We claim that momentum is conserved, yet most moving obje/q n(pzl13ul)) okia ects eventually slow down and iqan)( uk/le p31)olzstop. Explain.

When a person jumps from a tree to the ground, what happens t/n r.6amk4d wdo the momentum of the person uponrd/n4wad .mk6 striking the ground?

When you release an inflated but untied balloon, why does it flyi y7+ra2wc(/ v vil2/ xcfh.pvy /j-t9dsr, gc across the roomfxwicjsvtc( p/ y+.divr v -,cg2lr7 ah2y/9/?

It is said that in ancient times a rice62 9rj*oca01 ssi *xg6sb yafh man with a 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 6jsr*eg*6ss o 0b 1 2fiaxy9cadone to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space anoo5itq w vp5 szg79f03d is essentially izv3oqf07ti5p9 g5owsn a vacuum?

According to Eq. 7–5, the longer the impact time of an impwp*t uzgdp-+ 7ulse, the smaller the force can be for the same mt-gudwpp*7+ zomentum 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 possible to wyjz x9a f08 +j/mk2 zfxchb7+nithstand collisions. Today, though, cars are designed to have “crumple zones”jb + cf 0jm7y f8anxxz92/k+hz that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in the air byci 5-w0ze cx/azwc/-50 xiea c the batter?

Is it possible for an object to receivkgpo.z7/vg+ueae/h 2 e a larger impulse from a small force than from a z//+ aog2p v.khugee7 large force? Explain.

A light object and a heavy object have the same kinzykl9q-s83n*(my x:n/ifrw8 6vx rve etic energy. Which has the greater momentum? xnv8fne/38rz vyrq:y96mxi-lw *s (kExplain.

Describe a collision in which all kinetic energy is losf3q woehn k63-t.

At a hydroelectric power plant, water is dz*mqzjwjw.b oa6 pf44i). nw+irected 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 th w i fj*mo.a)q4+4.zwnbp6jz wat the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at w09+e.c.x i jbe4kom na 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 pla smnm :jy2-u,ite (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conservn:ju m2y,im s-ed during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward xsqgzx7 7by99l0j i,g when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is eo-r60dnrq5f + rbdaj*k. kj, not true for your arm or l.k a +q-dbj0dr,r *f56je onkreg?

Show on a diagram how your CMw9wob ; ),y l/w(jyq0z/l33c qygj pmk shifts when you change from a lying position to a sitt3kb/j/)wogp wj y,z;mly yw(9cq0q l3ing position.

If only an external force can change the momentum of the centerjx t t,vc2 u-mwt .acp*xxa2 +76j1jcd of mass of an object, how can the internal force of an ptja utx7x+t v1.2cwmj6 -*c2dcax, j engine accelerate a car?

A rocket following a parabolic path thra;o-k6b h53 dnm2iy8w 8p,l:i llsa ayough the air suddenly explodes into many pieces. Whaaynp w3d- l :,m;ihi o8bsay8akl 2l56t can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with fgp yue4k:4 c)aj 93zg(wo+ xca 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. Wbm6s y3 e/t9fshat is the skier’s chaty6es/m9 b f3snge in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/stkt6db u9 e .rvd ipth9f9-a7) is hit on a horizontal line drive straight back toward.i )t pth9 du7ad9eb t9vr-k6f the pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a speed of 1:;ov+o5uzsix b51 j bz0 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass x +zbvu 55z;:o1 bjisoof the 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 dam; 9kj54y uww4rsp ,on a rocket, given that the propelling gases are expelled at a a rp wk;u5d4wm,y9s4jrate 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 mov6oyh1ni7k*8+wfuel6 eb/tx m /c2g u bing 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 on alevelbe m*a/5iabd +6 x:wia frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto:di /ie*bx b5a+a 6wam the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling rw ;pa5g3) cv4/fdtk n d/:+4wa svmjuat $15 \; m/s$ 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 100km/hi 0ilsn3 k*co 8+p;3vmeqj -xn If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, es 8sqmi nol;33iecn +x- 0*vpjktimate 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 oflxbtrf yk0 9mx:;eg -3 5tuph( 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 sp(xhxtf5 :mb39- t0el rgykp; ueed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in th8og-s;qi xg17jme; p he direction of its velocity, and the remaining nucleus slows to 350m/s If the alphax7hq;p 1i ;osg8ejg-m 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-pui)o,f* 7 6:n d3lhqg gdsbh8kg block of wood and emerges cleanly at 170m/s If the block is stationary on a,3)dl7 d*bpohusng:f i qh6 8g 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 namz3tw 9k; i lr:b*dvho40 4zof $5.80\times10^3\mathrm{~m/s}$ 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 / b+,, q6zy a5-gc( iqrsbycgm3180 kg is traveling in outer space with a velocity of 115m/s To altb+/,rz,s y 6(c -y qbiagc5mqger 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 45m/s The go+h+.hkihp0pr 0jtkqbo9v /, olf club was in contact with the ball for vjp0+o /i+ h9rqphkhkb,0 .ot $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes to rest in ajpd4u6o+hz . s4w3eyg 8 xpb(z time interval of 8.0 ms. (a) What is the impulse given to +yx4u36hsj8b zg 4dezpo pw.(the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes a wall at z zs7*s7t 9(:vgh4lmhfo (ykk 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 n./3 l:8wd:tkkglq esf 1bro8bew 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. kf3brks:: l8/ew1.td bl g8qo(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 0.75 s by a k0rdcgdr; p 2e9 ui.vlt4 c.-nhead-on tack- .tdr .geucn; lkrp4di09 2cvle 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 aj 90dmq --nw,s.rsodd tennis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–-.0r-wjn9odms ,d sq d33 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 pnowdbq 5u6)s/v0 adb:erson 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 (foub)0oa6dsqw 5/ b :ndvrce 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 speed of collidy dd0pm7.. slres 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 after the collision?Let A represent the 0.440-kg ball, and B represent0sy d..7m plrd 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 /c92yfw/rt ih 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 0.450-kg puck, //9whfyi2rt c 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 perfu6;f iew/0 cd 3a3rerdectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball ;fwcaeer d336/ ui0drmoving 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 collides head-on 9,n;uz22t oj ts5kqytwith a 0.090-kg ball initially moving away from it at a speed of 1.15m/sqkut ;s, 29zynto2tj5 Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s collides hkz2lkhy4 8n/ ;zi:h pq4q9 cpwead-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backwardkn8/4;w ppz2qi9hkhq 4zc: yl 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 aiosncq9 171 ihmusement 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 cno97qii1 1c shar B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a6xayfwxt 4fa 3m351yq second ball initially at rest. The second ball moves off witx4 q ywmaxy3f6a3ft51h 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 frictionlekibp9 a)3 sbt+ss 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 floor, where does each cube land? [Hint: Both l+ k s93tibpa)beave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case fn)h .(1mudmx.be* b3n hat y/of an 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 intvf2 qg,d- reh-ec -gz9s:co9 a maximum height h of the pendulum equal tohdqc,gz-ee-r929 o- v f:cg ts 2.6 cm. 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 l s1deyi.xq+ af0xi f(-/ug)v3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components gx -xfe u.)fsya+q(1i0 il/vd of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kineti7 6s:*vg6 zprzzvtms-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, into two pieces, /qpu k9-65wqde kxhi/one of which hpd/ kiu/wh5ex-qk q69as 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car coa3l3r7dv bp:r llides 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 thar lr3v bd:73pe sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height of 1.20 m. r s6h83ley7 c1f-k 1;bkj rbzzApproximately how many rebounds will the ball make before losing 90% of itl k;71kj6zrf 8-rchsy3 bze1 bs energy?   

A measure of inelasticity in a head-on collision of twsp+ n7 m:h-b:kirnkg, o objects is the coefficient of restitution, e, defi- mb:is ,gpnn 7+r:hkkned 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 with three times ydx0i5us* qfq hol :44the mass of the other. A depression is made in both faces of the cut, so that a firecracker can beso 40qf5ihl*4d xyqu: placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides hea-l +tiz lt g(7,x)ntwod-on with a 10.0-kg object moving in t nlg(wt)-i o t,tz7xl+he -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 3 ,ua qsv,bu0q 3xr:jjdecays into a second nucleus, an electron, and a neutrino. The el,,a 0 q :sjj3uxuq3vbrectron 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 mass qa-x ,reeh. *dowx,h 0$m_\mathrm{A}=0.400$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 equal ux * y78euak.4cd.m rumass, each having initial speed the two move off together with speed v/3 What was the angle4m8yc re.u u7x.du* ka between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the orig: k6zf 5.ulilfin 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, assume 6l zfk:u.5lifd 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 elastic collis-ftj,ml3lpb+ 5b y(e tion with another atom at rest. After the impact, the neon atom 3jplt -( bb,5tl+f eymtravels 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 at4vx5sy+d we p6om at rest. After the impact,p5sv+4ew d6xy 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. Specify red9x;6ry v xua if+.g;)i 0tzznlative to the leftr)nztxi;iv+dg x; z.ay6fu0 9 -hand 1.00-kg mass.    m

  The distance between a carbon atomco7vznno6cm+iv49m-y y 9d4 n ($m_{\mathrm{C}}=12\mathrm{u}$) 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 1050m+;ctgfd e) )v4luec) ;q x*j*iof3 4uk j8tji-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 thi)uc*4l duoj3f4;vjg*k) f )ei;t +8mxe jtq cree 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 maso5uk2n ;ku1 (0j tqejich1a+us 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, (kc e5jiot;hqu02u1anu+1j kSE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesmvh m+vu/v z32 $l_0$,$2l_0$, 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 hxh 28:g wr)ff79ea y k2ujsdg2as a load of identical cases of tomato paste (see Fig. 7–40), each o 2782kgja gh :yxdfsw)9ue f2rf which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate 1ku8 +p o4kr)pzw ux-oof radius 2R has a circular hole of radius R cut out of it. The center of tk x)op u18zw-ork4+up he smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as thk p204t us6zqdose in Table 7–1, and calculate the mass of one pq ts06d4zu k2of your legs.    kg

  Determine the CM of an outstretc,v:,jag k3v yphed 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 j mm)gk5l-p 6cof an arm bent at a right angle. Assume that c6j )lmkgm5p- 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 are hang+n 0ngmx 5jf,ging vertically, and his trunk andjn5xngf,m+ g0 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 Earth and Moo4hrrpf 7vo8 jfube yp+2 i+9s2n 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 , ,6y6ntwqxn8 4rcnq nm 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 m4gfa+t;we61h t 6vvf kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 mvtfae64mgw;vf+ t6 1h, 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 of7hv -yr0u46v e;x foqovs q3h7 a 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, spinning, vsh3 qe;q6-v0 r 7x7h4vuyfoointo 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 Examvfr +//qzzj1pple 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, argzjav n6- g3kgtn/ddgd-+mh(01 o ll/ e 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) doesg+n g-a z1dog/gd vlhj/ -t(ml60k3 nd the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizonteyjm kl ab0a-,qd2w.8ally 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 ave8q ad.k b0lye,w- 2majrage force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travel 8l/qhi 8jf8095itkk qmuowl1ing with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot3bh :ykvs48m l 7vlyrh1b x,k5 shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall intoly 3 rkbx7hk,4h b5y8:l1vvsm a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires 2ie eh p0o-xjxib9:.v a speed of 2.5m/s by pushing off with his legs from eoxjhxiv p 2i-9be0.: 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 kgnnoxuh(( 92gfh7 (kmt, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astrk2(g fx(mh7n 9nt (ohuonaut has moved 12 m?    m

  A ball of mass m makes a head-on elasticwqlnft8(uk 4t kklb, g/x1)9 d collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth 8/9 bk gl ktkw(ndl41t qxf,u)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 expmz2g l; (xgy0z mz :9h8 qn,tpygc7zd)*o6rfy ert witness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the 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 dri,z: x07;zhd q* 8og(gzmcy2y6fyz 9gp l)mrnt ver 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 ,n3 f6avw )vswof a flight of concrete 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 perfectly elastic, what is the bounce height on thew6n )vw,afv3s fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into 7.z6 0yuppfj d- z4arsa 1.40-kg block 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 bullet becomeza 7udp0p.y js4f-z6 rs embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg bl1m,yw0v ez 7j6q p4nu/gz r,vqock 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 dnw6 y4rvq0g ,/,1umpqzvz7 ejistance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mw q/*0a :zqzm-;j jiwbass 75 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 f0:/jizqj-qm; wzw a*bar 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 abo q t9ysb :1,bztluhkh,z4x.j(ut $ 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 brokijt/jo 23(ii 8 dmqx+ken apart into two fragments by an explosion. One fragment acquires twice the kinetic energkomdq8 (x +ii3j/2 tjiy of the other. What is the ratio of their masses?   

  The force on a bullet is given by c/ 6p3jr770dvygb thsthe 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 massesciuj3 8.b o:acb1c3 zx $m_A$ = 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 alq4n8o2mc2z av;rgob1g/m w* smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is gngm1z/c2ov 4qrwol 2a*b8m; $ 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) isgn dj2kl3g5l6ga8la : fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.y lyc2ji+cokex81 4 w20 $^{\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 va5))kbkra, e upper limit on mass m if it is to rebound fro,a)b5va) ke krm M, slide up the incline, 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 plane6b/9qhm o i4k0x4smob1 d4l qtt Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is q0 6s/ mobq414x 4odbklmh 9ti$5.69 \times10^{ 26}$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