We claim that momentum is conserved, yet most mov2w 6,alu) a*yd bs:maaing objects eventually slow down aa*dl yb2sm6aa u:wa,)nd stop. Explain.

When a person jumps f4nt0lh3pmv.k/xu( qy rom a tree to the ground, what happens to the momentum of the person uplv 3yp/t4 . nk(xhqmu0on striking the ground?

When you release an inflated but untied balm1kt2* 4 m x+ odpk;rahe6*qhtloon, why does it fly across the room?dx 2thpa4* *o ;mk6qekr1mh t+

It is said that in ancient times a ric9okzcoa /6la;c a99tj.lc;hj h man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could a jkc;h ;o9z9cac6at.lo9l/jhe have done to save himself had he not been so miserly?

How can a rocket change direction when il)4j0bx j42ufzpzo+:, 2 fdcgdv*atpt is far out in space and is essentially in a vacuum2ag*zpjtux zv+b)o 4fl2d,:cd j0 f p4?

According to Eq. 7–5, the longer the impact times bjtgy f)ku8 4brjw6( 4z(+lv of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of thezrbjjbtf(l4vg +48)k (u wy6s object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand colli+ov gq5vgs ax/)u* )zusions. Today, though, cars are desigu*v) uz o gg/qv)as5+xned to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tw 3.gawrv7q lf;32t wkossed in the air by k ;wg2lrfq t7 va3.3wwthe batter?

Is it possible for an object to receive a larger impulse from a sb kc/;:gtltp)mall force than from a large force? Expl;l:)ttp gkc/ bain.

A light object and a heav-(7kg jndf0y0a)dpdx y object have the same kinetic energy. Which has the greater momentum? Exj7ddx na(y-dkf)0g 0pplain.

Describe a collision in which allodm +2k( )l ,qt6tpizmmlw- .d4;whdl kinetic energy is lost.

At a hydroelectric power plant, water is l*wk cqn5hmfiu,r : 7,h2 (whodirected at high speed against turbine blu7r,5qnicomlw2 *hwk ,(f:hh ades 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 water rebounds?

A squash ball hits a wj ok d0ove-2g)all 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 h onto a hard s0d6tx yn12zqxrbl.y 185 uj(tocsq0e teel 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 par.u2d1q6 q0tt lrj(zbsx c1o0ey5x8ynt 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 carrying a heaw*hwt/68ivts vy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is not tecncw foan73y 6*z4o)49jzk xrue for you4 wz4n9a ce7o6*fnykxjo 3c)zr arm or leg?

Show on a diagram how your CM shifts wh6)jka(b,m ifeddd: kr)b; e 7jen you change from a lying position to a sitting position.bk mr:j,ddi)fe6bk) a;de( 7j

If only an external force can changemhynz 30 r/,wj the momentum of the center of mass of an objer/zhw,0 n3 ymjct, how can the internal force of an engine accelerate a car?

A rocket following a parabolic path through the vft er21i v3z a(zc3m281,;i og (x bivgrhl/eair suddenly explodes into many pieces. What can you say about th(tf( zm, z3e 3igiheri8/ovgc 1v2x1 vablr2 ;e motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying f6d2t h d)8vwp 9vhy5bwith a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N q.4 m4fwic 0t;6tq5r6vdteqj acts on a 65-kg skier for 20 s. What is the skier’s change inect;64f iw4d0 tt5rj q6q m.vq velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a hor,bjcg)j s/ ; vj)k1op,v +mtbcizontal line drive straight back towbmp1 jb/,tjvck ; jsvc)o,)+g ard 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 package3+f )s :r0 zoc6,vresg tbuko1 out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately aftfbzt3 0or)1e o,r:+k6 su cgvser, assuming 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 propellifb/6so3: i nvic5qkz, ng gases are expelled at a c, z /qink6:ov bi3fs5rate 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 aw6as/*; hdqomt $4.1 \; m/s$ 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 track with a : ir iywe7*d-olizq2* constant speed of 18m/s A 5350-k-l *ry o7e:ii*idzq2 wg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling au;bg-6.jgxg z:a sr 0ut $15 \; m/s$ 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 10wfhixa+jic ;.z3 ptuv4t 8b 3c2n7 owh3 z(+ut0km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 mu3vcc3+8thw who t. 43f xtza +7;jb2i (zinpu 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 coast2swlrq:yb 1x+s along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is th2l+sbr 1y q:wxe speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an u)nvzed .c3g6 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 tn)cz.ve g3u6d he original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and l3q uqr6i(pl+emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after tq ruq+l63(pi lhe bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speedq cvde5 ,/:6mfhmz sq/et..ha+rn ;t l 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 with a velq*f)es-:xrhqi ts6n 2ocity of 115m/s To alter its q:6is*exf)n - trsh2 qcourse by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed of 45m/s The golf ce(j+div15ngl lub was in contact with the bal51g(di+jle nv l 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 tr9/ r u)kpkqby4xf4l/q+ 6s)k1.mv lt ok rq-mo rest in a time interval of 8.0 ms. (a) What is the impulse given qm9-)vpt1k uq6r frok 4lsq y x/klr)4+b /.kmto the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06)z /up*p.erw 3j 4lobakg and speed v=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 crashworthiness of new aut -uagr41o0l3qv x j-nuomobile models. Cars are tested by smux -nq4og10-rjualv 3 ashing 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) 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 easu+czfb6o1 q wrz(67etgwi1 zz1(,yjxt and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Calculaxu itwy(+z f 6 z6g11e ,zzqrj17w(bocte
(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) points il(agk7,f i.lt n the +x direc(ltkl,. 7i gfation and is given by the 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 75-kg person jump wina ax:9u4,;xllb3y3lm5tdhvthout breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person b39x5l4 ,na mtuvlahy3;l: d xmoves 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 m(+oy- zo vio m49vou,qoving 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 wi 4z uoqy9 +,vvoomio-(ll be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-onc :*yy1( jij(6 tx /ok9keffhc collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speehe1k9(oc: (yjfcf6jx y /ik*t d 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 a perfectly ( uq s90vtxv+belastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their spv09st+ vuxq (beeds 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 collue0 hab6bai/4 ides 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 directu6ei/4ha0ba bion 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 wg.xu a ntt5nerzi7;,yd.ca3)b)x qp 5 ith a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calcula 7a 5 i5xnqtzt)3c, .;geby)u. pndaxrte
(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 ae7mi*l k:sn5r7ho uhmtg/r-:g6 rt h2pproaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s kmr n7uh6:/ 7gh-lm re*oist5r:2gthand 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 wia4l0tvcjg 71 zth a second ball initvgz j17 40ctalially at 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 in :34cx2xsb+hmv+qs ne cline as shown in Fig. 7–35, and elastically strikes another cube at the bottom tq4: hcsve+ xbn+ m2xs3hat 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 object of maf(x hzln*l o8/ss 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 .(sw5 fw h.alrbhd:d- a maximum height h of the pendulum equal tobad d: -hl(whr..fw5 s 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s xg e4uqo9j n-l(zpzm izf. .)8buries itself 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 and horizontal comgem-u8jz4.)op9 fz(qzx. n li ponents of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fractiozyf0t 8t-v- lw 1k 3cv.1bdv*-ubonxbn 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, initially at rest, into v5wsequ8q+y rl9sxhr7z- m+(two pieces, 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 q+sm+vz7shruw5(e8-xrq9ly represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into theey,b5 pcfa ;6w rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A y6 bw5;afpc e,represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from2m 2a;7w xpxin a height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losingxin ;m7x2w 2ap 90% of its energy?   

A measure of inelasticity in a head-on collision of two objehm5dxk n9i0,izbvw)/ cts is the coefficient of restitution, e, defix09z i wm,hbnkd)v/i 5ned 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 eef9sh (22 hyl;gg(jwmass of the other. A depression is made in both face9wjfh gl22(;g (y heses 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 direction at 5.5m/s collides head-on mzsh 8f+zoj28wi/dw+ with a 10.0-kg object moving in the -x directih 2/ +wjz if+8msowz8don 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,7q.e 25zm q:afk 44ry,6jy7ngyi vtsc and a neutrino. The electron and neutri ev k.jr6i 47ynac7y2 sfz 4q:5,yqtgmno are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of mass qaafnh/z5yydc2 ohd (.l5 ++h$m_\mathrm{A}=0.400$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 o,v: dtjww l6h(2,bh nybjects of equal mass, each having initial speed the two move off together with sjn hhwv,:b 6yl ,(dw2tpeed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right ang k(j8qqp*ra 0k8ka: njh/v-h nles 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 q j akjn/08:qrnh 8ak*vhk p(-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 anotheu f hn/+acxqo ud(9td(4frt96r atom at rest. After the impact, the neon dndhf6+9qu9cx/afrtu t o4( ( 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 perfectlyxofmis4*0 g9j0zkv6 e49azi 7b l/wad elastic collision with another atom at rest. After the impact, the0le9w 7dfkoazi a/6mg 9z 4*b04iv jxs 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 threwl rbh s1/: jm76n,rax3pw eg4vv i3i93moi; oe-mass system shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg mavxwii33msr,i7 63b1a4h relov:onpw ; /g j9mss.    m

  The distance between a carmv: +z+m.alzah2 e+1lu m+lkibon 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 1050-58y /lhh aou6lkg car is 2.50 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 7luo a y/56lhh80.0 kg.    m

  A square uniform raft, 18 m by 18 m, of m.i w ufug:t2(dass 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 iw:d(2uug.tf the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides8r++fpcswk h iu4l5.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 tomato pastu-nn8;gjkf 1 te (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the h1kn tgj8uf n-;orizontal 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 h 9zdihg*ej. cj5c 6za:as 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 center of macj jc iez:56d.gz*9a hss of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Tk4bejw2dz 0d1able 7–1, and calculate the mass of one of ez0kd2wd 1b4jyour legs.    kg

  Determine the CM of an outstretched arm using Table 7jil:tyx 7 ;em(–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calcul 0+nda.q r/l hbqmil72ate the position of the CM of an arm bent at a right angle. Assume that the person is. brq2naiqd/m7 ll0+h 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a positioj1cb1) r kau,gn such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM cj1b) u r,a1gkbe outside the body? Use Table 7–1.

The masses of the Eartmm m.wji*bh-3 fw;g3le 1n.rnh and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kovs.t46y c in,g man stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diameter27a vj e5x)kbaqf 71xl 0.0800 m mounted on a unifo7)ejal27vq1 kxba 5xfrm 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 follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg pp;ds6ortk )mfg0. iw/dw * g2and 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 the point )gti wd o /rmkp;0g.pfdw2s6*that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29),+33df hvqjr va 7b6l9ny *z,ue $m_{II}$=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, ofin azf nu1m/.mx8o:c tx 9tj8/- dfd*1hg1hiz mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down anhz1doxcuah/tg ij. :81xmm1f* fn -98tzdi / rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horiz7.3x / r6l u/xy;ugsz;kcg;wj .xsmmr ontally 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 mr / lug;6/m37g.;z r;x xyuswcjx.ks the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with spee5iee,w aspct78 (0 jijd $v_0$ 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 sho. 69anneobc)ot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worrb nn.e6c)o 9oaied 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*mc* i-fssp q:eed of 2.5m/s by pushing off fm-i* c*q: spswith his 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 and the other 80 kg, are knl-vqe 0b94g initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut has moved 12-0gkqv4nble 9 m?    m

  A ball of mass m makes a head-on elastic collisiom/22 -luicha nn with a second ball (at rest) and rebounds in the opposite direction with a speed equal n il2hu2ma /c-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 e)*67-f4 e sddv zxoo:iog0fo.o czwq29; v qcexpert 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 measuredqox*v4wq:9c6g o2ovcf).dez0 o o7 f ezi-;sd 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 p 2l 0ly33z4wee.vrd jof total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourtw e l p02erl4j.33ydzvh 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 directly lb oa*k)uql5nh .o8;h above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will tk n)q* u;a l.bh8ho5olhe block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes an rpivh7sn4m) e)y. j:wo* hfl69*zwmxd becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m b*:9ovjp76)*)yxwzh4smw mlen.f r hi efore it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other oo*zvv dks -42xw5d .kof mass 60 kg, sit in a rowboat of mass 80 kg. 5kk-vo. szw 4 dvo*dx2With 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 move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abou 6)z t en-4qbr.vse;4*vhul xyt $ 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 brok/ uj 9x+:ezqqxen apart into two fragments by an explosion. One fragment acquires twice the kinetic enqu9xzj+/q:e x ergy of the other. What is the ratio of their masses?   

  The force on a bullet is gid lxf11ipe,ef 9eh+ yb6a 0ip/ven by the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of massesq0xh/o f2tkxof24 q0h $m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha particle/-3fny -;wd-d)r0zn rzolku m and a smaller nucleus. What will be the speed oy--noku /d)0zrwd-r; fl3zn mf this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) i ypkxhq +pf;v8uv 84 /ixd)jbx5n3 h5hs 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=2.2k ncd3aj cbbyp1q))2 f,g 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 rebounkm,2gq2pwe8ls lcrg6sh lao77 /6 b0pd from M, slide up the incline, stop, slide down the incline, and l, /776 glhes c20mb kgl 6wra8qosp2pcollide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshd +tgxw w44n5eot effect. Figure 7–47 shows the planet Saturn moving in the negative x direc4nwdex5 w t4+gtion 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