We claim that momentum is conserved, yet most moving objects eventually slow dowmo7a*yv6a zt 5n and stop. Explain*a a7z65 tyovm.

When a person jumps from a bavf ,dux137x y6zxt 4tree to the ground, what happens to the momentum of the person upon st4bxd tay, vf xz613ux7riking the ground?

When you release an inflated but u/wfba1.n k kv39i 7ukfntied balloon, why does it fly across the roombu 93 kk7.1 wkifvna/f?

It is said that in ancient times a rich man with a bag of gold coins froze tt tc5 w0: dlzi4.mmyh+o death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so cml4 id0.tmt5 wh+ :zymiserly?

How can a rocket change direction when it is far out in space and is essentiallmmqfh wns4n e-1 7l2;oy in a vam w 42ofqs hne1;-ml7ncuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller thmcqwa .c-1 h+y2 /maipe 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 intendm q/ .c-1hy2wap+caimed 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 c pbz vd;5afj92ollisions. Today, though, cars are desig bj2p9davf z;5ned to 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 - pq.fkja2 qpp9va xb02a f38bball tossed in the air by thfajax82k3p.b-0b f9 q vpqp2ae batter?

Is it possible for an object to receive a larger impulse from a small forc5z tj ekt*)3-/pdofepc9yy 0n e than from 0- o*c y /tedpk3) 5zfjp9yetna large force? Explain.

A light object and a heavy object have the same kineti gzjkc(39wavu fiqt,:h(i f++di 54ikc energy. Which has the greater momentu(v5giu4(q kf i9 atj f,:+i 3+hzkdiwcm? Explain.

Describe a collision in 2z36 hvezgvw*which all kinetic energy is lost.

At a hydroelectric powert1p1tl qz 9r3c/:r ruxg e;vq0fa0g-e plant, water is directed at high speed against turbine blades on an axle that turns an elc/v ap3r-;09q:x1t gqfeu el1gtrz 0r ectric 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 wal5uavv a*e;1os j55nicxo- :bhl at a 45 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel platehp.fxjr u+gcdi ex91lh()8)ka . 3hof (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 process is momentum conserved? (c) Answer part (b) for a piece of putty that falls andfx1 h .ilr fd)+pa3x8)hg9 oukhejc.( sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in your ar6 * 6f7bkrgqhpms?

Why is the CM of a 1-m length of pipe at its migg)zo au bk-w5(+.plz d-point, whereas this is not true for your arpz-(5)+kgau.bwo gl zm or leg?

Show on a diagram how your CM shifts when you change from a lying posi/uiwe- y kt7r3tion to a sitting positioner3 7iwy kut/-.

If only an external force can change the momentum of thvxoz*4b.cx()f j autfq(v j)m lt6.i/e center of mass of an object, how can the internal force of (xf(qvj. )malj fu)o.c bviz/x64t*t an engine accelerate a car?

A rocket following a parabolic path through the air s67bwnm u l )z5k7;epuvuddenly explodes into many pieces. What can you s7pbu v 67)5ewmu nl;kzay about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying ds x f /-5c1t0,v0 saxf wvpb3)lyv:p0jbmt 8rwith a speed of 8.4 m/s :w v 5x1 vmc x/f0s,0ptpbat8s30yl fr-bjd)v   $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. ekxqj6d9 t yzp*8b 4q7ke:kv0 What is the ski:dq70vkk4 qb 98k px jet6ezy*er’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizh7 mj8w*bynw8 ontal line drive straight b8m yh 8*ww7nbjack toward the pitcher 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 ws; bch 5 ha d:,t837gabo ep8s(caok-horizontally with a speed of 10 m/s Fig. below Calculate the cp 78hsd,acboos3- twb8 ah k (g5e:;avelocity 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 velocity of the boat is    m/s

  Calculate the force exerted on a rocket,bns) r ,q,k3zg pzp1f 6noti6: given that the propelling gases are expelled at a rate of 1500kg/s witziot3bzpnr ,kq66 sf:gp,n1 ) h a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an apparent breakaway for a tou3qjo, n *w8mtmaft.o-chdown is tackled from behind8ot j,wmn3t*.-m qfo a. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travelu4dt (o90ltokbho6d7q w(n/xs alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initiaokodxqtbd (lu07 no6hwt(4 9/lly at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar at rest. The two stes) 9wngaxuq 867hnk+ ick together and move off with a speed of 6m/s What is theunan9q+67hswg)8e kx mass of the second car?    m/s

  During a Chicago storm, winds can whip hori lcxk1:a0dmo1y.9 ohl ye-a1 ax9l+qi zontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimatxx l:q lo-o.0hkm1yc lya11e9di9+ aa e 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 an7cy728f-3djmnmgr llong with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills thec-nml y7djg 8f7 rn23m 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 a qv2 .a x3gf*ajc9,ykemits an alpha particle in the direc9xay.fk g2av,jc q* a3tion of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wooi,.vf+gjd: isoh*u)s d and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fu )jvh,i+fi.sgds: *oast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is trave3 /n1np:nt ) ilp(a jza+hys3zling 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 i+;m a rdct:,e/7 eo+el:uhg ims traveling in outer space with a velocity of 115m/s To ad:m+,r +:eum ti g 7ce;/oahlelter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed4yf1d (8 u2ualt;+mcma i+g gm of 45m/s The golf club was in contact witgf28cyuim;1gam +( a 4mdul+th 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 to rest in a hzjlk/w* h02o time interval of 8.0 ms. (a) What is the impulse given to the nail?/20 lzhjo*hkw    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 0*x)cya-u n9x gtugthe3+no *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 crashwort jt4pdr8s63kwf s*y f9hiness of new automobile models. Cars are tested by smashing them into fixed, mass439sr6 d ktfj8sp*y wfive 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 pq8te1tt;n:rr7m rc)e* p1z3zey:jg 0.75 s by a head-on tac1m1)rz 7y q: j3 tezg t8peec:rrpnt;*kle by a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball zc w:xgeu+tx6 zab g(+a/tdbf( 66 (fj(mass 0.060 kg) points in the +x direction and is given by the graph of Fig zt /a:bgb(f+u wej+(c(xd66tgfzax6. 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 without bregq 5otsuv4f(n-r,v*m aking 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 t*4,vngtrvs fqo5u (-m he 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 k66(8imuq cfpmoving east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is p c6 u(68fmqpikerfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed o vla1ivmt1;fp lodyp . 56v1i8f 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 represedp.tfvvml ypa8165i1ovi ; 1lnt 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 mass undergo a perfectly elastic head-on collioj uq.;) u6nursion. 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/qu ; 6uj.)ounrs, 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 2.5mwmtq k.9r s.i:/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, wtr:s..q9m k iwhat are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s collides i,k age1a - hk:3-ddxjhead-on and elastically with anoth-ed x-1a digk3j:k,ah er 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 elastica khj*wpyib;la:7jgi2ui 3o: q j -;6nzj39rbl 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. If cai: *-ozginj3yr bl6i3;k:79 qahblj puw j;2j r 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 map(qh ornlk x.o .lim(zlo38// kes an elastic head-on collision with a second ball initially at rest. The second ball rx q(8nl.ziko 3.lo/mo (hp/l 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 incline as s, ecqtl d8.kf1zk lz:wmmjw+cqg7+2-hown in Fig. 7–35, and elaswq1l,z kke7lc -w:mf q2dj+ +.8tgmzctically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an muvka0ru)y ; 9object 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 pendulumjpv wv,3l2mm) 4;c i(k yyqetw8ir;4t experiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the m ;83 j m)4e,ryqwkty(2t4vvcipli ;wpendulum 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 a i7ok0 mqo r;x* x8ey7.n t,/vnoszd*6eq-yj b3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Deteo8 e0oery -ndx*q mzyj /,7 ioqv6tx;k7*s nb.rmine 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 lost,mj: / 8w/b7 zjxann4ql $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an objectk. ejj lhv0 :h8ds.gh +;hint., initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particg+n jdl:.;0kji. ehs.h8t hv hle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped at a* 78 )an0mvernagllj) 65z w7 j3fynuq 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 the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B m 6lunlaz qfj yn0*wgjn7)v7r 8) 35earepresent 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.wwvezkx 1w3h)lx2 g:1 Approximately how many rebounds will the ball make before losing 90% of its energy?x lvw:k h1w3)gew z21x   

A measure of inelasticity in a head-on collisionh.1crw1( r) )0pbf) o:hgqffufu,yxk of two objects is the coefficienkyfofr gcx,11 hfuubrpqw:) )()h0f .t of 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 p 1zg-h)binfp .ieces, one with three times the mass of the other. A depression is made in both faces of the f)n.p -zb ih1gcut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction j-i+pkw 37n7:w owfnk+g3vc8 oa*ns xat 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final veloci -w7f+vin87oc*ksn: wa oj xw3ng3pk+ ty 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 i6ua6w l :ve0gg1y,x/dasn k+l nto a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted atagyw /:e,1asl0vdu knx 6l6+g 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 mg ns.u/nlx.gfaong 1ct,) * 38w9zdp qass $m_\mathrm{A}=0.400$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 c +hvcdpgyj .ld/k+92vollision between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between thed9 jvdp+2vy +c/h.klgir initial directions?    $^{\circ} $

  Two billiard balls of equal mass movfxh3cr 7c ;nv4e 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, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is vrcfcxnh; 3 74the 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 elt9hk j/(vrw 9rastic collision with another atom at rest. After the impact, the neon atom 9r(k ht9vr wj/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 4t/oge9 h8gf kcollision with another atom at restfk8hog /4t9ge . 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

  Find the center of mass of the three-mass system shown in e,.r6f xng v;7qc/dsthoy; 4ktft6u-Fig. 7–38. Specify relative to the left-hand 1.0ut,4q/-decf .;ts6 xhr; g6tov7nykf0-kg mass.    m

  The distance between a x,jxy8b/w s-kcarbon 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.uu-8kcusl9: b 9y .fxce3 szv:nu/b-h50 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 peopl-/.uh k9c z39-8essu :lync xbuu :bfve 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, (nt1:j+qn , ;4s-ytuphybnjl of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of tslnb;t ntqy4(uh :jyj,1p+n-he loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides a, set7 4l1d(opv9z sk$l_0$,$2l_0$, 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 identixafv wkr2rbny*7 7c75cal cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the a rkxvr52 7nfy*c7 w7bload without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radiu7 cz+ ( xn9olth.7nyios 2R has a circular hole of radius R cut out of it. The center of the smalleh7ciznxn 9+( oty7.olr 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 subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, andcm*k;a w6e .bpk if1o4 calculate the mass of one of your legso*c4kek mwai6f;1 . bp.    kg

  Determine the CM of am o7nxf,/ i)j :nfq8mxn outstretched arm using 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 of an arm bentm* g.6v,j9x. o mj soj,7ijkhx at a right angle. Assume that the pevm gj9hkx,6o. sj*i x,oj.jm7rson is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a posjgg-qsx1dv00oh. ka 1 0p2gmf ition such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside tgs 1hv adxp 0-g0m0fg 21j.okqhe body? Use Table 7–1.

The masses of the Earth ac9oz n,wr4j +nkc 0sm8nd 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 apart0pkr9ei9fuh neg /(7 p/ zrs4u on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform b7eiu:.h dvs1 dw**hg cylindrical 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. 7–4dw7db :* 1igv*hu.ehs2. 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,xkr d :b9np6e 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.nd6e9xpbkr :, If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29) c/p,y-vq*okcl-o + ah, $m_{II}$=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 stationh 9: ngj2pzv-xa 3j420f nr+/mropvrkary with respect to the groo j/x24z + :0r r9vn3nav2mjhgpr-pkfund. 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) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitc4djbq0bqqq-efl)) m5 hed horizontally at strikes a bat and is popped straight up to a height of bl4 q)q)dqjb0qm-fe5 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 travelin2d,6xaea: nrg g 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 pockee st.vo -s7p9it 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 dets- viep9os.7tails.

  A 140-kg astronaut (including space suit) alp-ot+n:7tq6 tj(vu h cquires a speed of 2.5m/s by pushing off with his legs from l(n6v+q7hp totut :j-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 tad) o*l0po9jk he other 80 kg, are initially at rest in outer space. They then push each other apart. How far apar0o ad) 9lkp*ojt are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elaw/am,5 vy05 t yimo6iqstic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the seciq aoi5wyv5/ mt, 0my6ond ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness1b9t of*s )zab 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 col)*bzafo 9bs1t lision, 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 th56 lm0dhqp( nhe top of a flight of concrete steps of total vertical height 4.(n0 dlh5p6qm h00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce 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 directf-0s hxy5mtya ,: qx5*ce 8yshp(nvy+ly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise aea,+0x5y yn5h*yyxqhstv p -s:mcf 8(fter the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes ef1 /isq )x*xj;e/t rnhmbedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction h1sf*rjqn;ti x / x)e/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 and1 7zfq(eh)ykh l xw.k63k+sjx the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two pe ek1xkjw k67+xs3h.q hf)z(ylople, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass wasfu ovvw0 t9t9x/a 29na about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is sudxilh7shj,w p *c0/e; bdenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. Wha, pcl/bhjish*x07;ewt is the ratio of their masses?   

  The force on a bullet is given byz8 6 j6*xk s7k0w mx5ax.fllyc 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 massesbra k32*u/ql 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 radioaj f;jq 5smx ub85a4odltey83elz75olt qa 2*2ctively into an alpha particle and a smaller nucleus. What will be 3 42y75 lmlq2j sej fdzt5oteal58*uo;q8 xab the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clayvq 88c1wxy g1r 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=2.2kg slides dog vbq9omda,xr1w e/( )+fjok7 wn 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 limit on mass m if it is to rrs 6(uzbs (x1 pj0gi(nebound from M, slide up the inclu js60(r(ps1(gbizn x ine, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slings) hlrp2;:oc)tmxw * mkhot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (w*2xk)cph ;rlto ) mm:with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s