We claim that momentum is conserved, yet most movizg80ug unkxr yb ,*b:*ng objects eventually slow down and stop. Ekgzn x :yug,08* *rbubxplain.

When a person jumps from a tree to the ground, what happens to the momentum o2jx i0:dgd ui/f the person u0du:2i/d xjgi pon striking the ground?

When you release an inflated but untied balloon, why doeh*25b)l** rg9:zw y6hioz 8gsa v bkanrrk: f;s it fly across the room?lh* w8snz 5:9*fk:6) vrr kaia 2gg ;ho*ybrzb

It is said that in ancient times a rich man with a 4vkt0yz yl6 8a6wu,4cr(m hmp bag of gold coins froze to 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 savel46hzck0rmt(,vm wa yu8 64yp himself had he not been so miserly?

How can a rocket change directi ovg9c; p :icqn4pa:-mkl;y,yon when it is far out in space and is essentially in a vac pkq ,vcml-y;4agi: 9:o nypc;uum?

According to Eq. 7–5, the lo7jm7i 1m 1gojlnger the impact time of an impulse, 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, explain the value of air bags, which are intended to inflate during an automobilem io7gm1j1jl 7 collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand2h8a;kix6. kpe 1+zm7+w djag+nwek x collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this new de+wa a;hkmpwi 2e7 6+ e.dj+knzxg xk18sign?

Why can a batter hit a pitched baseball further than a ball tossed i;vfqf*i.ka :o n the air by the batte v *qi;ff.:okar?

Is it possible for an object to receive a lar5w ma4j7qye1; )t thtb8v.z bcger impulse from a small force than from aqywv 1bctbamtz j4h7t ).85e; large force? Explain.

A light object and a heavy object have the same kinetic energy. Which hasq2b: azqcw 20t;0z+ pcegydp0 the greater momentum? ;p0az 0dwqy 2ct g2c+ 0bepqz:Explain.

Describe a collision in which ac2 qm/, nvrdv2ll kinetic energy is lost.

At a hydroelectric power plant, water is dir p8 +fug(o6tqrected at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brou+6uf gqot8r(p ght to a dead stop, or so that the water rebounds?

A squash ball hits a wag *wsi 4a5kchf+,zjk +ll 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 aq*;ict og9f: fp)v*q f hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty tha:vfgfoip9c ;f tq*)q*t falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavyi5i9axfku5cclw7:h wq 7my1 1 load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas thit,din pgvt1 3t e0+da+s is not true for your arm or leg?av +iet g01dn+,pt3 dt

Show on a diagram how your CM shifts when you change from a lying posmvor4h )x)dpy f( -t2s rh.p:thael 3*ition to a sitting positiytrphr x)d)sfe 2tam4ho*pl v.(3:-h on.

If only an external force can change the momentum of the center of fi y 0l ;1eug+b7g6nonmass of an object, how can the internal force of an engine accelerate a cgyu0+n1b noi6fe7;g lar?

A rocket following a parabolic path through the air sudjq/ingsmy 8934n sy,kdenly explodes into many pieces. What can you say about the motio n4/kq3 ny9smg yj8si,n of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a (pd,15*ss:e9a f /azhcod xmg speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65v( qj2,c3ghk 2qu(6vq dymfh:-kg skier for 20 s. What is the skier’s chamq 2(vyj2vf,kquhd 3g6 c(q:h nge in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive straig6(tal ii56m r**fnjai ht bac* ftlm56ra6naiji(* ik 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 packag o(iz7h (gm+y rew(+kre out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 2kzrhog+e (7mi(+w(r y6.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the proyih jhkhp(j))4wq *+a pelling gases are exph+ yajqh) hi4k)pw*j (elled at a rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving at 3gq: ancs ojd/:ih1je)304 pvu5 dlp+cnnd a2$4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionlessbt6z/q4kh7s rc+9ae e p r*0co track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be 4+a6*reche s/ctq0b9 p7z ork the car’s new speed?    m/s

  A 9300-kg boxcar travel zqwgs/1se o o/1qt0;(rcif35ysdgw ; ing at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of 6nbypcyv2jws 8b if j2+d-p-)100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, es wv8sdb -6b p22py+ycf-i) njjtimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of 8.6m/s go0ro.vol 5w9+d/.t g pu k2smon a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring fripsg.v2 o w 9m okt0l+o5rudg/.ction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in the diri),z j lcxrax/-cy,d(ection 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? x c-al(/dr,xcjiz,y )   m/s

  A 23-g bullet traveling 230m/sa1kgs3wl/a l 4 penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after thel4w a1g/lak3s bullet emerges?    m/s

  A 975-kg two-stage rockec(9qhxfnuvr)qb 8c 1)t is traveling 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 trq -1dbu4bdtg cfhx03n af6 b9;aveling in outer space with a velocity of 115m/s To alter its u9;fb03qgb1x -4cba6dd h tnfcourse 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 tt qs 83tg1yk.xhe tee at a speed of 45m/s The golf club was in 8xky3q g.1tts contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes to rest ini3jth1rbpvhdq(3+ / j a time interval of 8.0 m1/hq3+jv jr(pi tbh3ds. (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 andri-hci,k .:kq speed v=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 engineer in charge of the crashworthiness of new auto 3acngnp*n zc7j+*:lgmobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of *n:lzangcjgp* + 73 ncmass 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 0msre c7:j4kk +.75 s by a head-on tacklesr7+4 ekmj k:c 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 tef oi yz2-c22 5vlr/pkmun9/adnnis ball (mass 0.060 kg) points in the +x direct/ozdn /-cm2v2f ia5rl up k29yion and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breakco3pdto4wq1+oxy ,w v w 9.x2up /jr1ving 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 positio p+ .2/ xywou3w rd,1txvo4 cjvqo91wpn (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a sp1ir xssf5 4np9eed 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 ai41xsf5p 9 nrsfter 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,nk+boen7l 8w7 9 iqau east with a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the uk,n7 l +8q7wenoi9ba 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 mau 6ek ) koajgh -j9 wngos6*,qsm94+pnss undergo a perfectly elastic head-on collision. sq,a*g6n e4 p)o6+-o9ugjskmhkn w j9 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.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 2b w79c, qstlh3 c5d(xy.5m/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, what are the speed and direction of each ball after9s3,qdwx(tlch7 cby 5 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*ri93hll lpj8wj - oj8 with a speed of 8.5m/s collides head-owjl3l rpij8oj8*9lh - n and elastically 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 amu mxi: :jfekogr2 u..d.sement 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 passenger mass. If c o ki.2x.:.mrgje :ufdar 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 s l-y0vx)lcc .jjjn( y,econd ball initially at rest. The second ball moves o)ljv ycy0. j(xl,cj n-ff 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 fr . sivv+;wxt*l qdo-+yictionless 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 flqxydvtv o;s-+*+lw.i oor, 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 n :;lrtop0nqbq m. 3c3an 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 results in a maximum height ufb h 8nv)-tb0h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to s ufv8)bbh t-0nwing 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 tra3 tfu88fitb:2kj8 rf aveling 230m/s 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 com bk t:u88f3rfatj2 f8iponents of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kineti v9c-xfq, .)inwpbtk +c 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 rest, pseb)) b )7dtdinto two pieces, one of which has 1.5 times )bdd)) p7t esbthe 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 particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides)lg9d9*vi ec-8 n iitt into the rear 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 rn8*tcl iv9i9dtg )i- eoad 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 rebouxvx+(je+w wj/6,d ng ynds to a height of 1.20 m. Approximately how many rebounds will the ball make befoxdv+wyenj 6/xj(w+g ,re losing 90% of its energy?   

A measure of inelasticity in a head-on cox*i(k j -b/odsllision of two objects is the coefficient of restitution, e, defined aok(/i d*- sxjbs$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
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 withbnq sr1 tvk*v8)2e2n y pm1wq3 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 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 a2r)3yb *kqs1 nev1mnv2qt8 w ppart. 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 bh.bdk tckf0is d6279r n73r1vlsc 1x at 5.5m/s collides head-on with a 10.0c2vsf.xd c7r6kb1t9 30 d7nhl rksi b1-kg object moving in 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 nucleu n0-lm*g3fec b)zbj3is, an electron, and a neutrino. The electron and neutrino mbn)3lf-bz0cj* gei3are 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 masqav/:w3x qj q35ntzv- s $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collisioc8z5s j-0e: i8jlfob3q0ab*xipb,v n n between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initi88,ii3x jaqb ze l*05vo:nbs-pbf 0jcal directions?    $^{\circ} $

  Two billiard balls of equal mass movpy0*3pi1wco he 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, assumepo0cpwy1 hi3*d 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 pemng 53)ls:qh j, nelf;rfectly elastic collision with another atom at rest. After the impact, the neonmn;,hlq :3g )5efs ljn 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 perfect0a 2jq3pb(c+tnxn 0p8uz7du ely elastic collision with another atom at rest. After the impact, the neon ato j xz+nn8p70aeqbpc3d t (uu02m 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 th9lj95wxvnau2 c 8axx 5ree-mass system shown in Fig. 7–38. Specify relative to the left-9na 9xaj8cx5v 5l2 wxuhand 1.00-kg mass.    m

  The distance between a carqpo k/ic5: -ps6-lohp(xd+1 rhft)r e bon 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- :ppbeleh e0+.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 in the front seat 2.80 m from the front of the car, and three people p0.:l eh+ebep 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 as a ferryboat. Ifgx iibgot( qz4 9*-,c33kbma;v ep6 ps three cars, each otbsce,za x; kqg93p i -biv*4m(63gpof 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 sidesly f q(:sa9 s(8 sp1w ucv0m;tgi7de+y $l_0$,$2l_0$, 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 ha*kdk ih-pxz )fz 3vkt 9(yd:/bs a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube ofzp 9x ( :dk3ktkvhi f)z*b/dy- 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 plate of radius 2R has a circular hole omv,pfe h0cczu6:)d:198v w-pc tgq uif radius R cut out of it. The center of the smaller circle is a dist:ch1e0 ) cu c6vi t,9g-wpdpvqfu8z:mance 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, and canr9s y)w8sc8b lculate the mass of one of your legs. c8 wsn )8y9rbs   kg

  Determine the CM of an outstretched arm using Tablr zz1pi4n;j ,x:u-)m9z mqlsye 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 l( r*2aj.8mpwd bn:g barm bent at a right angle. Assume that the person is 15p.dragm jwl82:bbn(*5 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position /ma2tv d6 o/ b;kl4mcd zjqh(;such that his arms and legs are hanging vertically, and his trunk and h42lkq(;ca mb ohdd6//vz;mtjead are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon pfh gls1fes:/cs:f il- 05b1xare $5.98\times10^{24}$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 fric 4 +pc48pjp oyygw6q:btionless 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 kgam,5u:jzw,drtex)6 k and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and lengt 65zwkm ,r ut:e)a,jdxh 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?    cm

  A mallet consists of a uniform cylindrixd /yb* s+8sksrc -n(ical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrknry s/-cs(+bids8x *ical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Examplesy zr17.*dz5u+gyjus n g/0b d 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 mht5u-/oha:q 0n g w7bvass M, are in the 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 balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stot7nq:w5b/ ug ah0-v hops?

  An 0.145-kg baseball pidf3ljgdpl ; /l4( gdm2tched horizontally at strikes a bat and is popped straight up to a height of 55.6 m.3/2l(p jmd gfd;ld4l g If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speed wgny6rr hd91* $v_0$ 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 faced5mj on;va*y/)8lm g xx with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about/y; xgm x*oj)mv8n5la this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.ns9i9n /j jne3*jw7d d5m/s by pushing off with dnjn*di799j/s3 jewnhis legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, arevjap *:up3s, l3srwh( initially at rest in outer space. They then push each psj 3s(:p* ,vwlrau3h other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on ela ngeibn r); -0+drcb5xstic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its originanxr0dg b)i +cb ;5r-nel 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 courx) h53oyr/z:efpn g 9ct case involving an automobile accident. The accident involved car A of mass 1900 kg/n5z: rxycp3e9 )hfgo 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 of a flight of cerc,;u( 0 bj vqorja9(oncrete 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 step 1.0 m lower. If all collisions are perfectlya,;((jr juvce0q rbo9 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-kgwt-ngf 2rdqcre 2 )1k 38at;gfw(4 fuu block of wood at rest directly above it. If the bullet has u t2g31n uer8 (qk)d;4rf wgf ct2faw-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 an5y ,xh;bl+ts;o8 m dzhd becomes embedded 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 between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m hlsh8 5t, bomd;xyz ;+before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowboat midqq acap3-kj87h+ -of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at oppo-8 7 qipc+ kmqdhaaj3-site 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 ab qf:qyg, .s(oh ;jvq 1k-yj+was 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 suddenly broken apart into two fragments ;v-n: masm2bli x- *cd/rt4we by an explosion. One fragment d*cmnt lm; -asr- 2/e: b4vixwacquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula Ff ym7d a icp2ax,j8q)/j1irc- = 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 wuen6o x+e60mmq g5x :$m_A$ = 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 de3 m)b7pp d0d0ry q1kuxevgq0 *cays radioactively into an alpha particle and a smalpxp31gvmkqdb0y0u 0) 7 r q*edler nucleus. What will be 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 (clay target) isswzd 5g6m zuo.z6a*j7 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 s wm s 3sr:9 qg2)m.;0pcroskaclides 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 limit on mass mey)/ xzpgez )) if it is to rebound from M, slide up the inclizepyg) e)x /)zne, 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 Satua6q o l(yi5wm4mubi*.rn moving in t6*5qyi omwb lmi a.(4uhe negative x direction at its orbital speed (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