We claim that momentum is conserved, yet most+-xhu m; g/-hptfq0 ab moving objects eventually slow downtq;mh 0 -+a/u-b pxgfh and stop. Explain.

When a person jumps from a tree to the ground, whatek pch3 qxfxnoq7*1b+- p1d( a happens to the momentum of the person u3q pda*xx bkc-h q1 o7ne+p1(fpon striking the ground?

When you release an inflated but untied balloon, why dge uhzag 0n)xbd:62 ;joes it fly across the room?xg 0eh)ug6dn a:bj2z;

It is said that in ancient times a rich man with a bagaef k9l +,tdd-k mhy,mm8 7wz8 of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. Wh+ h8ka7k8mdf9yd ,lw,-ez mm tat could he have done to save himself had he not been so miserly?

How can a rocket change di j2smq h uxyj2:o0ey54rection when it is far out in space and is essentially in a vacuu sjq e2u25 hmo0x:y4yjm?

According to Eq. 7–5, the longer the impac romrh:5 iy1g)v ic2g q6k6l8dt time of an impulse, the smaller the fordhm o r6 qgl61kr)5:cvig8yi2ce 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 automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possib*mmerfb23 ; kqle to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. Wrfq * e;3mkm2bhat is the advantage of this new design?

Why can a batter hit a pitched baseball further than a bj 9xbt-0dwx; ydelqx90h67 mn( x; vuball tossed in the air by the9(e07 dbnxt wuvy;mxdj9;lh- bxx0 6q batter?

Is it possible for an object ftwd)(eqraupv i 9a*t/ q* s6;to receive a larger impulse from a small force than from a large force? Explain.(*itp/qs6fd;vuq)*e w r9 t aa

A light object and a heavy object have the same kine6 ul bm0py8vv6tic energy. Which has the greater momyl6m 8v60bp uventum? Explain.

Describe a collision in which all k gcxf.03pat7dinetic energy is lost.

At a hydroelectric power plant, wasn)w0wmrm2i 4 ter is directed at high speed against turbine blades on an axle that turns an electric generator.0s )r2 wm4wimn 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 walp:rgv45wpd+q hk m(* cq jyu5*l at a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixed ur a2 mlmbvwll.4.z,/x3 9fp snpo0 e3to 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 momentu m9xp33/rmu0es ,lo llbw.a2 v.z4 npfm conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward wh7zrbc j.7(g iqen carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe atad3g lzr/o4v:9e/o gm +/bhbr its mid-point, whereas this is not true for your arm or leg?lg /ba/:o3r dozmgvr+b/ 49 eh

Show on a diagram ho ywumthbdp uw29s/*w,/8:rurw your CM shifts when you change from a lying position to a sitting p8u, tm*/dwhsw:yb 9/pru2ur wosition.

If only an external force can change the momentum o6 o xlfi g2qpieu(l+.lf.7 v4ff the center of mass of an object, how can t.qixf fvlgo u. ip+2fel476l( he internal force of an engine accelerate a car?

A rocket following a parabolic path through the air sudw;+) uz tkyb-lmqx 3h*denly explodes into many pieces. What can you;)y*kxm-l+3h btzq wu say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow f0a:omkx2.hxh zsuh 702.-ws-ae il xw lying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What is the hozlz:;e 3,f ffi53y2bwsvc * skier’s change in z3e f z2 fh;v 5lscwb3o:i*f,yvelocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hitse b kx8(*s:s9 pst-hl on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time betweest*(s kxl b:-e 98hspsn 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 horizontally with a speed of 1r dqt(53xmhg rv2c 9y20 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of thr(v5m 92h3ycqgxt rd 2e child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases are e:qw/asdhc 0f/xpec0 aqw/hf /sd:lled 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 izg,4 ( 0e:ixzhha9er7 mmv)g at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone ond ac1o44te bo3 alevel frictionless track with a constant speed of 13oet41o4b c ad8m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling fgu e-g 3)s/*nugs(y - in fo5+usm3qiat $15 \; m/s$ 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 100kua q ;k:j)l1vlm/h If the air strikes a person at the rate of 40kg/s per squa1 lu;:klqvaj)re meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant vz*-liyn2fqiw 2 /v /lspeed 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 fnii2/yq / lv l*z2-vfwriction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus in yfb7vnus /3 //sv*ax h1zg4dvitially moving at 420m/s emits an alpha particle in the direction of its velocity, and1*hz s/f b3s yu/n4g/vv7xda v 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 wood and emerges cle8c 8dxz, js*yaanly at 170m/s If the block is stationary on a frictionless surfsdzc8 yj8* a,xace when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is t04y)tvr ubtl 9raveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling w f8kzr:1mq35 ji;ltiin outer space with a velocity of 115m/siqiz jt:5k183mf ;rl w To alter 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 tee0k4 q2o2cee wc at a speed of 45m/s The golf club was in contact with the ball fork22wqc4oee0 c $3.5\times10^{-3}$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 ofm eorz:4rexnce,ttz(9(da8 0 8.5m/s and comes to rest in a time intervc9e (tdor at zz 408ner:x(e,mal 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=0.06kgz/8(xq qu 2u,sh)fxd yc;.baj and 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 80uec*h2 jvvgh4 i(te3di7s rof the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) 0 4ushvc2ejv 7dh(teig*3ri 8 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 c ;la9 bfh9as3us::fo(1q aa(f tq9 -rkovs+w stopped in 0.75 s by a head-on tackle by a tackler r b:a-s atf 93ofr1c(o9kv9sfah( :;aqqs lw+uunning 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 ()l267m)h)jq+yvmydbf l e k7umass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical mey)j6f7+)lydvbq k) emhmul72 thods 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 7 rb)k5;k(gu,h rg/qzk5-kg person jump without breaking 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 fall). Assume the breaking strength (forghg(5z/)rq,bk;kk ur ce 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) fvnn -r*kaq s4hh(,:y e:7biv with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, whats *7 nhah4bnk -i (v,vf:y:qer 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 headvd5j u,n2da/pve r0-s8 umf 3z-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 0e,/d- 8ju a 2nfz0psduv5mr v3.450-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 hea i/uma k11 v-8jxvvx..of/nv zd-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.fovj1. avz/vi/u18nv xxmk - A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s colln -5fosn e((lg k63nagides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a(6k n(onefng l g5-s3a 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/s collid3im;zlak *tq +ckp:3res head-on and elp q3z*tmk :i+lk c;r3aastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement par ;+ 80vg2g* brwoayc6fxkbr3nk 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 car A approaches at 4.5m/s and car B is moving at xwb+bnrco 0*;k6g8v 23ryfga3.7m/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 cold36t*z mlv;qk lision with a second ball initially at rest. The seckzqtd v;*6m3lond ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides ds7cfhs; 2b/ 7am6 +ecv:kmheb own a frictionless incline as shown in Fig. 7–35, and elasticam +hmhskfsb77b/2 ca:ec6 e;vlly 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 object of man0vvl,ji9u 87k dum ,d.mnom.ss 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 sxf7 n(xm v9qnog3q)1 maximum height h of the pendulum equal to 2.6 cm nqxo(nsqv1)m9x7g3 f. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-k f:8srtc.d-+wai( 65kcwj gpg g pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and hori gw8w :jtfac.cs (p5g-6ki dr+zontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic ener 5nsayher+73;0kqwuuro ;0to gy 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, intozo*ys:1j7mv 9 so+2s ehs ,b7vn3dmbx two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released inz7 yenj2sdv* mbhob1v 7 ss+: m,3sxo9 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 y4)po 1w(iqntd ip o/3x/7dnys ebs//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 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 represoyswipx7d)4si/ny nb / 3 e /(1op/dtqent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height o m5c 6q4m)sxyof 1.20 m. Approximately how many rebounds will the ball make before l)65xcsym 4oq mosing 90% of its energy?   

A measure of inelasticity in a head-on cool4fc y4d .1agllision of two objects is the coefficient of4falo1. cdg4y restitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one withe c*oo wbayy2w4slpt8)0.r o0 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 loco2wyt )r0 y0 pw8oas.l*4ebit. 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 directit0zdvgq03 oi (on at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velov(qt0 g dio0z3city 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 , q9:fxfx/dh7if-etdztzi e 6w256qj nucleus, an electron, and a neutrino. The electrj dxfwf-qtzf6/et5exih:i67,z 2q9d on 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 mass6(c-fikg u k8/tdwkr vpot,/: * qetd( $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of e 6ljv9dkego 1*qual mass, each having initial speed the two move off together with spelkj9*o e 6d1vged v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass4vgc(1petje4af5f g - 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 and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? de- f4ej15tpvg4c(agf irection of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with another atom at t u- 2gz v4j)7p9/j9 jff3)pefwxhajfrest. After the impact, the neon atom travelxu)f jjz)e7a -pf/fh4 jv99 gj2pft3 ws 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 elasticr;wu(z 8 d eb(+qozpa7 collision with another atom at rest. After the impact, the neon atom travels away at a 55zwea8u( ;qrd z+obp( 7.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. q : r;m r0juvis5y-o,tSpecify relative to the left rmqt;ur5v:s io0-, jy-hand 1.00-kg mass.    m

  The distance between a carb d;a(sqn 9ur8xon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the frk5pw bumh ++b4ont 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 sit in the back seat 3.90 m from the front? Assume that each persomk ++b4wup5hbn has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 16fobny eh5h66800 kg, is used as a ferryboat. If three ca6efy bo n15h6hrs, 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 sides0f/w z l uyb0tyi8h88jdk34sh $l_0$,$2l_0$, 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 s:ul fe/aj qx;74mwt:+ma2zh 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 th::47zmxmj/l st+u2q feah ;a we load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of ra36ilobhn x5mpuy:5 (w dius R cut out of it. The center o ( mph5nl5xu6wbi:o y3f the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportio5 n*j7 faj*gztns are the same as those in Table 7–1, and calculate the mass of one of youraj7* gf 5jt*nz legs.    kg

  Determine the CM of an oug -o jwua3a(b1h18 k23ghgwlytstretched 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 bent at lc c4;)u(mt kbv, ,grua right angle. Assume tctvg) k4ucum,l(,r;b hat the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs l 0ohsp+yy f0tp5e)*g are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Wiley0fgs t+h0y o5p*p)l l this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moodhg/*r: idoo +n 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 frictionle vuj-) r:(d phln4t(fl5 kfch2ss 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/jmjizv +fmox 6sr+9;i:.+ z i(-dbjc sdyh* k uniform 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. 7–42. If this mallet is tossed, y6hd9/i:z;rkj+ j.v xci- obs j*(zsi+mm+ dfspinning, 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 x6qcc)d (yh7gmass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that x)c7hgy6 d(qc will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7l (/znm f,kk3u–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,nib;z0iuyblug : *+b 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 (relati izbl*+:yu b0 ,nbgu;ive to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horij6ni83 gv fvs6u )vy/lzontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force os6flgvj 6 83y)vv inu/n the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with spefwf)y 4pn3 nrk b3q7n4ed $v_0$ 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. 7n 3bcd 9dc fgi8fp,)-t–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 d8fp3c g)9bdt ci,n-f pocket? Give details.

  A 140-kg astronaut (including space sui ;o4 m/bgmtts7t) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-kg spags;t /ob4t mm7ce 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, are initially at restoelko 9o . w4m+9t)j b7gzno+i in outer space. They then push each other apart. How far apart are they when the lighter astronaut ha79 nm).z+ol ewb4o kj o+ot9igs moved 12 m?    m

  A ball of mass m makes a head-on elastic collision wit:,jr0y ;(j4yhvz gu x2wp( zrzh a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-f, vz4yhyxr(u0wzjj;2( zg: rpourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert z*tpe( f1+t wm1sds0 twitness 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 befor*(pz m+swde1tt f0t1se 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 of total verticaltca+w f0i 7 1kp)5qqss 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 tsqi q +wp f0kc1s7)5aelastic, 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 blocuau0,9 gs. ,3sezscmmk of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the b,sscz.euma30g, u9m sullet becomes embedded in it?    m

  A 25-g bullet strikes and becom9z+fbn+mpt pl i5 n75ces 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 z+ fn5 ct7p bp5mlin+9surface 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 l9fqlngu7r43d c7 s762xttgf 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 the26gufxql7st9 n7drt g34l7 fc 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 abouta0.jc l /ali5p $ 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 suddenlyvj csirj ,1ozu 5pz4l +58q*lk broken apart into two fragments by an explosion. One f54 p+1q,z rkulc 5sjzvji*l8o ragment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the forf t.fs gwh4o9xhk68i* mula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses r4 n1an5gw, 0f ttenx6$m_A$ = 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 radio2hgs:.iryd 3wxvi ).y actively into an alpha particle and a smaller nucleus. What will be dy.hiwi r :)sv2g.y3x 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 eqp 8t,f2wo 3atarget) 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 v s0*2fywgr 5lh iw//x1c+hhmslides 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 uppp05+0toun r tew* c:e7*i,pa .dfizkper limit on mass m if it is to rebound from M, slide up the incl t*npe+zdpceii50,7f* tu: p wrka0o.ine, 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 sh ))(zn.* bu .oomse3foczz v7fows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s Thezs3n.zov c) b(m*uo ffzo.7e) 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