We claim that momentum is conserved, yet most moving obje n-guhhki;5 uy8ieu4 /cts eventually slow down and stop. Explaink-uginh hey u58/;i4u.

When a person jumps from a tree to the ground, what happens to the momentum ofvxu - c3 v,a5sf 6g:)bll8iemn the pernai c5l)3vmeu s6,x: l8g-fvbson upon striking the ground?

When you release an inflated but sfvz qb:9/kk hh 2t: b(gd*.ayuntied balloon, why does it fly across the room?(9qys2h dbt vk.zaf/b:k :g h*

It is said that in ancient times a rich man with a bag of gold coins froze y(qj,f k/ez (ilui6:i to death while stranded on a frozen lake. Because the ice was frictionless, he could not pu:feu ,/((zl 6 iiykjqish himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in s 1p8if8b2:smia: 6mzod jf7 (ee*b ezspace and is essentially ja6m ide 8bbm *zi(s:ee:o f78fs21pz in a vacuum?

According to Eq. 7–5, the longer th 5)id4ci m*rfue 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 automobile colli 4*drmc5iui)f sion and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Today, thougp+sgzwsh/: bl:/4m9ulubpo4fw 9 tu 8 h, cars are designed to have “crumple zones” that collapse upon impa :s9p+gwm u4o/p948u buhstlbw/lfz:ct. What is the advantage of this new design?

Why can a batter hit a pitched baseball furejc6(hcc sdb,aa):+a ther than a ball tossed in the air by the batter?cd,c s)j+a a:(bc he6a

Is it possible for an object to rec-et8x (b cgk4deive a larger impulse from a small force than from a large f8eb-xkc d4( tgorce? Explain.

A light object and a heavy object have the same kinetic energy. Which has the mv ts5/r/3):+sz7 1+ikshyjf5yym acn q:y c wgreater momentum? Exp y:sv+mt ifsy+z yy5rw ):ch7js1/k naq35m/clain.

Describe a collisioncplb g*+b jw-sbq /+rw,k, s*ecew1x6 in which all kinetic energy is lost.

At a hydroelectric power plant, water is 3 prn/g( p) -abx-dsdhdirected 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 )3sng--brppd(xd /h athe water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a ,wa:.zutcnp1 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 he i 0of)kxj(*6o*fhxa height h onto a 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 that *o)h 0h(ijefkfx*xo6 falls and sticks to the steel plate.

Why do you tend to lean bay* 0gnx8p0 q:jks-nps ckward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point,rt) yf5g , hdwo)/u*uj whereas this is not true h *ujtd,5) wor)g/ uyffor your arm or leg?

Show on a diagram how ee p cm*43a8h4z g*awtyour CM shifts when you change from a lying position to a sitting mwz3t8*eea*4g p h 4acposition.

If only an external force can change the momentum of the center of ma r 1/,zvktn,iwt2*x clss of an object, how can the internal force of an 1*tlr,kt, vnzi2/c w xengine accelerate a car?

A rocket following a parabolic path through the air suddenl(y f)(gqv kit,y explodes into many pieces. What can yi kyfqt,(()gv ou say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed )) u4glmk*q-;nebt fb 3*vk/kuoq hv0of 8.4 m/0kbn /b3tv)h- **vkul gfu4eo; qq)mks    $kg\;m/s$

  A constant friction force of 25 N acts on ; wl((gzg20 rmuhxt0z a 65-kg skier for 20 s. What is the skirz2(ggw0;tx u(0l hm zer’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is wee oo6 5za+x4p r/mjb*6si x2hit on a horizontal line drive straight back toward o 62/sx*ezae4 rm+powi6b5jxthe 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 horizontallfw1ri wu)wdk w2l2 w+0y 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 boat is 45.0 kg. Igw r)l ww+u2dw2w if0k1nore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given tnoppouf): )0uhat the propelling gases are expelled ouu op))pf0:n at a rate 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 breakr:injq.kjx k(l/xlg f5qz0: y3 4tbt(away for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same dir5yi4bxr.jkqf/xlk zlq3( : (gjtn:0tection, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictionlewnkx70-)d ;tvge c,k css track with a constant speed of 18m/s A 5350-kg load,v c-) ;7dgxtkc,n 0kewinitially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a sec-a oemgooo*h68vmtw *c ypln+3 9 8pw7ond boxcar at rest. The two stick togeo 8w*o793ma p pe6w8hogv+*-cnmlo ytther and move off with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontn*i sfi2 sbt/3ally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, 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 typicibsist3 */n2fal 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 railrwu-vky) uex 8uf47h.s 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, what is the s-uk7 yfheu4x8s wu. v)peed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particl/q9j8 e+sn tlke in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alphsln qe+8kj/ 9ta particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block ofnw. 0v w21tuicivm,k0 wood and emerges clea vcvi0unw1t2w.0kmi , nly at 170m/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 speed ob1 pu6 6(sb+suwb nxc8f $5.80\times10^3\mathrm{~m/s}$ 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 travel: vwbz ;app4vg-. qe9ftz(l(ping in outer space with a velocity of 115m wplv-g4(t:z;9(aeqp.f bzv p/s 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 tee at a speed of ku(zzi 4l po1jl:/gs.45m/s The golf club was in c z/jl 1l:iz(o.gsp4ku ontact 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 8.5mo7k08mk edbke/(h2skvd 6vh )/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to th2s dhe)keh8kko vkv(d6 /7b 0me 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 vyy0. z0 -cf:dhmvpu-enr m;ap +6cg*vpl8)bw =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 vimf528/ dx p3bm b:qu- dscl/of 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.f bq/5b2imsvc m:l-d puxd/3815 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 ebyxo cg3,.z, u :(dznlast and is stopped in 0.75 s by a head-on tackle by a tacklezcl,yb.dx : o,(u3 nzgr running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (magppw0eb, h.m 0ss 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 me wp0bpm g.0,ehthods 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 breaking the lower ( 0 g5r v0zk)(ucyrfbuv7zux5leg 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 bv0(zfb5xku)z 7rvuyr ( 0c5ugreaking 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 rwh9 k-,nfj-a thq,,i(+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If t,khqfnra 9 ,w- ,ith-jhe collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-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 collisi )5y ql yr3bmvg ntp/:*zh7vd+q7:nufon with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of eac:d:* +uyn7 )5 /qn3qvtv7ry mlgfbhz ph object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastic head-on collik5ny(kmo, mr.c7r ab(sion. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speed,k 7. b(ymm5n or(ackrs 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 speeds o .8f:elr8pgu5uj g9 of 2.5m/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 after the collision?(Let A represent the 0.060-kg t u .:pu58olg89jsr gefennis 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 rc.2;qe yjel 6moving with a speed of 8.5m/s collides head-on and elast;cl2r.qjy e6eically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastica7n4/mj jexjf .lly as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B i7j j.njemf/x4 s 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 gqb a2mryaans/x(; qcl -70c: a second ball initially at rest. The second ball moves off with hycm 2sag-0:q xrl(; 7qa/abncalf the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as shown in Fig. /i9gx +qd;3: keerl g9gv4deg 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 gv4:eg;rl ke9 93g x/eqdi+dgoff 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 object6vwssu5 wt:1/w (i dnh 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, proje ;02 bg9n iu le :4jc(mwuiuz8q*upd:ictile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice a:g u jcqp9izl:uu8nbi i e(u4dm2 ;0w*s 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 burie4fo7eeslf *( cs itself in a 3.6-kg pendulum hanging on a 2.8-m eef(o*sf7lc4 -long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic *jks ,1migq8br/hr3cenergy 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, intoulfgx4df1*2g*ayh ( uo24-kql3w gci two pieces, one of which has 1.5 times the masaqkgwf**1i2324(h-uy4l c xdolgu fgs 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 into the rear end of a 2300-kg SUV stopped at h)65ur1/9n1wb 5 izhxwhcls h 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 fr59uz 6hh crws xwb1li5 nh)h1/iction 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 represent the SUV) $\approx$    m/s

  A ball is dropped from a height ofj0(v:5h- bwaj1j ;kkxh.msl z 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball makm b5shjx1;a klw v- hj(kjz:.0e before losing 90% of its energy?   

A measure of inelasticity in a heas.de fcdew/u:19n o w*/(jzm i8m(myld-on collision of two objects is the coefficient of restitution, e, definemei.je8 zlc(myw *n:(f sdwo /91/dmud 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 pp:l yv2hdn a yb:/w5p :i2rkc6ieces, 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 it with the blocp:l ya:bnhd22 vypi65wr:kc/k reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-o9a+ep 04t* 1 nepwycvun with a 10.0-kgaetw v4u9e pn1cy0*+p 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 d ib2wwp-8 hjfhq07 s)recays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right wb80if w)s-7r pjh2qh 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 mass1zsrwm:tlogc ;)w els hkx2op2 -/:f9 $m_\mathrm{A}=0.400$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 5u9 8+ l-nwtuccu7c/.oxp whm collision 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 wcpu h/u9umo+x. l857t -ccwninitial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the origin ohhnezd )a,tw q5-l,m :f an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving a ,,w:mhqt ehd5)-nzlto the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elasticl1dus 2h0 j,o: cmgj3b collision with another atom at rest. After the impact, thjjlm10 g:s3ouhb 2c,de neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision with another j:on+f /q6jlg atom at rest. Afj olf+q gn6/:jter the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. Spct euj*vp71y9 ecify relative to the left-hand 1.00- ycu 17t9vp*jekg mass.    m

  The distance between a cavvyw+ rlr/, q7rbon 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 front ofy,jst 4ns(jtfet3:m8 d pe (ym0q54pd 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 tqm:,jtsdp8y4t m4 dps0jee( 3(5 yfnthe 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 6800ldgqm4h;y(h8 (8)zi1kmm lsy kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, d(sd; z 1lghl)q hk848(iy mymmetermine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides8tfu vgp,f7t, $l_0$,$2l_0$, 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 i70p nc5avs x0cdentical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizon5sxc cp av700ntal 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 of radiu1insen )6ex r*s R cut out of it. The center of the smaller circle is a d 6)nien1xe*rs istance 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 propoxstf(o -1itc4i, d z3:q+ i;pb8fzskg7dhb7 wrtions are the same as those in Table 7–1, and calculate the mass of one of your legs. 4w f1tfxs;gh db+7 qb-p cki3ioz(7 s :8,ditz   kg

  Determine the CM of an o o95z i3 6/b 1ycwehb:*a2sc3tm fb *7nmspopputstretched 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 * ,n-hgmv/v pll/ tc;san arm bent at a right angle. Assume that the person is 155 cm tvlgs/l, -pchv* ;n t/mall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that p e0 umk7v5m;uhis arms and legs are hanging vertically, and his uvmpm57 e ;0kutrunk and head 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 Earthkl t9zcp,3ydy;8.fnv f -;xyh and 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 cxt0 : xo7uy sqe7 rz18:j y;21hbbwzqman stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diam bt0xc g(p a/jdmti(2z/xv2d(eter 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 tdp(22gazi/ x(( dbt vcjxm/0far 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 andjm tz/911kb yb a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and l1/1k9mb y tbjzength 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 Example 7–14 (Fig. 7–29),*jro4fi4n dmp1w- a+ p $m_{II}$=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, arerrml,l19 + u9 dhho*h 9jg1pua in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slidelhha1ur jg+1*9 lp9,h 9m rduos 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 pitchv;b.ntiaarg.sv8y34d;,olrkb i *0(1tsq l y ed horizontally 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 on the ball during the contacti* .rk,y3 .yvo;01 tntda8v4lr(; qgb libssa.    $^{\circ} $

  A rocket of mass m traveling with speg -z1y 6+w)sbw 0dnembed $v_0$ 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 cornee--2bo dku k-pjh5p6 ir pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which 2 --keiboh6pp5-kudjthe cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) n-j7a;9 l7z rfbvon3 2*ntrzbacquires a speed of 2.5m/s by pushing off with his legs from an 1800-kg space capsulerzaz9f;tr2n*vbol nj b377n -.
(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)hlv zfv6 .s3x and the other 80 kg, are initially at rest in outer space. They then push each other apart. Hoz h6lvxfv .)s3w far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-yvs)6zyg58*1b n: fmj y5nrijon elastic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass ofg58n n b *mzy:5sivy6)yj1r jf the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving anbko me3947azb automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of b79zba o34kme 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 concrete ffhpt u:7r6.;jsmv j;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 arths;:7f vjrpu .6; fjme perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest dirx0/n/guau hrrrjj q :. 7r;*hjectly 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 bullehuj r:/jru0r gxq; n.h *a7j/rt becomes embedded in it?    m

  A 25-g bullet strikes and becoe8d o7+7 (g1sp5 q* rxyd6gmfuhfqf:a mes 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 before it comes td7amhgprs5:1+q *q ef 78y fd(oufx 6go rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the o;bnzjx( r8 l9lther of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initialnj xrl l8bz9;(ly 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 the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abotf:(ea v6o a(out $ 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 fragme(y sdk n;xb*7z7sydt *nts by an explosion. One fragment acquires twice the kinetic energy of the other. What is the rz;sy* sx7bd(d 7tykn *atio of their masses?   

  The force on a bullet isjk5,(m)tkdr; p(aeez given by the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses 2/,t t5l;jplm4yxmo r46jjnpy k dh 59$m_A$ = 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 and a smc gyn7d2u 5+ mudmbqjw/if5oh- -2:epaller nucleus. What will be the wm-ynefhp/bi2u5gc j2dq+ o: m- d75u 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) is fired at hwj0l x6.)ads 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 sllp:ibshi 5.7l7*n rt t.ootd*.l8dpe ides 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 mas3pscu+w0ce, 6kmf fno e46 i4es m if it is to rebound from M, slide up the incline, stop, slide down the incline, and coes6e463o ckiw+f4p0n em,ufcllide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows ta;d wgi d:2jwc., d(omi7 .kxzhe planet Saturn moving in the doi,m 7a 2j.ddzg;(kc .:xwiwnegative 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