We claim that momentum is conserved, yet most movin..ki9uhc ci49 4jsj6cgb8 pr/e na t*sg objects eventually slow down and stop4.h9*icscj 6k. b /g 8asptej9iunr4 c. Explain.

When a person jumps from a tree to pl:t pkf0x.*zthe ground, what happens to the momentum of the xp lt :.0kfz*pperson upon striking the ground?

When you release an inflated but untied balloon, why does it fly across thecr9d+ra c7 m. 9y5icdg room? c597r+.dymdrg 9 ciac

It is said that in ancient times a rich man with a bag of gold coinsd,c-*tu.kwaq i fbe-c28,pijo q - xg1 froze to death while stranded on a frozen lakec,-w,oj*1- ix8uk -2.a ebtdqciqg fp. Because the ice was frictionless, he could 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 when it is far out in space and is essesg+(;odi r (ivntiallyro;ii dsg(+v( in a vacuum?

According to Eq. 7–5, the longer the impact *-n- r,wm 4jrzs.pcthtime 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 ac.-z,nc-mr4w*rjh ps tts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisia d)/0 9a qmyedai0y8)y *pofujloh6.ons. Today, though, cars are designeu/e la 0dyy8ajf0.q pdy* o6 )io9mha)d to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a bef lu9 h2:ei0ysd v1f+all tossed in the air by the batiu0v+2f:9h l 1edysefter?

Is it possible for an av;3gvzh9my 2u 0gjd- object to receive a larger impulse from a small force than fjdu 9mzyvh03;v g a-2grom a large force? Explain.

A light object and a heavy object haves *gm-mllih,1 the same kinetic energy. Which has the greater momentum? Explain, -i*msl l1mgh.

Describe a collision in which all kinetic env2/f5q18tfhs wr7 rrzergy is lost.

At a hydroelectric power plant, wa(*. elmie/+u orjfgp 6ter is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine b egm+*. ijr/le6uo p(flades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at1- ,w+miqa vcy 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 z,wsm2 v 47hmb4hiqg+h 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 our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls4bw+hh7,g4sv2 iqzm m and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in your arms?6hsdu0tn ;f0uisf 8 7v

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is nohmx te/yfu f9ev3 lq*2r c6zay-:;0eet true for your arm or le: 0/zy2re*t6- eeacf;u qyv x 3efl9mhg?

Show on a diagram how your CM shifts when you change from a lying pobh r9ve 428s:zf 2krv-g4reddsition to a s9vs4drreg kd8z22v r: fhb 4-eitting position.

If only an external force can change the momentum of the cenhuyp;j06uisuw65 v,s ter of mass of an object, how can the internal force ouw 60 h;pjus syuv5,6if an engine accelerate a car?

A rocket following a parabolic path through the air sun,(4 otq6ggci ddenly explodes into many pieces. What can you say about the mo,o(q 4tng6ci gtion of this system of pieces?

  What is the magnitude of the momentum of a 28-g s7zf ;u.v9 0e zjhgvc3uparrow flying with a speed of 8.4 h9vz0;uefz.u3jc7v g m/s    $kg\;m/s$

  A constant friction force vdfqu5zp7 .1 aof 25 N acts on a 65-kg skier for 20 s. What is the skier’s chang15upa.d fzq7 ve in velocity?    m/s

  A 0.145-kg baseball pitcgyixkjs9;kwbk375md 1 0wa y2 hed at 39 m/s is hit on a horizontal line drive straight b y7k5d a2 sw1;9kkg xbwj3m0yiack toward the pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a speed o n9)iy2/zaub9 9smdv.rl curudkc 8rz0 4w7k)f 10 m/s Fig. bw)u2vd 9n 9 srulir0a7brudyc9k c z4k/)8zm. elow 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 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted*,,ocqep qh:dl8 1o jz on a rocket, given that the propelling gases are expell8,jp*:,clh1dq o oqezed 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 7d3hfi 0,)cks25k ;z;eep-gpqquq f c4.1m/s on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at qkhf zs ppuc 3kd-q ;57f;gee0),c2iq5.5m/s in the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictionless track with l:to8.zte:z6-ds1ty vmmo 9 la constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car1.zdvt 9 8lyem: om6 :zl-ttos’s new speed?    m/s

  A 9300-kg boxcar traveling e79rk3m 8zxl0dal bh2at 15m/s strikes a second boxcar at rest. The two stick together and move off with a speed b3exmr0lhl82 akd9z7 of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds 5 flzf)d, ,xqbcan 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. Assume the person is 1.bqzflf)5dx,, 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 c 6 i 1p-2cl-ez(p fdwfrt4f.qskd zw-40mc7tyonstant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car atppze62 -(f4 dctfqr z01stw.c-f-liykw47d m 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/axe*4ayep(-ok wc7i 9s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 35 ecy-ax7w pko4e9 *ia(0m/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 cl6+4hmgvbgwrhuo2 eya42nfp- 87 uhn 9eanlhfuym 9n2hw4 4bg r68uv 7+p2-ne hogay at 170m/s If the 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 rocketi5wf4cmx3/5w ibgy ce6k-r6 s is traveling 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 travelinhf*p k ft7u:q0*pb:bz 1nyil ,g in outer space with a velocity of 115m/s To alter its c1fi* 0pq:u 7b:* zftynh,klpbourse 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 speh s;.xxzf5g +s*a .ptted of 45m/s The golf club ;5xp ht s.zg.tsf xa+*was in contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s anddb+-a2xutz 7ym tgmvt4 mo(6fh5+ pphno8 7 )o comes to rest in a time interval of 8.0 ms. (a) What is the impulse ha7ovo ox)t46bf5t8mnz7 p+dmh2 gumyp( -+t given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg ahizeyp.dr s9zx7+8b b1. p o(ond 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 arg.bk w95:e f 8hbtti-utomobile modelt85grbfe.kt- 9b: hwi s. 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 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 east and is stoppev;3vq 1e pni6td in 0.75 s by a head-on tac ie;3vqn16 vptkle 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 dlaq,cq a*o,a( ,hlv: (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methodaqd,:a (qlac,,*o hl vs 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 l cu;3whh )6) ro (ounqcgylh5x0ch51u ower leg bone of either leg? Ignore air resistance a x3hc 6 5(u )1ycc05qnuhol;u owh)rhgnd assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg le(9k 1e 4,ff apdk)mxmoving east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the ) 9amk(pe,lkfd 4f1xe 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-on collisi+dgnp(7cit lr(* eu.ion with a 0.900-kg puck initially at rest. Assuming a perfectly elastig.7*+ulp( iitdcn( erc collision, 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 perfectly elastic head-on collipx p22mzyc0 m yv-q :)/gkxln2y;n hi0sion. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be ycy2n0-:g x2xzplmm);v2hy /0pq i kntheir 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 a spee8onwm ( /i;p) zjyabl.d of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it /)lb8 p;an oi.zyj( wmat a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg 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 imhw-4 tk 7epi;t o*i) aexl6us8a y-)qs moving with a speed of 8.5m/s collides head-on and elastically with anote)-t4 -il p8ui6ox *); s7mwaty qakheher 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 collide elastically as oneyy)c*)xn6j 84a+ycqvztt 0rh approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450*)hy )6zyvnq40cyx8+ra tc tj 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 second ball 5p; rxuvz6-q) ig3*fuidnr0 ,l/ejnuinitially at rest. The second ball moves off withie-/ ,f6i n0 * 5l)urgxnrd; vqup3zuj 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 u cej*2m tl:6oa2jy0t 4 8yauuslides 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? [Hint: Both leave the incline *cy 8m6a2:j u4 j aluy0ttueo2moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object c j1dnq 6 wnuh33w5 v5l9qg,mv-q4jmkof 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 ,l7gdv/ z) ytqexperiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twicetv )l,z7ygd/q 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 n;6y i)tk7l umtraveling 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, wh7mu) ytk;i l6nich 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 krfan+a1p( ./oeld p*linetic 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 re3,q8jwjh uch .st, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, hoj,.hqhj3 8 wucw 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 cofh,g dw-cnw-1 llides into 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 before stopping. The police officgn-1wf -cwhd, er, 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 6pkwy+ lk* bh5rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its energy?pybk w* l+65hk   

A measure of inelasticity in a head-on collisiono7z)3egq*l a4c )jkt,f 8r bwf of two objects is the coefficient of restitution, e, defi b)ff)q8 kzlc3ajgo *,t4rwe7 ned 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 time k3j0betho8c: a6 d6cfs the mass of the other. A depression is made in both faces of theocc3fk68 b:je6ad th 0 cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on w,hud 5ow1m .vlith a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity 1 ho.m5vlduw, 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 electrohpc -d249 bod n5y:i7vo jq1vvn, and a neutrino. The electron and neutrino are emitted at right angles and ha h2i:y59vc7b1 vpddn4joo v- qve momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of m, i bmihgv29;bjzh(i+jwmm - 6ass $m_\mathrm{A}=0.400$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 * smg estduav(jb.;q t3.0yq1two objects of equal mass, each ha .j;sevqs t0mt*(.3y1d bqaugving initial speed the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at rnhw)poe-3miz zv; h 86lg n*n7ight 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, avnozhl6zg)7;w 3n -ni8e pm* hssumed 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 perfxu p* z 5m67*uuuoz62am0;x lcj 1vcnwectly elastic collision with another atom at rest. Afte5p06 21 u*uuu7c; jlmnowa*cvxzz 6 xmr the 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 collision with another atom a6vyuw(1vdi yw3knq +j5 sr/+jt rest. After the impact, the neon atom(vry +6jww si5d+unk vjy/3q1 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 sh )m.qcjt0x4 ;dv,zbsh own in Fig. 7–38. Specify relative to the left-hand 1tjmqc sz;bd.x,4hv0).00-kg mass.    m

  The distance between a 4sq ( j-lsgl7wcarbon 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 tp3kq3 n1 3pi9 xqtq6r2.50 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 pkt3p93r q6qx t31inqseat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 /kx8 iujqh63mo6kb zwr) 8rjg2vc51d 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 c6bh6j8 c2k3oj rz)1/5kwu8 rgxmdqivorners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side r;sj.vk:f7tyoj. azw* ybc/1s $l_0$,$2l_0$, 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 iefih5+ho:(xgd c mo-+ ch 3+gxfr/5ydg*rcx9 dentical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the ho 5(h-+i*/rf:r hy xg ggc5edchodm+c o+3fxx9rizontal 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 76,z 2s njssi8ceus 9ca circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R fro s,6 8euss7iscz2n9 cjm the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calculattahljx p*2 r h1)n-5rhe th1rp j xlhah5h )2-nrt*e mass of one of your legs.    kg

  Determine the CM of an outstretched ar:ji8 t ;ve(brwwe(4sxm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent0rb xrvg1q/ z+,u8)yxeznq 3s at a right angle. Asvr,8bz0x nyqes1 uz 3rqg+/x)sume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such thg d f9(, rovn6a2r5ao 8fazf5yat his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far belowfv25a ,nrf og89z( 6fa5roy ad 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 ar-jdu ,tepy/b1 e $5.98\times10^{24}$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.-e 2iu-b k9rio
(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 cyli a.r038v ,ag 3nnfcdepndrical 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 handle is the. 3fpd0 3ra,agvc enn8 point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform i9r 7ngf.))-1qgz (c/gn;ajfo- xi2tmy yegbcylindrical 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 tossb9 fq)y2o x. g1 z/n(t;ngc-j y7gfgem)ia-ired, 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 7–14 (Fig. 7l igbs(i:( +;gdamtj*–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 M3 s.s9h9aq bkdqq+ 1yn, are in the air and stationary 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 direction (relative to Earth) dqak9qyb9+d3 .sh1 qn soes the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a vggqmu;o+s 4a1 ( nt;fbat and is popped straight1;f;asv4u+q tm( ng og up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with sm/keo(e sm cd, / ,qv3 g1foif8cpmj+: v)hpu1peed $v_0$ 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 j 03h9wihc-. ico)xrt shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this wtx h.)9i0ro 3cj-chi being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by p6m: nk1spqe72 jt fal)ushing off with his legs from an 180 tnq slf1:ma kjp7)6e20-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,p*hnrrsu :vke f6+s6* are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut has moved 1+ r*6 v*fksh :pner6su2 m?    m

  A ball of mass m makes a head-on elastic collision with a second bavj 5 eltb(6y(kk:xhb ,ll (at rest) and rebounds in the opposite direction with a speed equal to onet((keyb,xl kh 5:6v jb-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 .y(5jvb q9nfy*yh d8+3 xsoydin 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 ydb35ox8jfq dhy9 s+.yv*n (ymeasured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concc,xll 7u5b jb3 n0aae*y.b)jyrete 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 diy b0j jb.cyn ,u xll)3ea5a*b7fferent 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 ad+.is 1ag2 wnlt4. *g sjbic.wt rest directly above it. If the bullet has a mass of nca*ti.wji1 sdl.sg+b w 2.4g 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 wood placed o oavmhy6 m:jn5v,vt io0;7 al*n a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, andnyv5*oiaj 0t vhm ; ov7,mla6: 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 in a xzp,m9 oe2y*ft17 m)fnjfny2 ph 8:vq rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sit:fxtyjvf *yoh8)e2nm 2pmf ,n p1z9 q7ting 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 abao( ro:zzbs,- *+(xw+pdtyyv9 gbl*d out $ 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 ycro9odake;4, na4vnv8 h5-cnae6 e 7suddenly broken apart into two fragments by an explosion. One fragment acquires twice the kin6 eaneh94vo,o cec84;nrvn-5aad7y k etic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by4xwbk:zmk-ef tj* j;. 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 masseslpl7: s. 8ea9ycjt5e h $m_A$ = 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 radioactiv)/w ba8, th: qha7ouujely into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpht/),uaw ah87qjou:b ha 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 (cla27kfamf0 sr6j y target) 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=2.2 qfz*6zq 2(g-kt;ou 3xpd4rkjcg2 (dokg slides down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), wumt61 atxkox;51aq l-e1 wjh8hat is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collidu tax 5l-mx 6t1wkh1;8qoeaj1e with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot e:p;yj;i ia) yoffect. Figure 7–47 shows the planet Saturn moving in the negative x ) o :a;iyp;iyjdirection 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