We claim that momentum is cox0qtpzd31qus .s(.j anserved, yet most moving objects eventually slow down and stop. Explain.3xp.j0dq qts sa zu(1.

When a person jumps from a tree to the ground, what happens to t 8atnj 5n8k( u68kx5 rbd0uvxhhe momentum of the person upon stri6(xd5j088nxub8kv a kunh t5rking the ground?

When you release an inflated but untied ,qhde 9:jek5 dy- aszzj6i/*lballoon, why does it fly across the room?9zzs:*di56qd/jeyjk h- e l a,

It is said that in ancient times a ri*8hu*k5 mk qmoch man with a bag of gold coins froze to death while stranded on a frozen lake. Becaus*muhk*o5kq 8m e 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 axtvffw0q0.- direction when it is far out in space and is essentially in a 0afx f. qwv0-tvacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smalle -ovns2a3d(zqdlj 1jyq33v fqi,w(3er 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,ev3zdyowqjqvaq3j(n1d f 3,( l 23 -is 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 withstand collisions. Today,k2t u;x syl8.d9x2jva though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this; 8lkx xty22ud9vjs .a new design?

Why can a batter hit a pitched baseball fur*r 7 w )-zf6 ndzzbf,fsh3g0xother than a ball tossed in the air by the d-f3)b7f0 fow xg sn6z,*zrzhbatter?

Is it possible for an object3mr i;z ihz6 n7a2+lap(v5 haq to receive a larger impulse from a small force than fr3hrnz mqilzi5v;(h 72aa6p a+om a large force? Explain.

A light object and a heavy object hspg2m -* zvc1hutwl05ave the same kinetic energy. Which has the greater momm5ltu g0pc1 *w2-svh zentum? Explain.

Describe a collision in which al wjdczqf 7540bl kinetic energy is lost.

At a hydroelectric power plant, zmj8v4 d4p h4i2 zidiwqb :)v3water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation,z zvijmb:p44wd8iq)i4vh3d 2 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 ) y hsxsz8f6z qwk)l u39q8c9bwall 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 from a height h onto a hard steel p5,g4e vpkpr0) v+e 0.fvm awy5t:nesglate (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 pas wy.)mga ,p5ef+vp 0e0 rvt:e v5ngk4rts 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 f jt 3vr7a8ck)e ua+9zheavy load in your arms?

Why is the CM of a 1-m length of pipe at i es4qe sd3qa kcsa,(*5ts mid-point, whereas this is not trueq5d ke4ac*,sass3 ( qe for your arm or leg?

Show on a diagram how your CM shifts when you change from a lyi6;y hw8heu o1rng position to a sih ; yw6e1o8uhrtting position.

If only an external force can c:iop3j)w9 shbb6 .ap hj*p0uvhange the momentum of the center of mass of an object, how can the internal forceps bpb:3hp *h6a9w .jj oi)uv0 of an engine accelerate a car?

A rocket following a parabolic path t., lhgswb09.vi4 bnnhhrough the air suddenly explodes into many pieces. What can you say about the motion of this syshgv.n0 , 9l4wibbh.nstem of pieces?

  What is the magnitude o rch+dq7 71bqgf the momentum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N 1 pi2(aumd3zfhaxl)ye 5 o:+xacts on a 65-kg skier for 20 s. What is the skier’s 2xm:5h+z1ay) aupode3 (xi lfchange in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horiz.wp+ bm2sudh 9amzyc ::6h8ge8j8as*ndx5l n ontal line drive straight back toward the pdunpasc:d*xegayz. :58hlhn8s m92j8+bm w6itcher 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 horizontally5wrb/.ru5a42lsvk wqp 1, ffbh0up9x with a speed of 10 m/s Fig. below Calculxp5b2uw/ 9rf40.b 5uhw lr,a1kfp qvsate 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 magnitude of the velocity of the boat is    m/s

  Calculate the force exert+1 z r- sp:ojioma: l*gad:zv0ed on a rocket, given that the propelling gases are expelled at a rate o odo z+l*a am:ji0z:-svg:pr1f $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movinmo:y;toou l-x+klv m m -35/wyg at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevetw8;/rq-x-uau2pcp) y* k btal frictionless track with a constant speed of 18m/s A 53y)*up2a/rcw;bu k8 apttxq- -50-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travikw6d cr90ylk4e0b* yeling 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 c7*3au 3khyssgan whip horizontally at speeds of 100km/h If the air strik3yh u 3k*gsas7es a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare 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 alont j-av s r18jp-4px7peg with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after1x8tp p jes-4pvj-7 ar 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alj(nm,gvqa10) i zugl emhl;7 3pha 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 gh01)m(lue37j ag mli zvn q,;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 exxqni(5 uu+l3s,o0 jpmerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bul 5i,l qno+jxxu0p(u3slet emerges?    m/s

  A 975-kg two-stage rocket is travel* 5 8l4rrorpkying 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 k ;rkrr b9q-* s,fze5)(pmj ozouter space with a velocity of 115m/s To alter its course by 35mb,r(-z r kepjk*f s)5qoz;9r.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 speed of 45m/s The golf clvx(;dwr52jrp oo4g 7bte) hdu)l1 sc0ub was in contact with the2h1j07(tuev podg rdxlc b ;w5) sr4o) ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes to rest in a tim 5 bfiju0:38emos. pike intervalfmbpek8s 3oi u0j5: .i of 8.0 ms. (a) 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 vafkt 73) .epw)k)9 ncqt8o8rqv m4.k cbnk1 jp=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 enginekry-r5 m66i hqer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fix6k6i -hqyrrm5 ed, 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 is stopped in 0.zzrlg 9l:x 1,sn.eyu 9o6rvx k- fv+(q75 s by a head-on tackle by a tackler running due west. Calcuyr+fv9k,xnego:r 96x q-vz lz u ls(.1late
(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 tenn 2l 9oqzc7jk6dis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. z q62k7cd9 jolUse 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 2sh7-dzgeq, u can a 75-kg person jump without breaking the lower leg bone of either leg? Ig eqd72 zu,-sghnore 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 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 mo3k ,xg9 sormplmp b.;/ving east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-k xb.m/ sr3 gl;m9p,pkog 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+p7/ lj-xyh x/8ihn+qth;gqf /s has a head-on collision wiqj;/h n + y7 -it+flpxx/hq8hgth 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 0.450-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 me 9 8j,9x zhu0myqkzh0ass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was9ymqh9jh0 0,exz 8ukz 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite 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 f a)xhsv5;lfoq ku;k*6jv-t. a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg te-6slkja;k* t;xu5 h v.vf)qofnnis 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 withov / ko7-(;n3vivvjnkqi/ 8zt a speed of 8.5m/s collides head-on and /8i 3vqv7tv k(ni ; /-vznkoojelastically with another 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 park ride collide elastically as one a,ov0ce+ mq b; nc,h-iypproaches the other directly from the rear (F -ymq ch0n,cboe;,v+iig. 7–34). Car A 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 collisidms7* 1z1molj+hig orxi t :23on with a second ball initially at rest. The second ball moves7zi mrjmidt 1s:*1oh+lx o2 3g 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 cube0x :uv:jwe:5rrmdat5 b- )z hj slides down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where doeszermbjd-t: wx: 0)ha v5u5:rj each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case o.u9ng8 bjob z8phbo,) f an object 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 resug)io.uxfusa93 7 nx h(lts in a maximum height h of the pendulum equal to 2.6 cm73 g(fn9ha)xiuu .oxs . 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/sdp 3qacb yngfrm3 q*1 rh;2.q. buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components ;h p1qbr3 *.m q g.2yra3nqfdcof the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula foqe0mihf f5n9o wsak76we95 a +7lq rm,r the fraction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rr47,pdg uj1a89wrbyl est, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J 7bwyg9,dlp 8rr4j au1were 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 SUV stopped at iuvx0,cy8ir c0e-ehir;c: 5y 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 betwyi ;yr0- ch:i ,8eu v0i5eccrxeen tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height of 1.20 m. App+86s l+t/efsw t p*j.s3aat oproximat6lss3p+j/ wt*es8 a .ot aft+pely how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is6j 2b9gyc aap .7omt(y the coefficient omayg.9b7j2a6pyc ( to f restitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the mass of the ota9jm8k+adus1 nly3ys8d8 k ij/dc2i(her. A depression is made in both facdly8 k9 skd2iuc/j8y18s dn+a( ijam3es of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object movingre/y* 0k w0l -zlppj6d in the +x direction at 5.5m/s collides head-on with a 10.0-kg object moving inzlp00wy *k-/ep6r l jd 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 ela6/qbo 0si zxn1+sgujq0+j4uectron, and a neutrino. The electron and neutrino are emitted at r o0z+qia 6/xun quj0bsg+ s41jight 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 masu q.2phc8t+-9wzdnj c71a fjz py.. lms $m_\mathrm{A}=0.400$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 ob b ;v-x3p- paprpio+p6jects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial directions?3-prv - ppa;ox 6pp+ib    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the origin .dfqw0i8 .ix 4)7ij-jhygkweof an xy coordinate system. Ball A is moving uhek. jxi- w7w84d.g0y)ijq fipward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? 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 anotcn4clw6ul. ex et(8)bher atom at rest.8)c w4tlecb.(le6 n xu After the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collis1:fjoq. .jm)woeym4 b.nm q3 v55ewsxion with another atom at rest. After tms:qo13ojx4 5e5w).jb .f mmev.qy wnhe impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. Spec j;cyvvrq+ 8-rify relative to ;cjr -q +vv8yrthe left-hand 1.00-kg mass.    m

  The distance between a carbonj- ftt *7an)qk 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-kvbcn5z h:u6) oh k4d6dg car is 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 h4v uc6h ddkn:)o5 z6bcar, 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, of mass 6800 kg, is used np72is5odhm ai ;(af. as a ferryboat. If thi5 ia2ao ;.f s7nmhdp(ree cars, each of mass 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 side vb xqfq; yuvgpv sc:b3;44s2,1-he ens $l_0$,$2l_0$, 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, /1vxvvfm( *xm nd/**mj mwvcne3,rn a load of identical cases of tomato paste (see Fig. 7–40), each of whmmwemd,f*3rvncv,x*xnm ( * v jv/1/nich 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 tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plmcb1c4cz94bmwgrp u xi 1 .q;-ate 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 positionc1p bm;cm w4z.1c9xbg q4iur - of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calculacbg8 kmdi9 g94 j8v.eete the mam9b 4v9g8i c.jk8dge ess of one of your legs.    kg

  Determine the CM of an outstretched arm using Tajko24l*0z vfm 5l dr ,d-isqv(ble 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 tsjk8, jy u2(ddhe CM of an arm bent at a right angle. Assume that the person is 155 cm tall. y 8,2ujk( dsdj$X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs/ssh*v )elsd 2gx*r+ u ee;8cv are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median l hex8*vs)2; vds e+*rgl/u sceine the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon aismf6z gspq10 6h..z4fdkndv 9wwutz0 *e)g:re $5.98\times10^{24}$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 frictionless ict i9jkj9d;f gaip(p0 qkt) y;*e.
(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 a )ns/xmw6z+ n)kxl7fmnd a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shm /klz)snwn 67 m+)fxxown 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 cylindricj- 5 j1z)yycowp be2p0al head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spi o2z p5ype0j)1y- bjwcnning, 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), a. uymzl0-b0x qh r0r2$m_{II}$=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 tjur 8o931xm lv- 3eo)ww(.dv0aalhechhd,3 phe 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 balloonla- l93hovhc we)v.1x33hea8 pudr(w,j0dom. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitchedrm 480 p h9g9zozitvs+1u )d s4a4spqa horizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the coap 04 ih4z ta9 r ss4pmsdqz8+19gvu)ontact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling w 2/kb9xpjt6k mith 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 showo/+q wb(,pm xx0; rh wln*e*sjo/crq9n in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scrarr w em*nqwxb ho9s/,/0lp;c(*o+jxq tch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) scj . f)y1a)xsacquires a speed of 2.5m/s by pushing off with his legs from an 180 )a.)f1 jxycss0-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 v z6s8k:je(n kother 80 kg, are initially at rest in outer space. They then push each other aparvz8ek( :nkjs 6t. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball*f+ j9tlfadx9sph.v- (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mxd*jt9s p-f .hfa lv+9ass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witngqi5t b jv*)fdiv)k)95f5 hog ess in a court case involving an automobile advh 59i joq f5)) 5b*gik)tvgfccident. 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 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 s b(gt luql8+b6 35rgdof a flight of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different srgsd b8t3 glbl5+uq6(tep 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*+ehmkh riliaxp*woi :*.4 b; irectly above it. If the bullh*:ha . wei+ 4rxlib*k;i*p omet has a mass of 29.0 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 of wood f 8a6le *tb0rt -ix +u/g-;zzpp.k jrbk+p4omplaced on a horiz p . z ;-ik/4tuj-pobgmxrlr0a+ tb6+ef8k zp*ontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the aq5s4ai,xru 2td /v-fother 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, no 4/itv ,afr2 d-xquas5w 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 lle8e4lp0dj :, vh n8xf 8akgap) lih* u*0wt/$ 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 a8w -q( t8 gd.fua7vdzppart into two fragments by an explosion. One fragment acquires twice the kineqwf.p atv 8 7z8u-dd(gtic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 580-(xl t5b1.08 fcjw1 v/ekl/o aym $1.8 \times10^{ 5}$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 (ite pt8yv1.g$m_A$ = 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 particl 5w)tb-ehp+/l,e o cf5oj;sijg7 le 6ye and a smaller nucleus. What will be the speed of this recoilib7ygh o)iej-6jl,et5 olspw; +fe c5/ng 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 (cla7i75e9o w7gnwj2blm gy target) 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=2.2, qi+vma8kysu1i9vi j;uv9(is.yxq- kg slides down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper hhdp+ /rftds 279sm0 plimit on mass m if it is to rebound from M, s9 0pdh/rp 7 smdf2s+thlide 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 slin .4prh8rirsa+ug wt;0gshot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respet.rgu +sr40i ;wph 8arct 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