We claim that momentum is conserved.:j p-v054rjuqd jya7ag jn/e, yet most moving objects eventually slow down and sjy0.4j- npu/va7qe: g5 rajjdtop. Explain.

When a person jumps from a tree to the grye5ie9 i+m br:ound, what happens to the momentum of the person upon striking the ground?bi+ee9 i5m:ry

When you release an inflated but unts((ex mr(ryzq, * gno d(7vku1ied balloon, why does it fly across the roomnvsz17(e(kd u x*, oqy(r (mgr?

It is said that in ancient times a rich man with a bag of gold coins froze to dee, vo) pr.r* qi8tk4raath while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done k.8 roqe4vpri )rt *a,to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space a0gy, )j1f e: lgli5iovnd is essentiallyj lfg)ilv 10oie,gy :5 in a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse,/pz pq9-u khl51sajc0 the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explaa us5-kpqzl1p/0j c9h in 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 withstand collisions. Today, thsm.nzuq -+sw5 m8 ca/mougs -mz8qsuam5nwm/ c.+h, cars are designed 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 ball tossed in thy85t miwu;i v4e air by uv;t 48imi5wythe batter?

Is it possible for an object to receive a larger impulse/u-s ale:y x,m from a small force than from a large force?uasx:e/ -l m,y Explain.

A light object and a heavy object have the same kinetic energy. Which has th 2kgptt fx41m:e greatertkxg:t 2p1 4fm momentum? Explain.

Describe a collision,zz1z7aqd 2wb in which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against turbink r,i:s)+ d t8uwa/aybmx7ny9e blades on an axle t aru9+mb 8: xsny,t iykd)/7awhat turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at5h6dx( nxtav. /(l0gdga(rxjs wf- v/ 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 plate (fixed to thhug m0)u zl- zuq/k7g.e 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 cons)qu-hl7 /gmzg.0uu kzider 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 leanv9z5 . slq1v v0d a+mbeh.j8 o8w*ngep backward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereo9iuo;1 qz1pka4,j ztas this is not true for y19pz,jozu4itk; oq a1our arm or leg?

Show on a diagram how your sujh)h kd).dia)bn -5,l bjmqyop857CM shifts when you change from a lying position to a sitting pbu)oh)dpyj7 .jmna, b dq8 - h5)i5sklosition.

If only an external force can change the momentum of the center of mx h zu85;*ln :m xcorb: (bj--k/;oodqisnzf(ass of an object, how cabb*zc;:fm /ro znlho5jk--xio nsxu (:8d ;q(n the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes in6o ti6in*)hrfto many pieces. What can you say about the motion of this system of piec*6in)h fir ot6es?

  What is the magnitude of the momentum of a 28-g sparrow f/ 2x2jn5e+fbo x)dx q*ryu9oglying with a speed of 8.4) y+* n9g2ofbd5/rxexx j2uqo m/s    $kg\;m/s$

  A constant friction forcets 6/2/zsjs vq of 25 N acts on a 65-kg skier for 20 s. What is the skier’s change in vez/j6 q2s t/svslocity?    m/s

  A 0.145-kg baseball b0l3v kd(j2zrh: 8nrfpitched at 39 m/s is hit on a horizontal line drive straight back toh v8zfr3:jr2(kn0 dbl ward 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 horizontallyeenwtq- e44( k with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the bete (n-we4q k4oat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gase c+4zjax9ix. fc 6p(nds are expelled at a ratci c.zan4( x6pf x9jd+e of 1500kg/s with 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 touchdown *lb 0f. 0kz+iz6d ilvois ta0id.b+fkizl z 0l6 o*vckled from behind. 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 ca buu b 1vk (35ngl,cwe9d+q8kbr travels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. Wh+d ewlkvc593 bnuub18 k,q(bgat will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s/ c 5jf9a l+hwpos5w,n strikes a second boxcar at rest. The two stick together and move off with a speed of 6m/s What is the mass of the second ca5jcfl5/ p ons,w9wh+ar?    m/s

  During a Chicago storm, winds can whipcj(.35:janakah xvej ffh xf663 :ke0 horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per squaj nafhj0xfvhjk5e:a . xea(66 :3ckf3re 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 railr( hqkf 6:t ma9b6tded)oad car coasts along 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, w:bt6)6d h (dme kaft9qhat is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpgq-1-oont2:;ro txfrha 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 22xotr-or:nqo2- ft1;g 2 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and emewb)1 wcx26ziel 8bv(s rges cleanly at bl v)e w6w 1czs2x(b8i170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speebg5v*fa +j7k gd 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 vev 5te,aiki7h uqg;zp8;o ,x o+locity of 115m/s To alter its coursex hu ,kavog5pizot ;7+eqi;,8 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 of7w,f ctzau7 /cf the tee at a speed of 45m/s The golf club was in contact 7fc/7tca,z uwwith 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 apd d3em/;q5v and comes to rest in a time intemed3apdv/ ;5qrval 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 v=25m/s sbuu6sam n7hh y7 )m,i/trikes 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 nuwl,4v4 l ;ks- jht.ytew automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 15hl4,4;yj u.lt- vstkw00 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 :c:9wje2 ddmp,r1i qfis stopped in 0.75 s by a head-on tapf,wdi rdq::2m cj 19eckle 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 ba( z e(2twbw+gwll (mass 0.060 kg) points in the +x direction and is givw+e2ztb( gw (wen 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 without r56n.-u*x b dny0u sxzh(c3c bf)pu+ wbreaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fxwb 6zu - ) pb.3uhsxyn0*uf(5+nrccd all). 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 direc5gs5n*p ojn6psy w-*etion) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic,pwo6 5ss**-npejny5g 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 of 3m/s has a head-on collisu *1tgoy)y; wlion 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 c;ywg *ytu)1l oollision?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 mass under7yephk:/qb )3 8sxy j*bbjb6w go a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Le)xje8yjk wh/6qb b*3b7y ps:bt 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 h+to(pd2tis*3s h6e)y j* 8 +blenmaqa speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving a6h8h)qent yl3t* oisbd spae+m+ 2 (j*way 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 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 i;p p3rjq4e(-wwjp;by rez96 /s collides head-on and elastically with another balp;pby 4z-p rj qwwe e;i(jr936l 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 amusement2i g:3fz*o6q 4vpiexc park ride collide elastically 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 passengepoifex34 *:q6g 2cv zir mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a second:n:6 5 khqcxmm ball initially at rest. The second ball moves off with halfn5qm m:c:6xkh 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 dow;j7np 3bh:gtv qq+ ;usn 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 3; sgpb7j+;q: nqtuv hthe incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object o wvf6un/pdi4vc)56jfcyw hm*zc b5 ,:f 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 ai3i or./i4t nheight h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as hir43 oin ia/t.igh, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg pendbj dc-k6q+:79 mjyhgyulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horic9h qj :yymb-jk7+g6d zontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic enerp)q qwa 90 7m:++ij8ub5m rv;xtvxms ygy 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 rest, intxd3:vmm,rap 4 tdp f/az8t.+wo 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 represvr. t dfdmw:4a3p/z 8mx,tp+aent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the ku(m8 w0gz.anoxm9 bq4g2la*p7pj4 zrear end of a 2300-kg SUV stopped 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 the speed of the sports car at impact. What was that speed?(Let A represent the sports9z 87a 4ax4 p wq(mpu02gz.lknjm o*bg 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 o0.;vth 2)w sj h1myszub+7s erf 1.20 m. Approximately how many rebounds will the ball make before ess h1thj;7 m+y2wzsbvru0).losing 90% of its energy?   

A measure of inelasticity in a head-on collision oflxj 47.n/vlzc yt7 d.f two objects is the coefficient of restitution, e, definedd7x.l. ntj zvyf/ 4c7l 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 /ubyf8 vu:o(c pieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in cb8/ vu:ofy(uit 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 directi01j. ymchn0ux on at 5.5m/s collides head-on with a 10.0-kg object moving in the -x directioyj0humnx c. 01n at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an electron,d7dv*,e0 z4/quz p szx and a neutrino. Theez z07,z*qs ddxu vp/4 electron and neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of massd+8on,fz6rk x $m_\mathrm{A}=0.400$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 b9* e c3eob*d(xu ly(ryq8ev-eetween two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial directio(e 3q8oy 9leb xvc*yu* e-e(rdns?    $^{\circ} $

  Two billiard balls of equ2f j.a;cg**lc *mo zso9net)pz5gd g;al mass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s a cej.c*a sg;l*poz g9 * g5t2odz)mfn;nd 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 :cv:-dvufq1ou)1ok f a perfectly elastic collision with another atom at rest. After the impact, the neonvuk1)-u: v1o :cdof qf 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) cihwjo;,c /47l zuvp3makes a perfectly elastic collision with another atom at rest. After the impact, the neon atom twlo;u, 4 /z3chi c7pjvravels 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-ma( . y;jc.;m lcg;7 orijs)zdhzss system shown in Fig. 7–38. Specify relative to the left-hand 1.00-k.r os7lihgcj cz;yz mj(;. d);g mass.    m

  The distance between a chei3d h/ci5(marbon 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 1050d5fg(y2hpsgo-n2 3zeo 7y2jg -kg 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 ind2oogy-pjg 2 nz y3h ef572gs( 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, of mass 6800 kg, e g+yf l5e5;v q5qvt(ves2lg m;l1q 3ois used as a ferryboat. If threeyg+m21e ;lqqe 55evqfo3;lvg (stl v5 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 sides /hm312-cv t.lvam0v g 3uka md$l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of toqxhsyd v33( r kh;(av r9:elq+mato paste (see Fig. 7–40), each of which is a cube of length l. Finds3h(h+vv3q9(ed q ar;lk r:yx 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 plate of radius 2R has a circu2oh( 1c +klnw0zicqt7 lar hole of radius R cut out of it. The center of the ck+iq t(nw107clohz2 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 subtraction.]   R

  Assume that your proportions are the same as those in re .;jkf). wepbz(z7fz kedoa : 6yc()Table 7–1, and calculate the mass of.eez fa7) 6;pko c(b:zefk y d.j(wrz) one of your legs.    kg

  Determine the CM of an outstre:o vyc/ .ft:iv pj:. thnne8x)tched 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 o2 qb 0dak9oqz*:ky ;b6ztvsm 2q94ujff the CM of an arm bent at a right angle. Assume *m q2zk:s 4j9y2fq6a z;vqob9kt0udbthat the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms an9d50 g1wlq;r bmv4q .jkyfkt; d legs are hanging vertically, and his trunk and head are horizontal,;j q5k0gtlrwd 9qyk;.f4 vm 1b calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth adnl 22hs 9:mzdnd 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 ffehp24j 3ba -;xpu3v;u eq 5yzrictionless 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 anan. ;. /4- ahluxx4t nmvuf3ojd 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,hftu.joa-u m4nx/.3v l;xa4 n 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 dkgf1,jm /l (h u:b4 ya8nc:tf1azu)rfiameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.5 b4uhl)k18 :fru,tfzfnc g:1y maj/( a00 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 Examp8d z dk tz,8dk) dv( f;okyca.-l-4fzmle 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, acf 36+:ugcfzdys+j0v *ajpb( re in the air and stationary with respect to the ground. A passenger, of mass 3svcdcjb+: f fu*z aj(g60 y+pm, 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 pitched horizontally at strikes a bat and is popped stra1rqq+eu7f i up3ut u16ight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the avet1uu i6ru3e7 q+qf1p urage force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with8 t: ufs-bqaextv1l,, speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown in Fig-9hkx dbkrr ,gpn)3e-. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in whickr p9eg) knx3bd- rh-,h the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by pz /w;b8j6xjtimi l7z7ushing off with his legs from an 1800-kg space capsule.lzxbmi8j w 77;tzj/ i6
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are initially at rest mpi-y1vk100 d nn *tvxin outer space. They then push each other apart. How far apart are they when the lighter astrona*d0n 10 i-xynkmvp1vtut has moved 12 m?    m

  A ball of mass m makes a head-on elastic ct5jbl tt8*judw*9l o;.0s ipdollision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its orwu dt*. ttolbj8;9* 0dlij5spiginal 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 courtzc*seb6t llz)6qi r7; 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 bri;z z)*l ecb6tsr67l qakes 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 of a flight of concrete steps h0iryr33edx( /6y wliof total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bdyeh60w xir/3ly 3i(rounce 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 res3 2j:x + fw,(rzm4y dgbjgkca(ec*-okt directly above itak rcfwygemkxc 4(gd-j2jb(3 z+o,:* . If the bullet 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 8f z qycs2bne(4z29aeblock 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 d9(fs ee24bc82 znqzayrives 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 7 jpqqsr8 *up99sue t,85 kg and the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will pss8rte ju*q8 q9p,u 9the 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 ,pwpit g0,r7x4 h92ce8laeccj sg2(y$ 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 ap b,uadl;zr) i.art into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio r; ).,bzldauiof their masses?   

  The force on a bullet is given by the formula o)ksy9yp2:m/0 do din:ny . fbF = 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 /ee l1f/bs8yo 5- ssj ut6w8i 0ptn)hc m.bl6n$m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha particle andbk kt0;f)+ ssp a smaller nucleus. What will be the speed of this recoiling nucleus if the bst0k+kf) s;p speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angle of 3 a6aq18*h7nn fqzl wj,0 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.0nm bk9isp-7k8 $^{\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. 7–463 s;bv+i7nwm l), what is the upper limit on mass m if it is to rebound from M, slide up the incli;i wls3m7v+ bnne, 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 Saturz1a/9x.m yxs0j2wds yys/qm.uhh;e, n moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6kmqsxyxu 1smay;0y9j.z. ,mw//she2d h/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