We claim that momentum is conserxt,im kuvj9 ,hq) .l w;cp0l)xved, yet most moving objects eventually slow down and stop. Ei ). wq;,mlvx0k)pjc9lh,xu t xplain.

When a person jumps from a tree to the ground, what (sr/o gi s*:pphappens to the momentum of t*(pgispso r/: he person upon striking the ground?

When you release an inflated but untied balloon, why does it fly a eemb27c2 zvjjc l2c8)cross the room?jv 72282bclz jc )emec

It is said that in ancient times a rich man 2rq w.ojway k a(2(h,hwith a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he couldh2y ow ajh, awk(2qr(. not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction whd,pi7+32xmojpcu 5xt6 adh4p en it is far out in space and is essentially in ajd7t d+ppxh,6 5x342uocap mi vacuum?

According to Eq. 7–5, the longer am dy 4kid2mb6**4vbli*, yq mthe impact time of an impulse, the smaller the force can be for the same momentum change, and hence kbq*dlm*vdb, m624y iay *4m ithe smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possibles xxwhn1t +p-/ to withstand collisions. Today, though, cars are design n-h+ swpt/xx1ed to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than )zweo.d)tr+ c a ball tossed in the air by)dwoe zr.ct) + the batter?

Is it possible for an object xgkpa.0ex y/jk+:1 c ito receive a larger impulse from a small force than from a large forcx ya 1:xcj+ epkk.g0/ie? Explain.

A light object and a heavy object have the same kinetic energy. Which ha43 9 gygr;1-zesi3m)wlgit:y/ tce gvs the greater mtc ieg)e : 3-mg49r/;g3vtwz1glyisyomentum? Explain.

Describe a collision in 4bevc r*p9e.xs +kjz. o1f 2ivwhich all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against d: 5.b f(5n gef/+ncomhwfmp3turbine 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 dew c53fn:.+(p n/h dmmb ffego5ad stop, or so that the water rebounds?

A squash ball hits a wall 2qczf5mqd/gk5vypq d+ 8+ ;x oat a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixed to the Ea svq +bv m,jzu-wohlgl32-+r*rth), 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, duri-w l+m+ul-jrvs*,vh2z3bgo q ng 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 leaqhw(d1ymj2*rz2 du zuf 4w8 *zn backward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas thi1 iuungp(r )nz2/( bhfs is not true for your ar1fnnu2( pr)h giu/zb(m or leg?

Show on a diagram how your CM shifts when you change from a lyinm2ecgh.p6oh: hm ; lx5g position to a sitting positionhh: pmog2lc .me5 hx;6.

If only an external force can chane fte;v40wufr0igmg4wl ipb3+y*0 d5ge the momentum of the center of mass of an object, how can the internal forc4eifmywlv efb0+gr0 g u;p*3wi 50 dt4e of an engine accelerate a car?

A rocket following a parabolic path througagfl2 6*t)exuh the air suddenly explodes into many pieces. What can you say about the motion ote6gfu)2 l ax*f this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow p- r n73nhxa*aegyd(u*tt2p/ flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N l2 uegb22bobh)04p -m*ertyi acts on a 65-kg skier for 20 s. What is the sklebu pbe22hto*)4r0yg bm2 -iier’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s ise(r+ znp7cf b. hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time betw7zp(.e bnf+rc een bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with -,jw/, cd jww3-c lsq*itsc9g a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 3wj9tq*igcj wcc/,d -sl -w s,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 propelling gases are6ccvpq,h+(w5uyqw ra*0n82j tp 9ejk expelled at a rate of h( uy05kajc 6qqcj pt*e982nvwpr, w+$1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback move)a2zvz:ott-s,r;9hb h c .hying at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless tracko zfo1oh7vdxz,jejwm0. 0edc(;/ yo- with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be v( cjfe-zdoz oj o7yx/ d,10m0weh;.othe car’s new speed?    m/s

  A 9300-kg boxcar traveling a lx4:iio(z pi.dqz.. ft $15 \; m/s$ 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)wcnj dk58(bdo tp.u1 can whip horizontally at speeds of 100km/h If the air strikes t 85d )kwu(dcbno.1j pa 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 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 8.6m/s on a lmwq j0gbq1h(dc5xqo6xy9p*m6-6clzw * dz0 f evel 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 90.6-0b xlwhyp6w6*5m9cqq 1 xoddq( fzjg*0z mc0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in thej ( ns6/jfz+zf direction of its velocity, and the r fz6(jjsz/n+femaining 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 emitted?    m/s

  A 23-g bullet traveling 230m/s penetratesd /xnoxkbuu65g9 wj yz ;2+up5 a 2.0-kg block of wood and emerges cleanly at 170m/s If thjgb6u5;ud/oz2u p+w5x 9nxy ke block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling ate +g3 wu.akgblm9+ 5np 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 ma;nmw mr5c)quh;. jlh.wef)bz*9g a* oss 3180 kg is traveling in outer space with a velocity of 115m/s To alter its )z*5; lbqwcr9g ;)mmehf.njowa. uh* 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 atkmrd wu-2pu6g1rbdj mnk(s v -;/6 nh, a speed of 45m/s The golf club was in contact withn6k- 2 n vmwpr1m;/u(d6hu - skgjbdr, 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 velocity626zf9 o; ls1a8bjsl 3r:8bo/xnbh ask g)lqp of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the imp:/anb8 q a l6bg6 9lojlh8kbps2;s zo)x3sf1 rulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass k8thjpa 93 p;rm=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 n (+* whfx)ze;ssiy.ox:g:ue s ew automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average foefue+s; )s xzx:i:.(*hwgso yrce 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,kygf8u :s :sr0u0nxs the east and is stopped in 0.75 s by a head-on tackle by a tasn0u fk,:ur y0s:x 8sgckler 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 .*mw57oxk qx/uab.v t kg) points in the +x direction and 5xkb 7 /.wuq.mvt*oaxis given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum heig8pj. xvrw7mlos a)73spumd;8ht can a 75-kg person jump without breaking the 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 staasdsmp78w)8uv pl3 x7jmo . r;nding 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) with a speed of colc7wl3 5o.hxt vlpz:70ulla*f lides head-on with a th *5pl7ll3:cuz w0 o.vf7axl0.220-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 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 witb+ nl(c85lh qmh 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 will be the speed and direction of each object after the collision?Let A represent thebml5hq lnc( +8 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- ufy,jioh k tzbjzar)93)7:j +on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s iyj9h ,j aj3b )zfr7uzkio t+):n 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 opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with aqf0 vnxb1tbs+x51 6np speed of 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 f6+x5qtb11vp0n xbs na perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed y.sd wbqcz:-1f6s,vy :ssy -vof 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softba,vsd:yzs1 v bys.-sqcf6 -wy:ll 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 ap k:) mi*b0dq6m(fvg js one approaches the other 6)bm:fmp v kjq 0i*dg(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 calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a selw h5l ;nk*k:wcond ball initially at rest. The second ball moves*;k nhl5 kwl:w off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as shown03-bmih*7/gltz v16t 5bp ycsn7 yv gn 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 offgc yz-7b m t sv6l3/g1ph5n *i0ntvyb7 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 of rjpy06y8erb0a( h+ zxt nv(*bject 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 h ec:yq9m xk4q5bmkcg8u:q+h:of the pqhx9 e8:4g:cb uqmykk qmc+5: endulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s burldqp**p98 :crq rrim ls,:e i+ies itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in s:rr*p9cl*,prqledq +ii8 m:an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the frac(ltmj -djv )7ntion 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,5a; 06vsl(o5 ezghgnf 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 each piece acql60shfgo(5g5 ;eanvz uire? (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 r5ri s2m mh;5dfear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the5r; dfsi25h mm speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height of t. iz/g xni:ipuy7g/c6 q:2jf8 -m ortlq)1bm1.20 m. Approximately how many rebounds will the irimu.t)gx im by7/-/ :cpl6o1j2n8 gz:qqtfball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision o,k + 3iwftk-zgf two objects is the coefficient of restitkz3- wi kf,+gtution, 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 of theh+bg3dnelpgk5b, go /90)3g u g; emrg 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 reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and3bmgke) o 09u/ l gb eg;53,g+gnphrgd 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 (a8heqcsek 3e: u,k9z)3qlya in the +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direceusqalz8 a:khc( y393 e),qe ktion 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 restkg9o nk3 qb mavis*c4(xc41 ( a8+wlz)dguu,g decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted ak mqz u,ug( 1a(cx4 bo id4s cv98lgg3kn)a*w+t 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 masqa;bt.xasi 5f .yy72ss $m_\mathrm{A}=0.400$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 inelasw4(+btq 0u kwt7ibac( tic collision between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initi(a47b(cw+b tt i0qwkual directions?    $^{\circ} $

  Two billiard balls of eje(8ttqi pd +y1o- gf8qual mass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along1dq8y o8(ie+-t tgfpj 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 ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with another atom at q/sl)n krqatpt1cf6 o;0hx( 7rest. After the;q co san61k /qt)xh0p7( ltfr impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collisa zgqat3nvc()o,p (hkn39fg 7ion with another atom at rest. After the impact, the neon atom travelspq3kntah) (vngg7ao(zc 3, 9f 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. Speci))tc(bf0zj 7inh 9w bsfy relativ9i b0hj btcnw)()sf7z e to the left-hand 1.00-kg mass.    m

  The distance between a bag8e(tn8+okx- z fc ,carbon 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 fro5m;.t/tnn xuont of the car. How far from the front of the car will the CM be when two peopl5.tomu/ ;tn nxe sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 1899y+ berkz qhv0+4w fo1ugo( p m by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryb4fw+yp9kb9e uqho z1v+ ( o0groat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesq i ;aenw/*k,v $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of i;na*gkj nr dm7xlp *l +f5l2o5dentical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane opera;o7a5 f*2xlrknl*+lpdm j n5 gtor can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circu0w+ryari-dll y4 ;vg .lar 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 ai0y dw+4vl.l;r gr- ycircle, 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*4z gqgln qr75, and calculate the mass of one of your l *5rg ngq74lqzegs.    kg

  Determine the CM of an outstretched ar0pjm6nl pi00r uem3y4m 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 arat*bna d24ek+m bent at a right angle. Assume that thk+d2b*at e 4nae person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs arw) pa9,9tc bm b41xss.d8o tjhe hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Useb .hsdo9b14)xamt9 , tpcsjw8 Table 7–1.

The masses of the Earthz2o+9eu tk)69 yn7 shk .vdczuq2 +okt and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg mankk+tq3pew *u4 stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diameter 0jo5k lctcd0-;.0800 m mounted on a uniform k0 o;d lc-tcj5cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cyngzz h5c)z9 z;lindrical 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, s5g)zc; nzz h9zpinning, 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 Ex0 f/j9zq:9wqn. kiz kaample 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, are in the air and statwp- ai30q wa2qnz2f*x ionary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and directio0qwa*p nx- q23 fz2wain (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 poppe(-t.py9p- 3 v(rd ex(k*zsmi6)ii yn5 yalwyod straight up to a height ox6 )ywy-lpv* y5(ky9e(mz ri3 pi ( tondis-.af 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 traveling 1;xv-u)6ddh jvq;s7xk s 8udsf0 c e)fwith 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 / (g8dy*y)k .*odhvze 2gjnox in Fig. 7–43. Relative dimensions are also shown. Should the player bgjd*d yxvekn) g 28*.o yz(h/oe worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut ()40k fcte u qb;x8xck5including space suit) acquires a speed of 2.5m/s by pushing off with his legs from a c)k;5 k0ufxx4 et8cqbn 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 initially at rest iywj 3fvj6;l-d 6u eb:wn outer space. They then push each other apart. lv;:jb e6ww3 y-d6fuj How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastics +-2lwam + jckzfgj)* collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fo)z+* jwfmc2jl ks-a +gurth 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 btm4g k/xv3mv*9a qd23anb 3 xexpert witness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show thd4n3ba ag*v/v 3qb 2tkxm 39xmat 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 skp* yine63yf1 teps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a differi n*yf3pke1y6ent 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 vertically into a 1.40-kg block of wood at rest dyg;;ua 3me7rphz9b p (ppw56firectly above 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 becomesgb9h(p;z;f pe6u pywpa7m3r5 embedded in it?    m

  A 25-g bullet strikes and becomcfd4ocq+)c bnp7 d:o:k)je-kes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comeebc:)kc+ dpf74qc nk)d : -oojs 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 in a rowboat of)j5 ;i eej ppcqo/0 bgzo1-nn: mass 80 kg. With theq51); /n cjiz0:o-eo np bjgep boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was anfp.b+ a/w-e jbout $ 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 tw+neafmj +be( lydh 243o fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of the+b3nhe2mj d(ayl +4feir masses?   

  The force on a bullet is give j 5kqe/8:m4tz5ud yadn 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 masses a,a*a6 cavz*;+uyli 9uzx)ke $m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha particle and a sma7a4vs xw kkabe(l(v 3/ller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha x k(( sewaba34l7vvk/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 tagvumm04- k--j tg (rqrrget) is fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides downll4 idh3gb66./cg *h9e + ufb3yxemot a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mass m if ,5i8 mmn i1 +yndmyaqi 8/ws(dit is to rebound from M, slide up the incline, stop, slide down the incline, and ci,a8wi y m m5n/+sd1y m8(dinqollide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshovgnz i dx51bf01 jajufxt89 (;t effect. Figure 7–47 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 of Saia (5nj1f8xbxjzu ft1 ;vd 09gturn 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