb4ql/9dxbi+rns 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 a wap1z)xry mc: l4 5g:pzrll at 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 dropped frojyn yf b 3a+e:6y24zdam a height h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed.jfzy4yn3:be2ydaa + 6 (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 76,:toravnuwfn-pa 3 carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe aani 3x.:r t6vkt its mid-point, whereas this is not true for your arm or le kx nivta6.3r:g?

Show on a diagram how your CM shifts 74zgy-6zpm kj3ujmm8 when you change from a lying position to a sitting6g-p 34mzmk7jumjy z8 position.

If only an external force can change the momentum of the center of ma:yc2zceyw2 q/t.i d,h ss of an object, how can the internal force of an engine at2e dq ci/c hy.:wy2z,ccelerate a car?

A rocket following a parabolic path through the air suddenly ex n3v448o i;krzzn8*ofpi l8hqplodes into many pieces. What can you saihzqzfpoi 4l r ;on84v8k3*8ny about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying wqb;) aj aaaq4r.dq9krc9 69ty mu9nq*ith a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N actv55 7nifmt ti)yq;kxs h2p 3p *tjhb(+s on a 65-kg skier for 20 s. What is the skier’sip; jsy5b5im*f v h2ntt3qt+kx7(p)h change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line 6i7b3w fl uxjq/c98 5 gc 0oiwk:qz4dedrive straight back toward the pitcher at 52m/s If the co :/qxwgob6udwlzi38cf70kc e 9j 4q 5intact 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 hox j6.v -ra1a+hbpase4rizontally with a speed of 10 m/s Fig. below Calculate the vev61 -bxe as4p a+ajh.rlocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given t9gdxzw.m6-i9 5 / bcslc 4ix:arhk4gvhat the propelling gases are expelled ati-a9v9zrwhld. bmcx6/x45k ig4 s:gc a rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving gz3v wagm7,p7at $4.1 \; m/s$ 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 t6k9*pgk o:x/wkim d0jk1dk6x ravels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onk6mwo*k 0xx6d : 1/9kkgk ipdjto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveli b6-qbl;f1t(r s6kfajng at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizonta4cnti p h/s glse)yaj gxi4(3w/79y;slly at speeds of 100km/h If the air strikes a person at the rate of( pyh9)icta4e 7jngxisyl3g4/ s ws/ ; 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 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 se4 rbso2 ld7mq*78iu opeed of 8.6m/s on a level track. Snow begins to f2i7oq84 esl*mor d7bu all vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an abm511w92gkkiv5 r34k owgvgxlpha particle in the direction of its velocity, and the remaining nucleus slows 1 w3imgwb21kgg9r54ko k5v vx 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 ods;( n(w0 f c(eh1ibs.i/cqdaf wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fa 1ads0sb(nd ;/.ecfhci( qw( ist does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a un0ue ah9t:1kjyvt5 0speed 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 ve 3u7qatx(zh :dlocity of 115m/s To alter z(x 7td qu:h3aits 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 hit off the tee at a speeo).kqrtyd* hc96 q9 dad of 45m/s The golf club was in )d6d9ta9okq c.rhqy *contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes tow/pg8 g5qz eb: rest in a time interval of 8.0 ms. (a) Whg wpq:bgz8 5e/at 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/s sp3);l7lu(fvz t*v wv btrikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthiness of new automobile m+nve9hmha;.:mvkyuj-k t *h )odels. Cars are tested by smashing them intoh *hm+)a.:ejuh;9-nvt m kv ky 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 east and h6h3 2oqg1mpg(l2e5v kx nj1iis stopped in 0.75 s by a head-on tackle by a tackler running due west. Coe 2vkh1q p hxm2l5jing61 g(3alculate
(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 (m jqt40e4.i zi6hubjikd3 p/2e ass 0.060 kg) points in the +x directioiied 4k3uqtb04/hjpj. e2z i6n and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump fw3cmk08fp03g )9qjv l km bm2without breaking the lower leg bone of either leg? Ignore air resistance and assumkbqjff2w 30m l9)m 3m08p kgvce 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 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 collides a fkd992cxav :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, and B represent the 0.220-kg ba9axkd:2a c9v fll. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a spe +to nik0v;utv0ps 7dc0i.c qe)vz/) ped 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 direction of each object after the collision?Let A represent the 0.450t.ivp)pcv7zo k 0c+dt0)n 0 uq;e i/sv-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 elastic h -jfqk+bji *d;ead-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 p j;dkb*qfj-i+ ositive 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 collides head-on with d/ ) mwk o61cv(c,fp jw(xlu-ma 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 ea/fcwp(j1l-om) km(v , cw6dxuch 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 wmif0zey 4d mm t(mufus1()+w2br bw;6ith a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incomrwibfy( ebt6 u;m4 fwd0+s1)(z2mum m ing 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 elastica+ i8, npsml+ivnxyq(x(lr*+y lly as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass.m yir*8nnl+(x s,lx ++vi( pyq 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 sez*b cee.at: e3f7+xqc cond ball initially at rest. The sqc*b :e3.cxfa 7eezt+econd 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 framntq8.s1w9 b-8dh mvictionless 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: Bothdh8 s.q8 mam-1tv n9wb leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an , uof)b m-y2zpobject of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a maximum height h op 56osx a;d/ ymkxl0 j0*qnw*.k+mz qdf the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swik0 m6dmlkxq.a ;ydz *qo/w*5 ps+xn0jng 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 tra23: q* stohjhrff z84sd0 :opyveling 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendhqr* dsot2fs3h: f:yj8o4z p0 ulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy los fe;yccrg6o6 + yf2p3kt, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into two pi2l10all /ob5c4d gopkik, 1ymeces, one of which has 1.5 times the mass of the other. If 7500 J were released kp/llcgd o25 mly,o b1k41ia0in 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 SUV stont.jm-m7 a;j 6 ,ewrxvpped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates - 6r;xm7 avjjnm,. wetthe 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 5 rg(lfec527h- yqxugto a height of 1.20 m. Approx(-gu x5 q7e2ryhlfcg5 imately how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-b */g7qh-ec6c dag.h tgp+2w uon collision of two objects is the coefficient of restitution, e, def*6b7u q e g.c-gwa +/dhhtg2pcined 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 clxywt7i3e 5l /3q.eq 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 tableexy i73l.c t lqqw5e3/, 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 collides h uh *.0*enwdbnte8t8 zead-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final veloz8 tu bd 0hn*eewnt8.*city 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 gwl2o5a/ aqv) nucleus, an electron, and a neutrino. The o/2a)a vwg5 lqelectron 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 masyk.db,zedbj 26u te2 +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 collidp+++9iyu wd hsion between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle wiy+d+ud+ph 9between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at rip -sn5j/ymd* fght 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 thj yp-5fn *sm/de right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with anotefdslp2cxy1l)bm:w /at ;-n( her atom at rest. After t1p2m;f-wlb dt)e/ay xc (ls:nhe 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 perfectly elastic collision with 1z1+v 2hcmw)cb:ds7yciv; a7:t vii y another atom at rest. After the impact, the neon a;s :2m)+ yz i 7c1cwv ahcvyvb1dit7:itom 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 to)t;rdltwd,u:r z/h; hree-mass system shown in Fig. 7–38. Specify relativel hddr) ;:t,uwr;o /tz to the left-hand 1.00-kg mass.    m

  The distance between tej jw86uzgi85sn3 i ;a 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 is 2.50 m behind the front of the car. How 5fhv 4 yy4 el5kjhm0l0far from the front of the car will the 0 hy4vyehjl 54fkl50mCM 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 that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, 0e.nny 0 evbhx*mu(1aae l4,vof mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy itsee(m*u a,n .h v bl1n4v0ea0yx NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides0fyhz )-fa,t t $l_0$,$2l_0$, 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 cd*s.m8g7 pa qoases 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 that7m qgoda.sp*8 the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular pl nim8cint 1s6q/wy v,4ate of radius 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try sum8,yt4win cs/v6iq n1 btraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and ca)yvn9v)v2 alaqi.lqwir 70z5mw rh,0/kb 0em lculate the mass of one of nr0)7) qhr i/l.a0mvz, 5w0blav2e myik v9qwyour legs.    kg

  Determine the CM of an outstretched arm using Tabef ) 78lnpda4i-vb1prle 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 a.8vcmbct):uqmza52d rm bent at a right angle. Assume that the perso2b8:5cdmc. a mqvz )tun is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hanging verxp 9ta678ucbhtically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be8a bcp 7h9xtu6. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth r92 .xkj:, yggyziuuyemd :8-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 on frictic ,ex i+yte eu*q6oe/5onless 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 die6aj1a 1rkyo8ameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–jaoe ar811 6ky42. 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 and a dia-mgn/ob +sj1(h 1edy fmeter 0.0800 m mounted on a uniforoygs/+f 1b jnmh-1d e(m cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (ky- l y/ ttfu3w,wj;280bbaufjo 7)wlFig. 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, are in the aid9 g7l(qno2dt r1hj3ar 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) do ohtl9jg3d 2q(1d7nr aes the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat ana+jlh9) j5e0 olb; tptd is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms,h 9)+ttl al;jj pobe50 calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m trave:ds0d ogy;s (tt 7wu1kling 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 fkk.9(bo6tfk is faced with 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 which the cue ball will also fall into a pocket? Give details. ktf6 f.kk(bo9

  A 140-kg astronaut (includ(dll 0u-hu-d8xg e w)ding space suit) acquires a speed of 2.5m/s by pushing off with his legs frhu (eu d0)dldlwx8-g -om 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 60yn;g4k.ly m-q kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lightn mly. ;yk4-gqer astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collisi, xxfeej2+ x11bb *h):nvzexvon with a second ball (at rest) and rebounds in the opposixv2+ h:, *x1zx bfe xje)nb1vete 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 involvinh +por1y3l :zng an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the dr:31zh+ ln oypriver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total vertical h kt j +oojv0re5(ge;i,p.h,tseight 4.00 m. The ball hits four time0; h t5 o.i, (jsjk+ep,ovgtres 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 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 d+t*h0xw i ;zp +uu1hfhirectly above it. If the bullet has a mass of 29.0 g and a spe ; ip+zu1*tfh+0uxhhwed 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 blocom- z,,zx.h *jrruify: -6mxrk of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speyzm jxr ir6-:r,-f,x uzm.*hoed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a ciist0o.c8-0vw-1 y9xtfj;s f-oub y rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends sw ix-u.oti-;0f1 yoj cb fy8 cvts90-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 about * 2ro)0sd g:eo0*i.(;sb fg 2tiuzrzl kcy 3ek$ 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 sudde(ar /3 gz 0ou)prko+nknly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the rati)/zror + 0a3o up(ngkko of their masses?   

  The force on a bullet i -;tt yovzrh*3s 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 masses 51rp1e j-j:f asnkn b-$m_A$ = 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 resyv m v).+w0qyh.r/fbut decays radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoilyb0f. /. mu+vvhr wqy)ing 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 t*rlp lfxi3+)eiogal 4t( : v(yarget) is fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slide1z,p1 j 8h n-qt6dlcges 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 *e:yszmcy a* *9nd0jzupper limit on mass m if it is to rebound from M, sli*zsd:zn 9a yj0yem *c*de up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn moving s/zp x k;jnuiroh6fz456;u9qh tn i1 )in the negative x direction at its orbital speed (with respect);;/59njup66 z ui ohtksx14rznfihq 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