We claim that momentum is conserved, yet most moving objects eventudkruc.(v z dvl:g/i3o6 k ;q6dally slow down and stop. Exvu3v /ikcdkz6r ; god6l:(q. dplain.

When a person jumps from a tree to the groujg:bz;4bbgb; p1v+ eges/t;e4 (a jwznd, what happens to the momentum of the person upon:ebb1/jsg 4eza pewbb4+;;jgz(tg; v striking the ground?

When you release an inflated but untied balq 5qqpcxsr ;,fub+m0 9loon, why does it fly across the room?,x; fqqb mqusp50cr9+

It is said that in ancient times a rich man with a ky-2lze e r(h:bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, hel2 :yrz-ekh(e 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 spac q70e02ofnwtt e and is essentially in a vacu twf7t0o0qen2um?

According to Eq. 7–5, the longer the impact time of an impulse, the sr h4*vl-b lyzp90bhq7 : ih6vxmaller the force can be for the same momentum change, and hence xqhlhz6hr4 0yp7 l-b9 ibv :*vthe 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 gsttg-*ye ypz)7ak s w0t-4 h5possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that colt5h4) 70y yk-sztgep- sga*w tlapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in tz,.kmdodg7nl( 83)q1dxe lj dhe air by thex7.oz)(1 d38 dnmkj d,deqllg batter?

Is it possible for an object tob gr u0j2pi0wy dw(2r: s8typ9 receive a larger impulse from a small force than from a large fg9tbp0rp yj :y0(sui8rw22 wd orce? Explain.

A light object and a heavy object have tu+ e2s0q7p /mty w 4g3irjd/fhhe same kinetic energy. Which has the greater momentum? Expi ft3e42h/+y rq /7ds0jpmgwulain.

Describe a collision in which al0ax75dgcg ci6i:pa j(uq9uvd(8m1 qe l kinetic energy is lost.

At a hydroelectric power plant, water idbfs ucyehl.q) (98h)s 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 dead stop, or so that the wateh)q y d).leh(ufsb8c9r rebounds?

A squash ball hits a wall at a 45 cnfu(1:hisls ,(/l l h3ds0ei $^{\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 heigh ve(0n1/b,gr fkmx n.wt h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steelrkbnm,xv nfwg /e0.(1 plate.

Why do you tend to lean backward when vh ud2wx +rtn9;z6* s8sqkne/ carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-vyfyoku8 q3;) point, whereas this is not true for yo3 )fyqy8uo;kv ur arm or leg?

Show on a diagram how your CM shifts when you change from a lying position to xdnsxlj56c z51 q)ak3a sitting positixc5ak 315sxn qzj6) ldon.

If only an external force can change the momentum of the center of maq /, ,qjebddpj b scr6e7/hk,+ss of an object, how can the internal force of an eng/,+7dqqk/6bdj , eb,ecphj s rine accelerate a car?

A rocket following a parabolic path through the a67ed3zsq t jv5ir suddenly explodes into many pieces. What jv5dtzs e763 qcan you say about the motion of this system of pieces?

  What is the magnitude ofab8k3q67: i,z9* * pemsxxwt*rc blw h the momentum of a 28-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-kg skieriwx9 9(uey +mw for 20 s. What is the skier’s cha 9e9+ww(umyxinge in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a ho8:j,8ym8plx vi-ey 7g5rocwzrizontal line drive straight back toward the yj y5- em xvw8g88i,7copr:z lpitcher 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 75hyql:zem+h 6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the b7y+ml5:h h ezqoat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a r4t:xkmc8)orxit 4r8 o ocket, given that the propelling gases are expelled84t8mi4xo rk:cr txo ) 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 movjxsakl*s pt,gy (;z/l,j-xf (ing 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 a80 k jr/xcwt*glevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car.rk/g0*wjt 8cx What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelilylvvxr3 a +* 3 o.-ixj8tpbf2f t99kkng 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/h If the wmbf,xcz.8 c+us(, efair strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m bm,fwf x c ,uze(s+c8.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 e)a+)tp qhi41r4 nfd rwith a constant speed of 8.6m/s on a level track. Sno4qe1 ph4i) f ran)+trdw 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 car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emi.nz+k. rvx+nkv60 u bhts 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, whbknx0 vur+h v.6 z+kn.at speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling u u 1u gwq 9by3s*2b25o*xmgis230m/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the blxug i 2bm9o*y*3sg5qu1wu 2s bock is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling a akj.*tln pw 6+eq08j.yklo xo.;z;zdt a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space withb:f, z jt6a 7dxrjo+q5ewi( 3n a velocity of 115m/s To alter its course bntjaboj5 :d f ,(76xe3zqir+wy 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 -rg1/z sl 7 xhmh81 a2svqx/gwhit off the tee at a speed of 45m/s The golf club was in contact with thesvg// wahgrsmzl- 1h817xqx2 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 comes to s:ondpb9 a00 nrest in a time interval apsndb 90 n0:oof 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 wall ailpc.q 9mf :ud y46l 0.gd,vnrt 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 crashw.o5-amprm :gt orthiness 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..rp gam5m-t :o (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 runnindw4 l4t a0.xxqb r+iyu,kw .x.g at 4m/s to the east and is stopped in 0.75 s by a head-o0.dqb w+a,.i4l y .kx4xrwxut n tackle 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 bal- : +fhelzl ss(e-qfd8l (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to es--dfhzsll +q:efes ( 8timate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking the lower leg;hh*3k j(9ywqo wsq(i:. rywa 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 brewqyy * 3;oq(w:9j skwa.ihh(raking 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 mo6k;h cy7jifymt4 h:z 2ving east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed ac42y ;jzhi6fy th7k:mnd direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-on cq9ui7*rc xjd r* inv7q4mv9v-ollision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object aftemdn9 *j4cvu-vv*xqr7iq97ir r the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastic head31)qyqsn7c9bw c hr5 x-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 qh)7qcsncxwy93b1 r5 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 wit/og0.2 z yy8 ktnrg6fwh a speed of 2.5m/s collides head-on with a 0.090-kg balgk g0yn roy8z./ 6tfw2l 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 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 colli2w/.zjz,r mf a r3ybe/des head-on and elastically with anotherm 3r fz./web2 arz,j/y 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 amusemmiox8zc3j v7g .wm 4a7ent 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 car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/sia.37 7jvc4m mzxgo8w 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 a second ball6zv*1fatqf m+ initially at6ft*vzqf+ ma1 rest. The second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline nmvy.auhs.-: ug4+ l.r8stzmas shown in Fig. 7–3r-+nzhmg.v yus.a: 48s. mlut5, 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 leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an objectc::3 kr, f t74inmmeqp 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 maoshg s jq./4-mximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum ss oh-m q.4/gjto swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg1fwc;0h7m t9qkz 5fcoff9wqy.+,v ug pendulum hanging on a 2.8-m-loqf u9f f t7zo1,;95w. mgkyq+w0hvccf ng string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinar(vjuxd/8u u,4o 9z jetic 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 explosionk51uwt/6 bz wb0bk, hu breaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how mu0,wukk6b/5wbu h b1tzch 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 SUme y9w(ac ;6cjV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The polwmye6 c a(9;cjice 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 height of 1.20 mq skj;m*jk+d3kfobgt0 93ri nwtajc ;954o/l. Approximately how many rebounds will the ball make before lo3jkq;/l0 woos ;mc+n j5d *kfikgj94ba3tr9t sing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the coefficio6hqv. 5jd 5xxvc4c)sent56vvo hq.xc5 ) xsjc4d of restitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three sxdh9s*2w (hlc0cq h w6uo 1y3times the mass of the other. A depression is made in both faces l(oh h31uycq9 0 6wds2s*wxhc of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is 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 directionosw)4m+ dy8b/ n pzhn:s:2ae l at 5.5m/s collides head-on with a 10.0-kg ob:4nbyn:2 /d+s8mea) zp ohwslject moving in the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an electron, and a n(+5 gl u)49ed nrjj hm,hixe,ueutrino. The electron and d4,5 hlnu ,ejj9eix)g +mur( hneutrino 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 ma qk zvf: lhpwt cjb9hvg(4ut9o8,)c61ss $m_\mathrm{A}=0.400$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, eachg1vq k2dg zgs0(i4-3o s orl9vf5ot; q hog ql2 fi(d-gzs4qr5sv o ;k 3gv9to10aving initial speed the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move a h:zqjfq 3 46c(sz*(tw+goqgpt 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 r*6q sz(og qzwh(+4qfj:ptgc3ight 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 collision with anoth tzk ,9 g8hxmu6br*e8ser atom at rest. After the impact, the neon atom travels awa8 *9h smb ,g8tr6zkuexy 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 cl bvuq/3n .-muollision with another atom at rest. After the impact, the neon atom travels away at a b. unu3v ml/q-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 qzabl 8g :ibz;c5:4yh in Fig. 7–38. Specify relative to the left-hand 1.00qab5zz 4yg:;8 :ibclh -kg mass.    m

  The distance between a carbon ae/nt( /-p2vtx zg bdo5tom ($m_{\mathrm{C}}=12\mathrm{u}$) 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 fronti99bj2ql9as.m x b;ft of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a masft2bsijblqm 9.xa9; 9s of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 636nygo /)g/ v83l ppw)dijsp, 7vlch b800 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 loaded fnp/dvj) bg8 ll7,v c3hs o /3giyw6p)perryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesa)tut0h. mn,r3il;2n hb9by- nez( qz $l_0$,$2l_0$, 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 identicauk60v os8ifvdnu +2 ;gja 9ga/l 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 the crane operator can pivoi/ada;kjsv+gu6g 0 892ufn ck up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hol kg2 ttlrr2;h ojqy4(q1qo0gg ..po8ae 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 8ok2qryl;42. aqgpgh o. t0gort jq1( center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are u 0k4-o2e0)2yp xoukvc xu9t3fl;tjsthe same as those in Table 7–1, and calculate the mass of one of your legs. ;u0y)putslvc0f-tkxoo2ej ux4923 k    kg

  Determine the CM of an outstretched ibh li+p2h;vq.q v/i9 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 posi07 j+ enjtugk(tion of the CM of an arm bent at a right angle. Assume that the person is 155 cm tall.0ukej g7n+ jt( $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is isipir2t7 xfykm/ ht ( 0), */ckjnk:wln a position such that his arms and legs are hanging vertically, and his trunk and head are horik s 02 n my:fljwxr/)kp*c7iithk(t,/ zontal, 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 akjvhy9hu3 ;+nvtp+2s 2osgn w4 qt 1n*re $5.98\times10^{24}$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 apar qbocq (5rz19p k 4ule*j8ukq1t 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 unifo8w ws 4w u-3fzldg2+xe*poy) b5vktw,rm cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg andvuf8 pw54x), wol*tw w3s b ezkg-y2+d 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 follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a di78tsr .3v fezjameter 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 8frzv.7ejt3s 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 7–14d9nz3w(y envjtp 71h5 (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, are in the air and stationwoo.a e:.(dpgxb-w)ayu9v 0mary 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 ballooumovdogw 9xaa)p( y.w:-b .0en. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a b non 3 *aspax)o4jri3q /o,h2zat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate 2s xzo*3o4nnqrop a3,a)/ jih the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with,lqu:uocj; w ni ;as+7 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 shot shiyp1(i,s9+:ek p *p j9lu xtvqown in Fig. 7–43. Relative dimue i9vx i(y:jkq9p*1,pls p +tensions are also shown. Should the player 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 speed of 2.5uumc:o 4 k74qfbb s s3 :w1e)bc2,osrmm/s by pushing off with his m1m:qbr c3eku:s, u4foc wbb4o27 )ss legs from 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 )cut 3qc /(eav-p(zh iand the other 80 kg, are initially at rest in outer space. They then push each oth3 e/zhiq(t va cp-c)u(er apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (bm:w / v j/ wutk*1i-sg-9q3l hoq0xkxat rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is t wo uq/-mitw01v*3q-/klkx9x :gs hjbhe mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as anl8 p.+qm wiuwpj08* se expert 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 0se8w + up8jwl.mip* qto 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 t jxfdlkj ;c1 , -bc3dh.4psc2vertical 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 collisionsjcls1cd-bpk tc 3. f2xh;,j 4d 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 rest direkyr/;ryd;e. drk ,ri 3lmzp0;ctly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high wilkymk3 0r zyr.d;d;lri/e;,p r l the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg b,z:3y6pcicrtv:l 3o + hs r5 4qus.kwslock of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction3 zp:+l4c3h wvqrius,rk:to s5cs6. y 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 kg8fbaq3x3 ip8 we mst(6j--ugi, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at oppositwp383 eba 6gj- 8mqsuitif(-xe ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was a p2i ri8s8m*,q5 bvqzkbout $ 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 suddenlwbg-7yyze9g 0 y broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their masses? 9-g7 e0zgbwyy  

  The force on a bullet is given by the formula F =ngw*i.vk 9 *a+.4ndx qxwffb1z2m ok- 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 massesy87);8xb muvwh- citxe3l7pc $m_A$ = 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 intoveh2 no o:22zi n-1lamkyv;(z an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha partvk 2oyinzom2vh:en a-zl 2( 1;icle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at m0/,m;xlv/ (kawm f,pl qw;vjan 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=2.2r;n- y9dk l4hlkg slides down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mass m if it is to rebounfwn .bj)blj :*d from M, slide up the incline, stop, slide down.jw nf l*b)jb: 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 h7olzfokpyrz5j( 5 5, shows the planet Saturn moving in theopz(o khr57,jy 5f5 zl negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s