We claim that momentum is conservp2xk mb* fu.1wkh*h,e sf17 oied, yet most moving objects eventually slow down and stop*m1hwefo72 *xh uskpfikb 1. ,. Explain.

When a person jumps from a tree to the ground, whaobqe f8yj. 35c 0)tx-gvak/pqt happens to the momentum of the persobcv0/ 5a.-fjtq okg y8pexq3)n upon striking the ground?

When you release an inflated but untied ball bejwn .kwv gf t*dm3n)4cp;)ew -oq8(oon, why does it fly across the room?wv)38cp.*(;-ot wb)mkd gnenfw q4ej

It is said that in ancient times a rich man with a bag of gold coins fr6kon+f0 vv k:1m,8b lsh(naa zoze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself toan, 8 noab 106vvfzm(+ lskh:k shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is wzt0 omz; 3l*pfar out in space and is essentially in a vacuum?o *m0tpw;zl z3

According to Eq. 7–5, thx tzyu3,1h ,ab3;3 8q./gyyqjmateie sxd) :ue longer the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this bas3 )j1qt 8;ya mqe/3yi: adzbu,ex,sh.3 xgtuyis, 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 possguu 7s 5a2j z7:.2epc (rjlorvible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advar s jugle7oj2.r:(za5 u 2cpv7ntage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in th9 i:b. 20:sfw,vz((e gdoz bzbtc xri4e air by the bat(e ,4sibdz:g i0(cvftzo r.2bw:z9xb ter?

Is it possible for an object to receive a larger impulse from a s ii ;jzp8l*+p9gq:mlu f1*ebj ezku /1mall force than fr/jl *mjzi+ub:ek 1*pegp9qu ;z if8l 1om a large force? Explain.

A light object and a heavy object have the same kinetic ener 6xtrglfq- 2sgpd+k5*gy. Which has the greater momentum? Explaq2 *d- klgtr6fg +5xpsin.

Describe a collision8x9mro)3exv clr(n x 5 in which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against 8l.8xsrte67f-h stjn turbine blat jn fl87e86t s-.xhsrdes 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 wall at a 45*guh9(erpgk a+x v/q ( $^{\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 h onto a hard steel plate (fixed2wssn r9;l il2 to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a s29wll;i n2srpiece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when cl+gwq5k*me3 xek1p)marrying a heavy load in your arms?

Why is the CM of a 1-m lend*mi9 xo x7sd)46n 5ydjdo:awgth of pipe at its mid-point, whereas this is not true)d 9oosj*i mx67ddaxdw:n y5 4 for your arm or leg?

Show on a diagram how your CM shifts when you c4( 1-st674uqolzzx ckx-bm u ehange from a lying position to a sitting positqsc t47zo6b-(1uzu k- xml4 exion.

If only an external force can chang bh.w)os35xa fe the momentum of the center of mass of an objectb)wxoh3f sa5 ., how can the internal force of an engine accelerate a car?

A rocket following a parabolic pathy6xpvu9 wju uvx/+( r9 through the air suddenly explodes into many pieces. What can you say about the motion of this system of pi9+wyxv(p 9vxur6 uuj /eces?

  What is the magnitud ase dje/:1w aei;.t5ue of the momentum of a 28-g sparrow flying with a speed of 8.. sjd:ut 1e5;e ie/aaw4 m/s    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier vgyotxn+uhrq8 , 4 w74for 20 s. What is the skier’s change in gv 8+ wyuroh t4q4,x7nvelocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal li 8f-rmy71c3yga4ew fsne drive straight back toward the pitcher at 52m/s If the contact time between bat am8cesw f 3gf7 -r1y4yand 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 6.4jtc fftj3-g . m2*9on yw5r+fj0-kg package out horizontally with a speed of 10 m/s Fig. below Calcula*f +ync25.toj gm -twjffj9 3rte the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerte0iwb u)ht1x*0zqrx (-tynn 4i d on a rocket, given that the propelling gases are expelled at aiwu*yi th1nxr)z q (b0t4 -x0n 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 apparenf) 95jpm gkus,l, +lwnlvr5p;t breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in thepjw u n+r, ;p,)mfvk5gl9lls5 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 nnvmt, hdy3 9g f6s0(5c 5sogrels5(v a constant speed of 18m/s A 5350-kg load,initially at rest, is dr nesgr(d ,v53 smvltf(5g o 5hcy9sn60opped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strib.848bu7iz 6grks og-pb ei)kkes a second boxcar at rest. The two stick together and move off with a speed of 6m/s What is the mas 8i.zk8ke-6gg ru)4p b ib7sobs of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speeds oi6ditq 6plsc y;.vzw,3c4) zuf 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. Assume the person is 1.50 m high and wzzcyql66d 43i ic )sp,uv;.t0.50 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 witp+ -gegist3t tfd z;9*h a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed +zig t ptgf;e3sd9*-tof the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alphaq*elrqclcpl c( / jd.p.*sxbu ;: 77sr particle in the direction of its velocity, and the remaining nucleus slo c*c q 7sljsqr.*lub .:xpd;pe(r7 /lcws 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 4uw/ ypc1fz)p of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless sufy p 4zwp/u1c)rface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveli w(*b36 c tec6yrhktid,,c s,fng 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 ouum r+ cxi,h5b7ter space with a velocity of 115mur 5,7+ibxm hc/s To alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a sp9s8;d xzok r/feed of 45m/s The golf club was in contact with tdzxo9rf /;k 8she 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 8.5mqu5 h;*-gnd1sdoqy9w+c *yqf /s and comes to rest in a time intervs1 ou dw*+qyg; dchq9yfn-*5 qal of 8.0 ms. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass,e*7jf q ,wgal m=0.06kg 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 automobiu(y39f uoqt6f le models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.1(ytou96 ffu3 q5 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 thef00 e 9sr4zy1kx7w2scif rh;e east and is stopped in 0.75 s by a head-on tacklxwfise hkcrs0ey9r 1f74;0 2ze by a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.01.r 7 ndk*hbki60 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of .bin7 dh 1krk*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 without breaking t 7evo :m2*)d kbusd-fxflev pijd539,he lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of2jd m3o fd -57l9vi)k efv*ub,xp e:ds 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 sp0pf,zegsesi- 8u0 f .xcw+ vr1eed of collides head-on with a 0.220-kg ball at rest. If the collision is perfeu 8 c-rxef,e00 vf 1zpg+wsi.sctly 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 7dsxlzt ;afh18vaqim jr 1/ /1east with a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what wilha d rli q/s11t/7j1fv8; zmxal 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 perfectly elastic head-on collision. 0//dypic q 5g ctvywa9ph/- .tIf 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 in the opca 5pwy/pv q/ g itd90/cthy-.posite 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-oraq303 m6opcbn 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 c pq6b3ram30o speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that hwaf gp/6-hbba z1)hf9 -rapy4(g. ihis moving with a speed of 8.5m/s collides head-on and elastically with hf41 yzg/h.aipb6p)hb-h9r a- aw f (ganother 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 ridhj yssnt0d6jr*hg(t l,(l 7n.e collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is movingrnjd*tnhlj(7 (sh0 t.6,glsy 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 collisi0go6-q.scd3l b (jm tfon with a second ball initially at rest. The second ball moves off with half the original speed of thjl(o6.g- mtq 0csf3bde 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 frii 3(ap0bi 9yklctionless 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 ab3 l9kpyii 0a(nd 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 objectul(2u;kal02 -gv *c-tsttgoo of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a maximum height 58yqjdm w4 1r7uwph)v5f+wxkh of the pendulum equal to 2.6 cm. A second projectile causes the the pendulm k wyfpdjwx r71+54h8qu 5w)vum 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 3.6-kg)qzh/is ,2kms pendulum hanging on a 2.8-m-long strin2h,sqk/ ms i)zg, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kineti/pyn upxf ,pz+ z*i 76ieom1y2c 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, ini - fgin r8qor7b*7nz)/ .skzlxtially at rest, into two pieces, one of which has 1.5 timezr.x)*zq7n/7s k noblg 8fi-rs the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end ofc.aq4pg: g-nc 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 coefficie p a-ccgg4.qn:nt 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;n w rxwa1nww3hk.9p:s to a height of 1.20 m. Approximately93rkawnn w;hxwwp . :1 how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two oaglx du /79b-objects is the coefficient of restitution, ebugoax -d 7/l9, 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 inxt2 tch*d*y3yyw2 och)z8i0 eto two pieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be pt32ty80 )yewohix c*y2zc d*hlaced 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 with a 10dx pw;0xq5zo uwy ((r:.0-kg object moving in the -xd5zr:pwywx0 ((uq xo; direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into ah*w+0f d qxr8h8;m uua second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momenta ofw;+fm a q*uur880dhxh $9.30\times10^{-23}kg\cdot m/s$ 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 mass6 c 70.hgeafu 9i1bpxr7 qzkf8 $m_\mathrm{A}=0.400$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 tc93clozbl++( a1fo 9b+ahcu xc)gx;uwo objects of equal mass, each having initial speed the two move off together with spe)a u9+c lxh + zou xcab(9+of;3gbc1cled v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass j4o:4*eegfinjfu1mz(*cwf;o1ws u ( move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of baluwjf(m* j ( 4*f4ucnze:e1o fwgosi;1l 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 wi4.aouw+5 flna,yiv; kth another atom at rest. After the impact, the neon atom trave.+i a,uaf y;5vnkwl o4ls 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 perfectly elastic collision n0f+mlfxb64 o *eajj7 2.ybl rwith another atom at rest. After the impact, the neon a+*o4jl eb72f0jy bnm r.6fx latom 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 th d.vlauqm0g:xf8q( -grlzm 5f3iv(;ue three-mass system shown in Fig. 7–38. Specify relative tog xlrvfd qf ulzgi; m a03uv(8.:(m5-q the left-hand 1.00-kg mass.    m

  The distance between a carbon atomw5py) +m mrzo 4)k9on5,ygwop s pq/2r ($m_{\mathrm{C}}=12\mathrm{u}$) 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 1 9yxkt*hrn5b:050-kg 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 th h: kryn*59xtbe 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 0rvz--kmf 3ra, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferk mrv-3 zf0r-aryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidekw-ww/ 5qa m02ip .ywos $l_0$,$2l_0$, 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 m1 n6t z2u 1a2hlz9-ef.htd c+rqt7umload of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the h.zdt 2 r-mt16e9aln2tumuc 1 z7 +fqhhorizontal 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 hdl,l;px*n)q *v6jx *z ai, srtas 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 *j zdnlxs6iat,r, )**pxlqv;center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proporti dksmbcr10m b7. t69hrons are the same as those in Table 7–1, and calculate the mass of on690kd1b r 7rmcbh. mtse of your legs.    kg

  Determine the CM of an outstretchedwq m4)flq u;pyl:5pn3 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 px8 j bxl4t4e 2vpr,r(iosition of the CM of an arm bent at a right angle. Assume that,xipl r 4vreb(j8 t4x2 the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper icww,j3lhyt 1i.20ey ws in a position such that his arms and legs are hanging vertically, and his trunk and head are horh y j2cl,ew10y.w t3iwizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon areif2 y)zeg ks.-wz(yo n0w4kk/ $5.98\times10^{24}$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 o6uvx d/ycy + fqadisc. -op.+a17s k1vn 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 cylind7akr j d8 itew)hdn 9y7;0tgw:rical 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 is0 )8 yr:gdidth; 79ewt wn7kaj tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diameter v.(/u 6l5tvu t0 gjg 8w/kdyav0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as showak.8dtv(v 5j /lgut / 6vywg0un 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?    d    d

  (a) Suppose that in Example ml)) v: w-yjyeuvc,n/ 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M,+ya-ek4mb 6 vm are in the air and stationary with respect to the ground. mbkvya-e+m 46A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is popped a9/ ,ib1;.u hi atchrbstraight up to a height of 55.6 m. If the con1i.ui b,aac9b t/h h;rtact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travjg+t-s86j1+ o5pcsu +bvievveling 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 sny ic h;h us)ro*1:5a )i sj9+5: muqevy8rkcwhown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a poc e+ m;yr5h):yjwr o1k s:iniuhqvacs *5 u8)9cket? Give details.

  A 140-kg astronaut (including spar)4c+dp il;y*i*qnzz :qjq 4a ce suit) acquires a speed of 2.5m/s by pushing off with his legs cdii:qpl4; z +rqnzy)jq* a4*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 initbk2rylxx j jt-( b;s6.ially at rest in out;yt. xbx(k2rs-jj lb6 er space. They 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 elastic collision with a second ball (at k8r k4l cksct8v4) r-3 *wsdmurest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What ivu c4*4rmrk)l -ckt s3kw8d s8s 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 aullr rj/si)40 xb 0/p.wfj*a aqtomobile 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 wq jw/4aix *.lrfs 0b 0)alrj/phile 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 -t.-b7w6 ohv ww swn/ntop of a flight of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the nbwwo7- t n/v6w .h-wshorizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired verticallycbwd,m55szbw, r a57e into a 1.40-kg block of wood at rest directly above sae rd5,m5 bwz5w7b,c it. If the bullet has a mass of 29.0 g and a speed 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 1.35-kg block of wood1g cvb f2zco4 h;w/k,o 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 tocc,g41wzb v oh/o ;fk2 rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of 469 *;y7m9 sfx kbax:xijtsif mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, thef i7 jss94a 9t;ixky6xxbm:f* 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 about ze/:zuwq7hb. $ 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 brok9cm vu v8 9r9laxiun3 as97qc6 f1uud*en apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of theiu 9939 ic l n7x9dv*qucmvua81aufs6 rr masses?   

  The force on a bullet is.vt 30gzd i;tj 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 massesco ).kizv*7td $m_A$ = 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 2byl;m70;xco , s5s uhuo.d bsdecays radioactively into an alpha particle and a smaller nucleus. What will be the speed of this r ;u0bmx;ho 7s.5 s,luycb o2dsecoiling 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 ,bx8 hv-fw)zk8 s u0gran 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 +ieepp yj(; u:+xt:igdown 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 uppet3u; awih )jt1wt./ nn:w2 bwxr limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the :;xntnua)w .21btwih wwjt/3incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slosyjm 3 ei.7s,,ap 8sdingshot effect. Figure 7–47 shows the planet Saturn moving in the negat3ao.es8dm7 sy j,,psiive x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s