We claim that momentum is conserved, yet most moving vp zff1, 4hq4(3gt, e+jk3)svfwmguk objects eventually slow down and stop. E 3hgzq 4)fjeskgk,u 3f4(vf+t m1,pwv xplain.

When a person jumps from a tree to the ground, what tcnz lf1nl vug.t).,. happens to the momentum of the person upon striking the groundc1tltn l,fgvn zu. )..?

When you release an inflated but untied balloon, why doesv4dk w)ex ((-k3berxnl v, h:q it fly across the roomk3(-kvhbdrx)wv 4 enxql :e(,?

It is said that in ancient iu prwsht6 s/hrh se,tm-) 8kde3z2/2 times a rich man with a bag of gold coins froze to death while sth/t sur,2rz2t3)sw8his m/ek6-p hderanded on a frozen lake. Because the ice was frictionless, he could not push 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 space and is essentiall;( a) boxdztf.qrwt8e++orz k o j09x+fvr8 r6y in a vacf9ob) 0 j z6e ordwk8orttz r(ar fvq++x+8;.xuum?

According to Eq. 7–5, the longeee(ksx0d( kz :r the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. sdke0xkz(: (eOn 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 withstand co 94 fjsimt22yhllisions. Today, though, cars are designed to have “crumple zones” that collapse upon impam2h4ij 9yf2stct. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in the air by (laf 5nla(vt2ay0 7ut auv7lf5naay t2l (t0(the batter?

Is it possible for an object to receive a larger impulse from a small ford d0w+m3i mcn x:tt5.yce than ft+.ni t0xy ddc:53wmm rom a large force? Explain.

A light object and a heavy g(1vky g/k5 ceg,hy w;object have the same kinetic energy. Which has the greater momentum? Explainh;,kgc(5 veygg /kwy1.

Describe a collision in which alvq:8 6jg2eaw oda yovok.9b31l kinetic energy is lost.

At a hydroelectric power plant, kcw jcje.y4j35 )qr+ cwater is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a decj3 cj4q+.rwyk j5 )cead stop, or so that the water rebounds?

A squash ball hits a wall at a 4)ce,vh4 x// rprw7xpe5 $^{\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 heigh6 p64ixyy lh7u w2hxi5t h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly itswypx ilh7625xh6 uyi4 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 falls and sticks to the steel plate.

Why do you tend to lean backward when carr hcx qfgiq 0xx+35.k:mying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereascla8+qbls8 /7m 7k nxy this is not true for your arm or leg?7bn alm+ /xlcy8s87qk

Show on a diagram how your CM shifts when you change from a lying positio ;*dhss(od d eq6m4i8un to a sitting position8*du (md hs4i;e6qsdo.

If only an external force can changecm+-3 gw dd,jg the momentum of the center of mass of an object, how can thgdwmgc3,-dj + e internal force of an engine accelerate a car?

A rocket following a parabolic pargstr ki3o1+4 (trh7cth through the air suddenly explodes into many pieces. What can you sar7 crg (3hstt14r io+ky about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with 53 *cmudo9r0wq.h -7hqoje5gaw/ o yda speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts d6vk;s(:yv :i qtntsu t2zjgs;f.16don a 65-kg skier for 20 s. What is the skier’s change in velovstg ;k :ftvju6ds;(ind6tqz2y .s1: city?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizo ) :bn(brvjnz+ntal line drive straight bacv b)rjz+(bn:nk toward the pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a spx0;8csxogq6 :r9du8eq gay ) xeed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, acr ;q0exy )6ao qgx98 :8udxsgssuming it was initially at rest. The mass of 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 on a rocket, given that the propelling gae 6iffv ju mm-6u96ka7ses are expelled at a rat69fk eum7a- 6vim6fjue 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 movinmb5j+*ak4p h gg 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 alevel frictionless trackdt/s 5 gg4hov8 with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speedt h 84/ogsgvd5?    m/s

  A 9300-kg boxcar traveling a * 9vo +ln6k g)5,auud byjr)ii4+jhgtt $15 \; m/s$ 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 spe:o: /tc c*as6ykz sz80gf)cleeds of 100km/h If the air strikes a person at the rate of 40kg/s per square metertoc 8)zgsc: c *feasyk6/ :z0l 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 speed of 8.6m/s on 8e)fl5 kjufsxq wc* -xw5i1eb p .f2r9a level track. Snow begins to fall vertically and fills the crsk j2i)bq5w5u -pxexlfef c.1w*f89ar at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha:dh e ,icz0.. x*krakl particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what spc:d *.z ka.r0ih,kl xeeed 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 wood5 kb oxw::)7y vyzmd;u and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after thmyv)7w5:x; bo yduz k:e bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speed gg ev-.5n+z9ld +ohw 2kfjb-b, xu:ajof $5.80\times10^3\mathrm{~m/s}$ 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 in7aifoy.k:.d cw 49jb q outer space with a velocity of 115m/s To a79yqcoki4 jdwf a.: .blter 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 0.0t1/5 go5s:hvglx26p owura.bg 2su, i45 kg is hit off the tee at a speed of 45m/s The golf club was in contac uiswp2ol .6xvg5o gg2,rubts1:/ h5at with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and ugda1:dd+:m yx*x w-rcomes to rest in a time interval ofa-u1*xdwy r: d:x+gmd 8.0 ms. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes a wal ,x)lyr.5jmaq l at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of/)zvh v2vv5dh ( lsth7 the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, mas l d5v/zv2v7 vh(ht)hssive 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) 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 .7abwq 24f)yd/ozxygin 0.75 s by a head-on tackle by a tackler running due west. g/ ywq.db24 oxzya7)fCalculate
(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 (mass 0.060p/g :fpy3eq ws4y9i 9g kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to ew9py gs/y pf94:e g3qistimate
(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 cad-0z6m/m p umun a 75-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of theup/m-06dumzm 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 (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of co2: pqx;z-fk2gdur ep)llides 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 represepked:2-fxg p;)r qzu2nt 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 colakoo.ri+e6wt q8 /ky-lision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be te o/+-y.aiok kr86qtwhe speed and direction of each 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 /i o5ykvs 4/fui/i3r qa perfectly elastic head-on collision. If one ball’s init ivfs/yq/5i4 ukr3/o iial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, movini1*hr svc9 4n*k+vsvvntbp 7 f/n 3u(ex .n+qwg with a speed of 2.5m/s collides head-on with a 0.090-kg ball initiallne9p nb xvq4s.*r 7 3 *ctuihs+vn(vk1fv+ w/ny 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 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 nwri+jeo :rxgu; 4i2 8 nwkz)+with a speed of 8.5m/s collides head-on and elastically with an 2;jwz+x +gi)o:4 uwi8ren rknother 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 elastically as one appvdh)v( dp9q8o, nt 7inroaches 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 nhv ,9 po7q8t)vndi (dcar 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 ela6mupqt.qy bs,6 o+d 7gstic head-on collision with a second ball initially at rest. The second ball moves +o 6g.ydt pu,sqqm76boff with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless inryuye,h; b)11 g5iyiycline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If th5yg,r1h;byei )y 1uiy e 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 obj,imz m63i 1okzect 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, xvf(up5s g :/)k0gskiprojectile 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 asugf0kisp(g : /s5vk )x 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 23, t(l:rdvdgc dlo5 w*f7gj6 +j0m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which mlg dd7l*tv+5f:j gc ( odjw6,rakes 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 fo *cb if lp)t58w u8(aj4hkosz;r the fraction of kinetic 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, initialu7 )nh2 br d0kxzkj2t ev89;hgly at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the 0bkje g22kht hu x7dzn8r;9)v 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 a redy 0uy exbj1.7o light. The bumpers lock, the brakes are locked, and the two cars skid forward 2x7e y.o0yubj1.8 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 represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a heighqn 5pmr/a5lx9*qer v 2t of 1.20 m. Approximately how many rebounds will t rqqpelx r5mn52a9*v /he ball make before losing 90% of its energy?   

A measure of inelast4qy x). z5n/ecz5n:h)uis3yu r fp p*jicity in a head-on collision of two objects is the coefficient of restitut)z.h*f3pp)s zx5y4:ic/ nue jnu rqy 5ion, 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 with three times the mass of theh/o9i ).f g.4uogal lt other. A depression is made in both faces of the cut, so that a firecracker can f olh lg) g9o..i/ut4abe 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.ck n44ega2uvb.9 ,noa 5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final ve nu9,.bk44gaove2 ncalocity 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 za hscz n(y+ 9rsj21k9h;x(jglr /r v*at rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momenta xnzv(/92zskja*g9y1r c(rhs+h r;jlof $9.30\times10^{-23}kg\cdot m/s$ 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 mbwlx-j/m ig s,m dx;e:9l1zm; ass $m_\mathrm{A}=0.400$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 y4bih akekmy8m s9u/ u0+5sq,objects of equal mass, each having initial speed the two move off together with speed v/3 Wh s uyqs, 9bekmyu i05hm+a8k4/at was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the origin of tgpd eq8i4 w6(an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball Be4gipqwt6 8d( is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic 3t7r+2rmvrwr collision with another atom at rest. r273tm rr+vwrAfter 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

  A neon atom (m=20u) makes a perfectazjg ic/.t (a4amr7/ tly elastic collision with another atom at rest. After the impact, the neon atom travels away t/4 amarca( g7j ./tziat 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 sq*yy+ch/s t0l ystem shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg ma0+*tqsh /clyy ss.    m

  The distance between a car-8jc j--z qrvi.x sbe 09.bvfnbon 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 of the car. Howg6(xzj-jnjn87l 7a,nfhhu w : far from the front of the car will the CM be when two people sit in the front seat 2.80 m from, wxz87j nnu- (ag:f7j6nljhh the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m,u)xsyzu0u/*n-k aph4 qpk1t 4 of mass 6800 kg, is used as a ferryboat. If three cars, each of maszk* s-t0n4auup)y /u14k qh xps 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 side+pb8n8hvm esq6c jg84 s $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of t+k uj8-9gxfsd6z gk*c-f g f/romato paste (see Fig. 7–40), each of which is a cube fg f6/s+*9gk ckfgru8 xd--zjof length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R+p(q8hs3o k6cn :n:zsz:n x c9 4chmxb has a circular hole of radius R cut out of it. The center of 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 centx :s: 3x:m kpn9 6hc zsqbn(cz+8h4nocer of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as vv2hbqc6d3k5me4g g . those in Table 7–1, and calculate the mabk5v3qg2mdhg4. cve6ss of one of your legs.    kg

  Determine the CM of a i r-+tev( t+t(hirz.pcg( cli3n2v3 mn outstretched 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 a.zl1) tgnms*h p :zvwbxu0 (w1t a right angle. Assume that th0.bl wts (phg1 :zm)un *zvwx1e person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that h/u u9y8cn7c wd4+t kaais arms and legs are hanging vertically, ana84u+/tny 97kducaw c d his trunk 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 Earth and Moon ar(diq* y nra84me $5.98\times10^{24}$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 frictionless f; dcnr3 g w s0mk4w1/0f1uactice.
(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 cylindrical2jwx+r7 l .bws 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, into the air,l j.w2xwb s7+r how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a u; a wo0wb53l2kh6,vyfqopsv;/ )cn dqniform 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 byvo ;fopv/hk6cq)l s,d2w; 0wa5 3nq–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 7–14ulxf:w cz*p1sm qa9zx hg:kk6,+5 h3g (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, 2 3of 3dl6h n2wwytalt-w;v2nof mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloonl2yvf;3dwww t-n2h ltao 26 3n then move? What happens if the passenger stops?

  An 0.145-kg baseball pgd vncvvc u51 )6ejm2:itched 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 fo6jvv)cvg n2c5m: 1 deurce on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with ejq afmk6 wg .kf3e+.5/rw4ry 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 clx1v8:.qpq ule 9c+a forner 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 the 9 .ec qvlxqua+8p f1:lcue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (incl+jwc t3a+ 4cqbuding space suit) acquires a speed of 2.5m/s by pushing off with his legs from an 14bq+wcc3a j+t800-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 c+ owekpc u9,r2i6m0okg, are initially at rest in outer space. They then push each other apart. How far apart are they when the ligh2m9 r6op0u i,ewc+ kocter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic colliudy/8 5yhddp3sion with a second ball (at rest) a 5/8h3dduy pydnd rebounds in the opposite direction with a speed equal to one-fourth 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 witness in a court case involving an als2 y4+s*7xzx,fp yk lutomobile 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 m7 xxklzy4s f*2+lsp y,. 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 vert,depb p2h.5)qhj - ew aav/,qmical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different stepq. -e)w ,apbhhme5j dv2/a,qp 1.0 m lower. If all collisions are 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 :h9:,et se5 /sf(e ujb l)88ifuisstm 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 becomes embsit (lu98e iejt:h )f uf8m, s:be5/ssedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood1ja5ssf,am -p g6fb 5m placed on a horizontal surface just in fr,fmmpa5 6a-fs 1js 5gbont 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 to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 h: 0/y 2jfbettkg, 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 the boat 2/hybjf et:0t move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was ab)klyjidf;mjpct85 e;* 2/hcbout $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments by an ez5 w diq:w+4);lrvq imxplosion. One fragment acquires twice the kinetic energy of the other. Whatqri vw +wmdz4: q5l);i is the ratio of their masses?   

  The force on a bullet is given by the formula +bch.vg(ed3ey(jck 0 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 i aznfx+d 77w)$m_A$ = 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 intoduh0c8zur q*nuq9hm,f 6fk28 an alpha particle and a smaller nucq 8u8qc 9unfd6hfr0*h u,zkm2 leus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay tar 67kscuo; ga(hb n dvc..0)2fypv+qjrget) 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 slides downrj8djyg+ny5 7yp6le6 - cu3kjg g37zx a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mass m if it is to rebsv yh8tg9 21bdound 9ht2 18vbdgy sfrom 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 effectkx s*)l) :5oqvnvqsx5 . Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturvss q)x5on:5) qxv*k ln 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