We claim that momentum is conserved, yetemgg7ud aw5j( bdxrcx.k t-iv*-e9 05 most moving objects eventually slow down and stop. Expljd. v-(g x95-5ieca0x utme*wd gbr 7kain.

When a person jumps fro4r tvs2rg3r8 xm a tree to the ground, what happens to the momentum of the person r24vrgt3rxs8 upon striking the ground?

When you release an inflated but untied balloon, why does it2m)wvvic :cy7 fly across the room?:c2i)m7vy w cv

It is said that in ancient times a rich man with a bag of gold kq+i6 inf:zn:ivd( p- yk j2y0coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he no 6::ypnin0- y2fq ikzd +vi(kjt been so miserly?

How can a rocket change dibzf3yl.*m;w6 mx tzp) rection when it is far out in space and is essentially * lpfyz.6) z3bmmw tx;in a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smalleevjq,ty3b8 g4r 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 of fractur t,83je4 vbqyge or death.

Cars used to be built as rigid as possible to withsqs irc2.).sagwb u/1 otand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this new desisu oc g/rw2a..q)bi1sgn?

Why can a batter hit a pitched baseball fuuw,t8 cg ncmm kb0z(-2rvrrto (7f 7.trther than a ball tossed in the air by the batkr7o0c7rf(gt r 2(.m, tb8nzwmu -cvtter?

Is it possible for an object to receive a larger 5oz9r p8fx nw bb22dfyhb*:5d impulse from a small force than from a large force? Explz *x2n5b rd8ho9b w52bfyfd:pain.

A light object and a heavy object have the same kinetic energy. Which has the gr5r )8vgajmr9a3qdjo0f 5 w(uxeater momentum? Exp 38jjr5a0)g x(m a9 ovwqdru5flain.

Describe a collision in which all kinetic tz.dc t k1o1.;+dlm c e0f,t3komgo;senergy is lost.

At a hydroelectric power plant, water is direo 9y11r53vsy.yt3yly,c n wtv cted 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 water rebounds?.n3ty,l91yoc tr v31wv 5ysyy

A squash ball hits a wallo y2ob5jfpo:1 at a 45 $^{\circ} $ angle as shown in Fig. 7–30. 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 9: ozd1-w glbrh 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 od wz 9-1:lgorbur 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 leantak4b 8ljq9 9yg f)o:(q sngm+ backward when carrying a heavy load in your arms?

Why is the CM of a 1-m x--8l rufbuidczt*rttfwz x6:(4l85h g q9e/length of pipe at its mid-point, whereas this is not true for yoqu--*58r9 (gtzlft/ ei:x fhrudwl8 bt4zxc6ur arm or leg?

Show on a diagram how your CM shifts when you change from a lying position to .q8 ilqb41hxg 8ggviww5; ppt8u-v:ma si mg gwq8h488-x.b:it5 lqw;pv ip1guvtting position.

If only an external force can change the mome4c ngumh/ps(b z0dh 74ntum of the center of mass of an object, how can the internal force of an engine accelerate a cp /h su40znbd74(mhg car?

A rocket following a parabolic path through the air suddug2v1 .1r0, drzcafueenly explodes into many pieces. What can you say about the motionvu.0 , 1edc1zagr2urf of this system of pieces?

  What is the magnitude of the momentum of a 28-g s8r;qextxbio4u0vg u3x z+a5;parrow flying with a speed of 8.4 m/s 05xxov4qu 3;8 ; ag b+zietrxu   $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s.qmt op f2c pm+1x,ws pagujgn+x,c/ ai:n, :22 What is the skiera2c2,o,au cmgx i/t+xpp jm:,ns:wq21p +ngf’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 msgs9+btp(( pdr b1g5s/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time between bat and b s(+rdpt95bg gss1(bpall 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 package4o*q m(/ b/zctkkc;aos59la x out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assumino/toa/4 59*;zxkk a sclqbcm(g 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 velocity of the boat is    m/s

  Calculate the force exerted on a rockj (r gr9q44 :qkd,vsp9yo+s sret, given that the propelling gases are expe,kqgr+vrqr s499( po:dj4 ssy lled at a rate of 1500kg/s with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an apparent bre9 i4oxjq)7ebeakaway for a touchdown is tackled from behind. When h47)io eej9 xbqe was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad d6c l 4pzhw1+si1 (vb97sg fkccar travels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car.4g 6cd+1zc kb 9s1p whlv(s7if What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling 8es rzxnqw :(3f w 535fbgzp* h/wuzzr+y.*i jat 15m/s strikes a second boxcar at rest. The two stick together and move off with a speed of 6m/s What is the mass of the second 8eh+bw w.5/urzz* n(rqs3fzf:w zipxg5j* 3y car?    m/s

  During a Chicago storm18)egg0 pl gn9p; rucu, winds can whip horizontally at speeds of 100km/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. As;g8cg 0p) ru1lpgn9ue sume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of 8.-meeu8o /lql6 6m/s on a leee-o /m8qlul6 vel track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alptke ff+)p1npr* i36/f)m eyswha particle in the direction of its velocity, and the remaining nuc fm+fy/)fpt1ew 3)nise*k6rpleus 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 emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and emerges coh8 ef98/n:sd, ao-j )m qe h9rud-gxvleanly at 170m/s If the bloq/ dv9sou)ng fh: redjh -exa,o8- 9m8ck 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 y8k5b51s.ls :g )ttgiapxci 2traveling 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 3180 kg is traveling in outer spacenql j:jnq01w mob-.u 1 with a velocity of 115m/s To alter its course m0q1-onbn1. w:lju jqby 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,3bz)cufq4 lq off the tee at a speed of 45m/s The golf club was in contacq4b q,f )lcz3ut with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes to rest ic4 s4oxo:zkt6 n a time interval of 8.0 ms. (a) What is the impulse given to the ct xsko 4oz4:6nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg anhwm j0s3 kpp/s63ws4kd 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 automobilebj7: iq5qcd*e ws 7+bw models. Cars are tested by smashing tw7 *+iq5 bdqbcj7se: whem 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 )japk) byq(f c1mv8+n 9ew f*neast and is stopped in 0.75 s by a head-on tackle by a tf8p e ba+j()y9 nqvncfk*1 )mwackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) po.p;i0e8pd y* p: ferzoints in the +x direction and is given by the graph of Fig. 7–33 as a function of timepp0: deo*; iyp. 8fezr. 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 without breaking the lower legvl+f ei ajc5p)m u(ld /t:1cv7 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 poc5/) 1vvj7:i + lat mculdp(efsition (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speermdo1t5 on+ n.who(0fd of collides head-on with a 0.2.0o1hfwn( mr5ood t+n20-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east2w0mvb 6iw d t5mpe2y7s0v-wo with a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collw 20wbidm2tw5 vp-ov e60ys7m ision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfe0ycrq8 tmnbm/2 youp2to o;9(ctly elastic 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 directiom(bt y0cu;pyqr8o2 2noo 9/tmn 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 ofihja m9aq7 sr+5z y of4nm0.k6 2.5m/s collides 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 spee n70 arkqja+ sm6fmzoy5i9 4.hd 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 movwja:ea5g 5zxbvz :7 1cing with a speed of 8.5m/s collides head-on and elastically wixczwaj: 7:5 1a 5vezbgth another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collf7r 48us yew )ejavy6;ide elastically as one approaches the other diresa4;u7 ev 8ew 6yyf)jrctly 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 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 anc51bjow,wsw8. z)spl elastic head-on collision with a second ball initially at resj) o,cpblsz8www51 s .t. 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 slidesifloxg3 /(yq1 :4 xre7mr-xep+jy ft2 down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land?pfqf2+4 -e13x7my( er:ig/jxtox r yl [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an objeriwm (q: s8g7wct 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 8 ; b 0iuyol-fxp+qkp7in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendluq8 ;bxf70 p- +kpiyoulum 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 /dj8 :ezctr6.iyr1eoe m2 5ppnyi -1p 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 hormoy8e pp/je:p121z y-r65.e i n irdctizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fractizsq5 pm* -9 tpwaav8:lon 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:/8 zh;nt bqhg 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 each piece acquire? (Let A rep ;zh8:g/bqtn hresent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides in56 vj*zt e;vykto the 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 betjvyk* e5z; 6vfore stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebound u-kmmvhdm1 w: , lwrf)(9.ntts to a height of 1.20 m. Approximately how many rebounds will the ball mr utk1fnw- 9() mvl.t:,mmdhwake before losing 90% of its energy?   

A measure of inelasticity in a head-on collision o /e;-hvl-ov1cc-kgqh*- da yqf two objects is the coefficient of restituti oy -/g-qk*cv-ae;l-chdhv q1on, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the mass -c os pfh(ln27 cu.lj*of the other. A depression is made in both faces of the cut, so that a firecracker c2fc.l-s c7oup*n(lj han 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/sz/t 2 *bktc6ys collides head-on with a 10.0-kg object moving in the -x direck 2b6ys*z/ctttion 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 ax7 wkqs(y 3v4c neutrino. The electron and neutrino are emitted a7 w 3xq4(ckvyst 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 m3 d/zy 7iknljdcwy :h5t2g65iass $m_\mathrm{A}=0.400$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 object,xafr n6y( cp jqy 13n7up)mjhtq75r;s of equal mass, each having initial speed the two move off togetherfu)7(; na rp pr5y6nq ,x3tm7yjqch1j with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and 2o wc aqd9s3*0 kvvirb :ntk,*meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of bal* 2kb wt rdn,siv:0*va93co qkl 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 b8ks*oz6hcj0b g cp .d75mhr .collision with another atom at rest. After the impact, the neon atom travels away 6g7r m0s.pd*cbkh cjbhz 8o. 5at 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 elas,)rf/qdx84vqb sdc2 ttic collision with another atom at rest. After the impact, the neon 8cd bq24qrfx/ ds,t v)atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. Specify sq08.r i.f zlerel0f8.sr zil .qeative to the left-hand 1.00-kg mass.    m

  The distance between a carbo q(ojt- t0v, ,,ixgrb nj:vh.bn atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of the car. How fmq6koaktocq. o./ zh.v)i :odt( v0,war from the front of the car will the CM be when two people sit in t6o) .0ovam q c ,.(ot:kthzid. o/kqwvhe front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 68oug4 f* 0b60jss 3wqns00 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine thb fso 4q3js*0u0gw6s ne CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides oz,pxkbamg y1n) p w/1)1kd+q$l_0$,$2l_0$, 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 h jf8h*nmtr 0 lvit-;;74lw. grto xfcps+d :8ias a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of l;;ixtwrtr7.8:v8o* is d 0 pffl+mh 4n lj-tgcength l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole (frcx1pw8;-;vz yas iof radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of tyc;1z(;v-fr apxi8 ws he 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, andcoyj68j: w16d )g mudw calculate the mass of one of your legsdy8d:o1u) 6wjjmw c6g.    kg

  Determine the CM of an outstretched arm usytlbym. 59k x5ing Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the pol p0;9jd .0p)t fqdv/ skfqi6wsition of the CM of an arm bent at a right angle. Asq9/pp00kl sidv) t 6.dwfjqf ;sume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is m cj/3czdvwl)u l7.dbrz-8g x(oa9t, in a position such that his arms and legs are hanging vertically, and his trunk and head are h) a7t jlb3wo/ vgxdc-( u.c,zzl r9d8morizontal, 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 aijpto 981iynmr. 1u0,k rqww5;zpex0nd 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 stand 10.0 m apart on frictionless ice. ed05bh-c h +ooa5sv8t
(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 cylin17fr x8o. et+mv gvt7 z)()fdfm4nufv drical 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, ao 147t mtmzgvf.)u)rv fvde8(+7ffxns 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 p7c9axk+gpr jq3b0c 7 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 bottom of the handl9cr+ 7 0c7bag pxpkj3qe is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (p o,*tkals1: wFig. 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 staxa);ywu j9 rx9 mhb3b2tionary with respect to the ground. A passenger, of mass m, then climbsbym;uj xrwxa h9)329 b out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched bws/ :,dtr iv19r (pgbhorizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, irbgrd v1tsw,9b p/ (:calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with sluw*ac06 n u z)ss.du*peed $v_0$ 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 co ctd- 820n+ln we1) a*trzcbubrner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Shobtz 1 tc wc*r0n-ula2)n+ bed8uld 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) a( e/-n ymz 4xnrb)mt:pv i/:dtcquires a speed of 2.5m/s by pushing off with his legs fromi:bz)v /ptnt/ ymn :-mer 4xd( 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 initiallwhpj99.txx 4t.nz8( :gk+zj o7cnq y gy at rest in outer space. They thewgh+kt x8qj74tx9 (cyn :.on g9jzp.zn 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 elastic collision*.ka4 ,p:qzr okw9cop with a second ball (at rest) and rebounds in the opposite direction with a speed equal o pp:49. ra*ozk ,qkcwto one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving an automobil.-o16idxifnn7v :l xg9r l9iue accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h)1r:-gd v6. lno9 x7f9il uinxi speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concr3,kqw4a1a8 psr /xywa ete steps of 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 fourth bounce when the ball reaches the bottom of ,wsa8yxw3apk/ 4 arq1the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood3d/z mtni0p,k at rest directly above it. If the bullet has a mass of 29.0 g and a spep3dm nz/ ,i0kted of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.3jy 1rncv* *k72ylmtb-5-kg block of wood placed on a horizontal surface just in fr *mcbk1ly- vr7*ty2jnont of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit zyg*m wt(sk/ 9shvas f(on09-in a rowboat of mass 80 kg. With the boat initially at rest, the two pesyk(nz-0 fw/9astm (vh*o gs 9ople, 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 w8x4 3iufreg2 tas 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 9v1 84e*m bda)xsuh lssuddenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the otb*xs1shaeu)m l98 v4dher. What is the ratio of their masses?   

  The force on a bullet ckiuu99s)1 mgm;:qr r 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 massesrp.q b18x z5zg $m_A$ = 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 radioac 7sp70ojf-u hstively into an alpha particle and a smaller nucleus. W j77sop h0fu-shat 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 an anr2dz( ) f s(* q3v6kyavwb5efpgle 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 6h5zlu3xcuaq.8h y n.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. 7sz;ajdi l 2pcq-qy 1*5–46), what is the upper limit on mass m if it is to rebound from jzyq s-1; 5l2* idapcqM, slide up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. j6,jl96wxf 1urxc a b,Figure 7–47 shows the planet Saturn moving in the negative x directiwj,69l,a cjf 6uxb rx1on 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