We claim that momentum is conserved, yet most mopdja3p+- mhx 4ving objects eventually slow downpjp3d ha+x- 4m and stop. Explain.

When a person jumps from a tree to the ground, o4wey9-e o 6k te/tja,;zt vu3what happens to the momentum of t -uzjoa; t6wo ,y4e vee3k/tt9he person upon striking the ground?

When you release an inflated but untied balloon qbfy 8r4ue;i(aa: ec7, why does it fly across the room8ib;fu7qe4(a aecry :?

It is said that in ancient times a rich man with a bag of gold coins froze t+,evlo;sa.a* anf. z ao death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he hanl oa;+,afs*. e. zavave 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 utt8+1zz t c+yessentially in a ytz8++z utct1vacuum?

According to Eq. 7–5, the longew9 ,ky0gly-vtr 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 whicyy -v,lt9g 0wkh 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 wit s+)*; micjkndhstand collisions. Today, though, cars are designed toj+ kdm)n isc;* have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit b6 5s4tvnx3*b-rshc pa pitched baseball further than a ball tossed in the air by the batter?b-vh 5brs p6n4st cx3*

Is it possible for an os 7xqa3pafg:pq b0 t2+bject to receive a larger impulse from a small force thana+:b 0xpt qqf37spa2g from a large force? Explain.

A light object and a heavy object have the same kinetic energ )iaqr31-pzs ebytq. 1y. Which has the greater momentueri1.stb q)3y1q -pz am? Explain.

Describe a collision in which all kinetic energy is loysc5ugjic8 +zj r ;0a:st.

At a hydroelectric power plant, water is directedp c e/c9o44pm vty-q kc-id54r 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 wa-c9pc/ vc45epq -di t4k4mryoter is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wamni7p:sz6b 7x h +-hszll at a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height huu0r.; xb05s h goe.ak 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 ourgrue.h0xb;ou 0ak5 s. 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 carrying a heavy load in your arms? y)lida.;vv wg 5q3v2kp;zr/k

Why is the CM of a 1-m length of pipe at its mitibv, 9 s1zgu5yc)*p kd-point, whereas this is not true for yo)ik, y1gt*b9 u5vzscpur arm or leg?

Show on a diagram how your w/* 3)hcviczkCM shifts when you change from a lying position to a sitting position.3cz hc*kiv /)w

If only an external force can change the momentum (s n xd+h-:q2ui-dl riof the center of mass of an object, how can the internal q(dnhxsr: u+2iidl- -force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodesze5berm+vvz2vayf t0.67nx n jil i8l g/w14 3 into many pieces. What can you say about the motijmii 3nzaf81 7nv5xbl 4vezv/y6w+ltg0 2. reon of this system of pieces?

  What is the magnitude of the momentum of a 280 -lzqfb).su o-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-q .tlb ;zq)*slkg skier for 20 s. What is the skier’s change in veloq t);z. lqbls*city?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive se4qlf x kb4,k7lp v*s.traight back toward the pitcher at 52m/s If the contact time q.eskllf7 b,x44* pkv 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 6bp1kd:an hm8r.df0ckx zi gw )n, u;3with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest.idb ; )8:.n0 uxmk,1af3ncgpk rzw dh6 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 proh5az* c pys,95bk4 lxipelling gases are expelx 5skcz5pal bi4h* ,9yled at a rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving k4mj0p * ck5aeat $4.1 \; m/s$ 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 trjawpw2w) f4 3iack with a constant speed of 18m/s A 5350-kg load,initially at aw pi3 2)w4wjfrest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling22vn5c -9akxx x h+ws(i,f mjl at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of 100km/h9l29s4d 9j* ek ovxdxf If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the forc2 exds dlxofjv9k9*94e 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 v +wme-ug(/yxs )tkh iyc 572owith 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 speed of the catsxv5mey kho2 wuycg)-(i+ 7/r after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits izz lkh*5ij.- an alpha 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 speed does the alpha particle have when it ish*zi 5-. iklzj emitted?    m/s

  A 23-g bullet traveling 230m/s pensr):dx x p+t,y2, zx,6nl 4c+ukkg yqtetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary,tln 6yx t:,ud z pcrgy kx+k,4+s2x)q 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 + l2l 1xpp)qzfel2 .vq u:ih*fat a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is travelingz5hl 0tc )i:sd in outer space with a velocity of 115m/s To alter d0cs h l)t5:ziits 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 0.07xv68eb iipa8 84(rtwsf1(lf) ue ga h45 kg is hit off the tee at a speed of 45m/s The golf club was 6u7 i4f wta1ge(xvl)ei bsah8r8p(8fin contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocm(*kr)xt pxz2ity of 8.5m/s and comes to rest in a time interval( r2ktmx*) pzx of 8.0 ms. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed of +,ip u1ld4ox .ydw5v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthinesxhn+3xis,piwh ;k*ray 89jz0 s of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) 0 a 3hyi*iszhwj+rn 9 p,kxx;8Calculate 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 eaifcfoyyw(h 0e r. 79x.dioe/4.ss)q zst and is stopped in 0.75 s by a head-on taq f. yw(r.)oy. i f/dses 94oc70zhxieckle by a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) poiniz7soaun-: q16 xq bufbgt5x0/bl7 j8ts in the +x direction and is given by thef5qgsn 76t :8bz uj u0/qax-ob7ixbl 1 graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 7v5wweu g 6*0iyd ow07e5-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (wov e w70g6yd*ewi0u5that 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 sp0hzeo6 yp/vmn o *(0bzeed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg *y0hzoe/ v0bpn(m oz6ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a 4zt7 p v;a 6z+ cy3c(yqbnt:tyspeed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elaz:c+(z n actpb4v yyqy ;t36t7stic collision, what will be the 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 o2a/ ,e+b0o qnh-c asgtf equal mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, b-a+t g2 s, ehc/nqoa0what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collndhb cz/ ld8q t4:(hd1ides 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 tennis ball, and let Bncd (qz8dthd /hb 14l: represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.2a ;:n4 )swv hv9v1chyd)rpv5xonu ,f2 20 kg that is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces bacpr v5,vfosv) nh a2ndcw941:uxh yv) ;kward 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 elaro 3u o k5m+-s8wonux9stically 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, owin+9mu noo-kwo x3s8ur5 g 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 wivs d+ cd,dtywlgo: dh. 3esq94kd1 7h6th a second ball initially at rest. The second ball moves off with half the original spekwqy4ohh d ed1s9l :76vd.g 3cdds ,t+ed 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 cr 8ln4z 1i5sp+mlz6d 4cpw9 isube slides down a frictionless 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 tp w+65lns9p844z1lsdmirzci able 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 oz ei 5utjg.4ke/1e*i tpbuo2s8wzo0 ,bject of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a maximum h9cb d/vradl ga jm7fxr,-k;8:eight h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as higl-8r kb;ca 9m:ad,jr x7 fdv/gh, $h_2=5.2\mathrm{cm}$ 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 itsel,6a2 nsu r6jyuo6k;lkf in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical aknus6 u66o,rykl ja2;nd horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of ki+eyze(pm(g1 di( raz.netic 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 piecefd 4wgzbvi-0 m*3e+ecs, one of which has 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 repr4zvfe *3 wiecd+mb 0-gesent 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 re ukcr+z6k xl-s g)m;3hd light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports;z+r lhs gkmk6 )3ux-c car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and reboblsk8c-7*dl /ml0 cu x;ezq5dunds to a height of 1.20 m. Approximately how many rebounds will the ball make befo ; x8bedqd*5 zlcuc70mlks-l /re losing 90% of its energy?   

A measure of inelasticity in a head-on collisit.ijkx 0,s lks;a4cd2f p/ sbdud;5c:on of two objects is the coefficient of restitution, e,,ud 0:f/l5k;c 2kas. pd xji;4csdst b 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 threey0 s9iunzs7wptg65/b times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block 7p5 /s6b9w syi0 nugtzis 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 colau 5 b,6ahwiz.lides head-on with a 10.0-kg object moving in the -x direct5u a6iz aw,.bhion at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an electron, and fa8+ a/y js9sca neutrino. The electron a+cas jfa/y8s9nd 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 m 750 :xqd3uxecux cst85 b)ievass $m_\mathrm{A}=0.400$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 mass, eachwlu ty zk3:x7qz+wiybam o:13q2u3u * having initial speed the two move off together with speed v/3 What was the angle2x q q aoumywy+uzz33i *bk3u7tlw1:: between their initial directions?    $^{\circ} $

  Two billiard balls of equal masspp,f5;k z6wf84 rxb lkn+7uqg move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final +65rnb47pq8,kxl u;p gkzffw 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 elasuyc st 4v)pj8.tic collision with another atom at rest. After the impact, the neon atom travels away at a 55)8u jtp ycs4.v.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 aow w nx0v x/2.vv;+fontom at rest. After the imp; nvxxvvo /2 fw+ow.n0act, 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-ma t8*1 .jr+*iglaiz .w tcunxr6ss system shown in Fig. 7–38. Specify relative to the left-hand 1.00-k**rn rwi8u..t+cjla 1 xi6tgzg mass.    m

  The distance between a z.4l8f k,yabp carbon 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 car0crhdou4+amc ok(* o3. How far from the front of the car wi c3m0d+kacro4oho( * ull the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 1k ;i+kxrw12ux8 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loadeikxx+;rk21u wd ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesd8r k l5kkdlxjm .-72) sq9uuu $l_0$,$2l_0$, 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 akzlq 8f .aa118ug4ozh load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that t1fh 8qug z4alz o1.8kahe 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 ca7z7 vrwq n;+gdatb78 ircular 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. Wa7ntb+v 7gardw;q8 z7hat is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as thoseyjt/ :nahuy(0ziw kwye-aq5 hx: qz0;3 n87x t in Table 7–1, and calculate the mass of one of youh;u wxne0:y(30j 5 -xzaihnyqyz/7 wt:at 8k qr legs.    kg

  Determine the CM of an outstretched arm 5q mqn(3)gs/kc 48s+xignenm 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+sbx*yfn ev; , at a right angle. Assume that the perso; ns bv,ef+x*yn is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs xod z)7dlnsvtpx 5x 7 :p(ln69are hanging vertically, and his trsn7p)t 65 l 7vl:9pdz(xndoxxunk 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 areo7pk0h a)scf9 $5.98\times10^{24}$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 apafnre;h )n o(ni2);*dmb/cdbp3qqr e *rt 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 uy1z-v- ba9kxd0 z1qb o7 hal1a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follo 1bo yhk1 blxzqzv1-0-d9aa7uw a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.r6jqxkvv+d-.o )km0v00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is thvq d-0 o v6v)rmx.+jkke point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fi 2ndd lzbtnx555c,o7 fg. 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, are in the air and stationv x15ady;dclgoud 43 (ary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stop ;3dxyc5 ldvgoa1(u 4ds?

  An 0.145-kg baseball pitched horizontu c+y9;suw x;rally 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 r+ucxus 9y;;w ball during the contact.    $^{\circ} $

  A rocket of mass m traveling withyp0raz 9mm5t37)zv h hwi ,v:h 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 ;y wwt+ht- rp)shot shown in Fig. 7–43. Relative dimensions are also shown. Should the playepwyrh)t t w+-;r be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a sp x(13vmaep;y8 qjz i)keed of 2.5m/s by pushing off with his legs from an 18jim yz3 x(ae1;) vpk8q00-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 8vby*ww0uz 3qrbtm;3; . j6iln 0 kg, are initially at rest in outer space. They then push each other apart. How far apart are thln0 jwu t ;*zb36q3.y mwbi;vrey when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (a pai *x(qxz o89cbb;28*fpjrejsr5 c;t rest) and rebounds in the opposite direction with a speexa zb9 o5;; 8rxpepjbfj *is *crc8q(2d 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 cou 9/xi+o 3qmrhdrt 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+imq9oxd/ r3h .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 conch*gc/3,)w :cuzijb j6ea1 z ecrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horz,cecgzw6 ju ajbe*/:)1h3 i cizontal part of a different step 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 wooywu0xo 6* c;zfd at rest directly above it. If the bullet has a mass of 29.0 g and a speed ou yfxoc06;* zwf 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded mxah he bt f;2;qkcgjq6a( )-/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 surfac)2;/acmjh6(thgb e qa x-;kqfe 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 kg, sit in a rowboabbq6ra,1p, mygi(+i i t 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 directiom,qi bgy 61r( iai,p+bn 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 o jpx-:e/+hwh about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into tw l.3v,73fo uqsr xujh+ (b szjxae2l9)o fragments by an explosion. One fragm 2lh. 7zqv,e bu9fsojsj a+xxrul3( )3ent acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formulaid 6 xpuh3+m:j;bk( ju 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 *z-ekd; 8xsmh$m_A$ = 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 p 4rgaqpq lt8f9.nrlo7z3 1,q radioactively into an alpha particle and a smaller nq ptpnqra9,4z8 1 q3 frollg.7ucleus. 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 (clarf 0i2;- kut/fxog. hny target) 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 down a 6a)1t . mqoqg s1,ftwuf voa1/30.0 $^{\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 rebousyt.89f4s(gj xxxv3u nd from M, slidex83jssx 4y 9u .vtfg(x 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. Fig b.r; v25tjsji- 4gqyg5fp icsif(j 6;ure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sir(c;;s j5biyj.ig52tp 4f f gjsq-6v un) 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