We claim that momentum is conserved, yet most moving objectszz 0+ng+/1 akwj (qpt5ysc6cu eventually slow down and stop. Explaznpjy+zw q/cs(+1uk50c6 ag tin.

When a person jumps from a tree to thryrez kespx) * y8ct9, 4)1obt;wdjl(e ground, what happens to the momentum of the person upon striking t)ltd(rszek8* c)e;px1r bj4 o,w9yythe ground?

When you release an inflated but untied c d x8)q 3hgl95,vpvcq)itlvbim0;;/ m j(qhd balloon, why does it fly across the room?mdi)8 vlic3vbmgh(lx;c0 qj;d t h9q/)p5 ,qv

It is said that in ancient times a rich man with a bag of gold cxacu-bhaf9 ,7 oins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What 9fa,h caub x7-could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space ,07rc zkc8d x mx;xmb7and is essentially in a vacumdzc 8;xx,c7 0b7mrk xum?

According to Eq. 7–5, the longer the impacfohzw.8h besu4x2(zk2 ve2,p/ o - pvht time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility (he/2u.bfzk4v hzevow- sphp822o x, of fracture or death.

Cars used to be built as rigid as pop81 iwupv+d/ w: s p0j;uibh 63h;qhysssible to withstand collisions. Today, though, cars are designed to hp qv h0u:iib /pwdh+y; phsu8j36ws;1ave “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than vac/jd9d;wi 0 e5dq9 ca ball tossed in the air by the batte0ivq /c99ddew;cj5a dr?

Is it possible for an object to receive a larger impul4v,urb qj4ajpl y3,0yea)wo7se from a small force than from a large force?0r euy4ob p,aqj 4)wj yl,37va Explain.

A light object and a heavy objecq kqrg;c67s /at have the same kinetic energy. Which has the grs qg7q6c;ka /reater momentum? Explain.

Describe a collision5n p+jgmj11k ju)kqbq jtu2+- in which all kinetic energy is lost.

At a hydroelectric power plant, wat;q (fogsb(n 1t +jfb/aer is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so ts obb+( ffqn/; gat1(jhat the water rebounds?

A squash ball hits a walvk.be9 /:lhcfdy:)e2txnx- hh mx 1d:l 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 onto9)k+jr 6 knycz 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 r)nkcj 9+zy6kand 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 heavy.x 9zd8pt +ruz load in your arms?

Why is the CM of a 1-m length of piperhs3q2y;z:j kh g;-af at its mid-point, whereas this is not true for you3h2fkhs;rz y ;ja:-gq r arm or leg?

Show on a diagram how your CM iys6(1f*zbzme73j p xshifts when you change from a lying position to a sitybfis1jz7(* pm 6x3ezting position.

If only an external force can change the momentum of ) mdxzj3fz up6d*18edst(v.ythe center of mass of an object, how can )m zd.y*3xj v8ued (ztp61dfsthe internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodesopqzh xfvv2ugn zp758v gl+a1:((-h u into many pieces. What can you say about the motion of this system o(l:h g(p nu8hz v2pg5o1 vvx+ aqzf-u7f pieces?

  What is the magnitude of thxy uj06m5zy g7e 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 skierw7v y )h6odye79s84s5 zsjkmb for 20 s. What is the skieobdkw mz74 yyv8j7sss 596)ehr’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive straig 9 ..r6qj/htkuw(xwpuht back towar/xk(j 9 ..uwt6w hrpqud 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 nh 3)vjx )ml 6dv g3ism/7l78p,amfon a 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 initiallyl3 di8mgfjlpam6 nsx/7vvo)), 73n mh 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 propellin t m.veev3j:n5rq(bq2g gases are expelle2qvvmjneq3 .(bt5: red 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 3 e3uu-l u56ujmykwv) mtla cl8mys(n1fr6*8at $4.1 \; m/s$ 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 friq8r bts z6+v;l5s1ajr)0qh zpctionless track with a constant speed of 18m/s A 5350-kg lobp szsq8 hazt; 1rl5v)6jrq+0ad,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travel bgrn68dl bvow*; 2i4 aq1os8ting 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 si +e(yq dk2g;nnsi1*If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimati2 dnekss;n 1i+ *(yqge the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed)q2)jvb+0xr(k(xh3w ooxi px of 8.6m/s on a level track. Snow beg )bx)k((xh v+ow p3oq2ir xj0xins 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/jhv94tr kl .9es emits 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 is rh evl.9j94ktemitted?    m/s

  A 23-g bullet traveling 230m/s pen*gzmhpqqi2m421d t 8cetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet em2qc42 mgz dpt*m8qi1herges?    m/s

  A 975-kg two-stage rocket is l 7 ,ha;3sqau:gxg1 aqtraveling at 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 31v23( a j vqh/v8s.hh;6asxhte80 kg is traveling in outer space with a velocity of 115m/s To alter its course by 35.0 ; sa3vs(v8hqa.v hht j/2x 6he$^{\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 sq;g* x678- bkjcukhen0 asf071n xuu golf club was i0kus fe7s* ub0nxc;n k-1 7x qa6h8gujn 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 velocity of 8.reu-5emsby0fgf6 3 a.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impusgb m3a5fef . ury-06else 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 walljr112m 6+4mh1 k wyhrmm mbs5r 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 :u0zg-7:* clc;zd lvqejs ;n qof 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 i c; zvllq- z::cje*qu70;sng dt 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 runniz ca2+4e4- rck+qrneh 8sktf 0vi w/,lng at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Calcu,2 zivta+ ewsl c-hnekr+r q/0k48fc4late
(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 in the +v( m;w1pntll3x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to etp1 (3lnmw;l vstimate
(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 height3*lvfs ,/aa cy can a 75-kg person jump without breaking the lower leg bone of either legc aa* vy3s/lf,? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (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) withgdq di21+bqqy :mh ;wj: v)r z7egx84l 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 and direction of each ball after the collision?Let A represent the 8x bv d qzde::1gqm4+)yr lq2i7jwgh;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 o90l). i .hjxo-rr )zdcha9he6 tce6jif 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A reprehd9-orzc.jhac9tel i. i)r)xjhe6 60 sent 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 y:+9kq tuh2h2m ikod8 head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s +kth2oim u2dh9:q8ky in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides head-on q i:, d1k0eh)iwceiv: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 teied) h:k0 c1w:i iev,qnnis 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 spv/odt5 zqlrh0 on /w/ y v1zcao2b6o65eed of 8.5m/s collides head-on and elastically with another ball initially at rest. Anv/v5/ oo 2o6hy/dc56zo1z laqtw 0rbfterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as oneelus ye8x cmn um r7osm6+230/ 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/s and car B is moving at 3.7m/s calusmmrux7ym6ols c0e 2+/38 neculate
(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 ana8ygyn+5 idd. elastic head-on collision with a second ball initially at rest. The second ball moves off with half the ori.8 g+5 dindyayginal 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 as shn;y g3c,qe wekdc *f87own in Fig. 7–35, and elasticalln gkq,d *78ce yec;fw3y 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- ijhs;lp 3p/asd3a g/ of an object of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a maxie8 il j9fxb +vgoctwgv;,33 )umum height h of the pendulum equal to 2.6 cm. A second projectile causes the the lcxtw9+3fu), ;vg83 jv o giebpendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3tjc 5 kh,giqth,- u7(szzu 9t1o1f x*z.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.verhui(t1z, jo gf x1-k uzc q57st,z9ht*tical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinw(s ha yo2:ij*a, h1rdetic 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 breao2wx0sz1*qn uks 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 much kinetic energy did eac02qxz*s o1 uwnh piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stop4) ) 8mrlqnghkped 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 warmhl)48qg ) kns that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped froujqd h7d8r*q7e)of xf+y.u-f m a height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will odq*hj fdfq .x7 7r8fy+ u-)euthe ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision o/ z0wm;lr+u yof two objects is the coefficient of o+/; 0wyzrm lurestitution, 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 thrt36cmnd(h e +see 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 renmh6s (3dc+te assembled 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 directio zocp1p5yp503zphb lq* hx. u9n at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of ea 5zh9uholxp5 cpy 0qz *pp13b.ch 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 nucleusjia,3dnrcj* j ; l)td7, an electron, and a neutrino. The electron and neutrino are emitted at right *) i3jadj,t;dljnr7c 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.:cn*oaabbtj+;y2h q ass $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between/m+3o5m gr4-rbtcw +ai;:qrwr l 2mw z two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their iw3 r2-bi5qgw/ l;a+wmr t:orm+ zrc4mnitial directions?    $^{\circ} $

  Two billiard balls of equalwc+yw/zy6u((5 qjl2 ghq o 1yg mass 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 myc52lwjy(1w o+/6 zqu g(yhqg oving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfec8z7z4 zzt-+ e erhhys.tly elastic collision with another atom at rest. After the impact, the neon atom travels away at az t4s+8hyr ez-zh7ez. 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision with another at -6 7wpsv6i8qdv;iiv5.;f 1qqzutru *ekc k g/om at rest. After the impact, the neon atom travels away at a 55igp6skievq;u v-kqt /;q7i*8duc.w v zf 561 r.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 st2ipjg e: 1t8jw)xxl1; - gvjiystem shown in Fig. 7–38. Specify relative to the left-ha1w it il -)1gx8egjj j:tpx2;vnd 1.00-kg mass.    m

  The distance between a c.1tdq wy-d+m0bo3 3 lu:esp mgarbon 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 theabu z2cwqe 8,- 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 carq,c2a 8u-ewzb, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a ferrybp3h:4/bjh, dlti tiu 7oat. If three cars, each of mass 1200 kg, occupy its NE, SE, a:p dtl3ihh,7tbi4/u jnd SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side *nj,4 3yinnkcty4g6;i- gygps $l_0$,$2l_0$, 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 oqln uu*hx,rp ;e(80c tf identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the *, n0t8e(lp;c uuxrhqcenter of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of x8 3w8vrhkk;o radius 2R has a circular hole of radius R cut out of it. The center of the smaw3kx8oh8 k r;vller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and ceg3 y*2+xbv pmalculate the mass of one of your2g3me* +xyvbp legs.    kg

  Determine the CM of an oru9y1yy z 3y(lutstretched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent at 1pxr rm1fig2 dz18v,h a right angle. Assume that the person isrzp1h1 8x,ri2 fmgvd1 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hanging v8 lt,x5x ii p.d2**ps juo1vgzertically, and his trunk and head are horizontal, calculate how far below the torso’stlzoips,1x.2xd i* gv 8j5* up median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth an9p/chwsvkg1k* ztw+ 7gb-(tm d 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-kg man e( xcprh90mfm +m;og1 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 k,2v+d9m6z ff((gu- d doxzzak1odsi (g and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as showd-vs,g m1 6 kzduf(2 a(z+do9oifzx d(n 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 d/b3(ipgfy6z a uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottogb d6zy3 pf(i/m of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7ruut:pk9o voqn h)2*,s5jh l 2–29), $m_{II}$=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 stationary wi1d4qfj/wnt1;ty 89syps p4y7 ikn4hx th 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 directin/9 d i114 f74y ;4tjstnskyppw8hyx qon (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally8ag8i;uq ycy, at strikes a bat and is popped straight up to a heigh;8u a, y8cigyqt of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travela/ler;ray +fa *6zr-f ing with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown in Fig. 5rfe)dy eyi8xz- q 2o/7–43. Relative dimensions are also shown. Should the player be worried about this being a “scray fxre8q i2 dzeyo/5)-tch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a 2t 0hb+gd+dn)gyr +m*lek p+bspeed of 2.5m/s by pushing off with his legs from an 1800-kg space capsule.*+hg0n b++ +y2bt)lrmddegp k
(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 anu x33mlu (0n+yzsq7(.z iakwun . n1wfd the other 80 kg, are initially at rest in outer space. Theyaz0 m.wzu kn xu.7uws1i((+3 q3nfynl then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elasti +el(f3+xz-yds -usn1wbsziqx mb 8;1 c collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its o1;zs+i81w (-zyxb us lbem3+dnxsqf-riginal speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expertkk-xj -y ,xr6i 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 rk ,x-x6k-iyj A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the 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 q- xqm8/w ddd6szi h.,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 m xdi6,d- w8qsqh.d/ zall 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 1.438u*p* 7 wjyw+n1tgajn me0rr0-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will thepwy+ngj e70a t*mjw*8 1nrr3 u block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg ft gt- x 93uurbd1 d+,ux/pp1vblock 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 before it comes to rest, what w/3xb,fut rx d91u+ pgv t-up1das the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg an.1glholh4p yn 6lh.p)d the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direc l ph y)hl1ng4oh6l.p.tion 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 w8:- 1 9 k:vg syi6tatx8y;brr.4xlzf,vfh ctjas 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 two fragments by an explosi,s5snea d 19iaon. One fragment acquires twice the kinetic energy of the other. What is 5aes ds,1i n9athe ratio of their masses?   

  The force on a bullet 7yunjo;-eh:iz wc 98a is given 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 masseseadu jqaa/9xbb69w,w- v(5 ok $m_A$ = 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 radblr7p, z+6l*jv g8k enioactively into an alpha particle and a smaller zp v8l7,6eb*rl +gjknnucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at zu1z a/tc47xl an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.0 sp ;urbshm 30ym (k;3b$^{\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 jvvnmkt0(yz0 fmb 34)1w nco:upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide with M aga:m41( fzo kbnt0vy cn0wv3 )jmin?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–h/y 7 tn3tfd;m47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass 7 /;fthm nydt3of 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