We claim that momentumq ( b4zlfb0sdm9f6 6+e4uhx pp is conserved, yet most moving objects eventually slow down and stop. Ex4sp0qe 6b+bxzml(d fh 469ufp plain.

When a person jumps from a tree to the ground, what happens to the momentuzeunth -01s61r69yp dinm6so/d xg3 nm of ts gt61d6mn3s r0/9x - n y6d1ezpiunohhe person upon striking the ground?

When you release an inflated but untied balloon, why doesr4l)h-c kj l a)ro6x(b it fly across the room?l)r4l r-h )ac6xko( jb

It is said that in ancient times a rich man , cwju w82v; wzo kl2-i7vr*gcwith a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was l* rcc zwvw ;kw27u-i,jo8g2vfrictionless, 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 essentib;wz1p5*3.x xgw,pgth( y joqally in a vacuuop bh t*wxgjp5y3gwxq1,(; .zm?

According to Eq. 7–5, the longer the impact time of an impulse, toql)iaoc5r6 b 2s3x*k he smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the valbo)2a5xsrio3 *lq 6kcue 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 collisions. Today,g6k-5h; zq opbz5v4il though, cars g;z-6lz455qki ophbv are designed 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 ball tossed in the ak qbj1 sf6xqfes1/-; zir by ;j/ ske1 6fbqz 1-fsqxthe batter?

Is it possible for an object to receive a largert3w*zto:9 dvz impulse from a small force than from a large force? w3*voztdt:9 z Explain.

A light object and a heavy object have tfv 5twwn vn ,x*j1;03unfs-ks he same kinetic energy. Which has the greater m0f jw-vsfu,kx*s;n nv wtn315 omentum? Explain.

Describe a collision in whichke:tfn9z b7,k all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against turbinej3z5 8z;u0mrhtmj9mj u)q,bg blades on an axle that turns an electric generator. For maximum power generation, shouur,z8jgqj)th50bm u mjm;9 z3ld 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 wa;:.se5k4:4c k ubuqsdxxj1n bll at a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped9z*mxe u* **f q(tbp -ytn:8hznr3ho y from a height 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 proz z9uy(oxt-my*b en*8tr*f3hq *n :phcess? (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 falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load iwo w/ ;d*euwx6n your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is not .8h i )kjben-94murs atrue for your b iu8asr9mejk4h- .)narm or leg?

Show on a diagram how your CM shifts when you change o+*1g/: k9+ebyaxg a wwyj5vwfrom a lying position to a sitting positi+9 1a5 *gvyowxg/jwek ya+ bw:on.

If only an external force can change theg6qrhc9ll+ (d(ezzr - 1hywz / momentum of the center of mass of an objeccy 1+zr -d6(r 9wzqz/(lehl ght, how can the internal force of an engine accelerate a car?

A rocket following a parabolic path throupqbw ,7ne7a7vpf 8; sogh the air suddenly explodes into many pieces. What can you say about the motioas ,b78 pvqwone77;pfn of this system of pieces?

  What is the magnitude of the frltc/ t7bd.(momentum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a dj:fcih4eyf 9w;2 : ue65-kg skier for 20 s. What is the skier’s change in velocity:hf 9;:e fued 4cijwy2?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizont)*-/.trwbw 1u gcavuwal line drive straight back toward the pitcher at 52m/s If the conv- ubgrca)w*w./ wut1 tact 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 thhsnl0ys80x/c.ed 8 e erows a 6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat imme 0ydl se.n8 c0exse8h/diately 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 magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gasesc9 y(orq qm7:tpwxdk7qr z;) buf ,h,4 are expellew z97c,b4 u:tfkhoqy d;rx pr q,()q7md at a rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movinodmim9;rs +p (wwc6 bu;2e ,kbg 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 o:wsa*zxrsnd, )li/4 l)g0kwb n alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is droppedl/) swn )b*si x4 ,kg0wald:zr onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelin y td3xk3gg9*+ he(j: hm)poqag at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, windhc8p nmf-wbaa8 z zp;* ;yo-r*s can whip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40ko-bz*awymp fp; c8z8-;*hn ar g/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 )(u/sq1)n8 0 nx puisl letxe-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 of the car after 90.0 min0lnu8el)u x)q x pi1(-n/tse s?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s 0bmyd*s8nv4a*s l7 cy ) v3uscemits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of sb)yn*83 yd 7saccu* lv4 s0vm4.0 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 t qn 4lsj8z (y3arr7x7penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the bl4yqrl x t(8sz7ra7nj3ock is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocke rp 1uf6cwzv25t 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 traveling in outer space with a velocity of 1gb 4 m-,3fusqj:r ig8c15m/s To alter its course by 3rbsqgc mf,8:u-igj 435.0 $^{\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 is40mw ,j ann5ij) ahu8fkva q7+sqm 6,k hit off the tee at a speed of 45m/s The golf club was in contact with thewifs mnqaua k547khq6vjm,80)a nj+, ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and c)g53evjp fhe l8 sz)/qomes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nai)/g )efz spjqhl35v8 el?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes cg0x,ld6y;u6 6wl 9eny0 abcsa 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 automobile o qg/9oh70yuomodels. Cars are tested by smashing them i0yoh o gqou9/7nto 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 st -):z6 l my/xgt 6mluhsx*gc/nopped in 0.75 s by a head-on tackle by a tackler running due west.m)szlt c6ng6*ugx l/x:-/ mh y Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points in the +x d . )r4a cak6vc:x mvy*ph::xfoirection and is given by the graph of Fig. 7–33 as a function of time. Use gry*afc: v:4)pa kr:xxo h6vmc.aphical 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 2 4h,n )lawiv6zh6iosjump without breaking the lower leg bone of either leg? Ignore air4 is2)nw66vloi ,hahz resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of 3du4 mz;/-p.udjpzku 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 k;jmd /3d u-uppuz4. zA 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 with a speed of 3m/s has a head-on collision win2yilkjtum (,)6(bzvt-) kah th 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 the 0.450-kg puck, and let B represent the 0.900-kg puy), kmijtv6b)l htk(a(z 2-unck. 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-o/1 u8e.k:b ,inlh zzfylg6j0mn collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00:n6lyml/1h z b ,0 efi.guk8jz 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 speed of 2.5m/s collides hefm7d jg3 )pqa5ad-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and directiojf5pmdga7 3 )qn 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 of 8.5m/s collides h,-:b ,db emjltead-on and elastically with another ball inl t,b-edm b,:jitially 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 paynd9)ky f5lk+rk ride collide elastically as one approaches the other directly from the rear (Fig. 7–34n ) lky+d5yf9k). 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 bae,8 c,ecstz1gll makes an elastic head-on collision with a second ball initially at rest. The second ball moe,z1e 8cgtcs ,ves 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 ifl2t,gxn r*d5qgi3v;d4 zf t0ncline as shown in Fig. 7–35, and e xfnd;v2df4gzg0tqltr5 3 *i,lastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an 7zl4rrj4, pdz object of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, proj pa ezg(;wbm3 yfuvy+dl4 4u:b:qj0x5 ectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projecbmdlu+:y5y xz(j0uq 4e3 bgaf;:vwp 4tile 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 buries itself in a 3.6-kg pendulum hang8 kw:z-dv or)iing on a 2.8-m-long string, whi: r8w-vdo)ikzch 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 kinetic energy lost,cps6xjm4 t1pycba8a, /u -w+w $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an ojdxk 7isixu a5p;a d)(g-kl;;bject, initially at rest, into two pieces, one of which has 1.a; dx;-l;j7( g kda5)ipux ski5 times 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 of a 2300-kg SUhhn).0w soj 1ljqfob ,e2j8 * ge3i7.:fpyay kV stopped at a red light. The bumpk f7gjfypa .yj3)nlhb0oh 1q2e 8 o*swj :.ie,ers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What 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 m06ot qvc2,y4y3scq7qvh(m n 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its e0yytvoqs47m v ,hmq(nc3qc 62nergy?   

A measure of inelasticity in a head-on collision of two objup8uxg ) l,xzv l9; f*05;iq 1v4tg/ wferdoptects is the coefficient of restitution, e, define qlpwz1effv og/0g rt vtx4 5i*d9u8;;,u)lpx d 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 j u0/sblo,3z9m r asp)mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecrp 39us,/jl rz0obs)m aacker 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 s+mxzc:vr r6ys*3l6gat 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of xsy3c 6*vs 6:rlm+grzeach 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 8fl(/lszm rgaqt94,,r l; ez r;ei/nxdecays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles /eq;elsazg,89x(ftrr/ ,z lli4 nm;rand 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 masqmmo.i:wo i zsw 1(: jtfpgfgd 17:;)ys $m_\mathrm{A}=0.400$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 inelast so7jd:udrjrw:*u jq/; /qo:i sl 3b8jic collision between two objects of equal mass, each having initial speed the two move off together wj /;u8 dlo7s:rd/ :qb*js j jq3iu:owrith speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet avp .9 q4utyjefx40u 5yt the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B45f4vtyuqej 0y .pux 9 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 elastpf:n j 2ltpd tzb wu)oo6tw/6j2w 4:(fic collision with another atom at rest. jodw2tf/b:)6 w6l t: tzpow fj(4pn2u After 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 at re eouc,z65qr 1n1xxic1u/em jia0m 4m .s.ue,qemrc4x1150 ocanj/i1mix m 6uzt. After 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

  Find the center of mass of the three-mass system sbu;:b0ow g-ac k y p,2rp1ysqm-(zy-zhown in Fig. 7–38. Specify relative to the left;- a byurp y2bs,k:z10qowz(- cpy-mg-hand 1.00-kg mass.    m

  The distance between a carbon atom (jpmj.lw 5fn m(h).i;n$m_{\mathrm{C}}=12\mathrm{u}$) 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)*++ -cowmmn xu1ko uy.50 m behind the front of the car. How far from the front of the car will the CM be when uxo *ywco-muk+)m +1n 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 the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is uskza9 c gsvzve*l 0.b02ed as a ferryboat. If three cars, each of mass 9ac.sl zv g*00zbvk 2e1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides f n.qw3+n 9jcb$l_0$,$2l_0$, 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 identical cases of tomato paste (see Fi97yam 9 az,e kgw8ryo. tt(f3qg. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without aawy3.m 9 o 8k,7yttzf9 egqr(tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cgj6 60hk0n pss0 6j-sty0who rut out of it. s n r0sh66oj hgs-0py 00kjwt6The 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 center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your propf1q qc xnko1+(ortions are the same as those in Table 7–1, and calculate the mass of one ok1x(1 on +fqqcf your legs.    kg

  Determine the CM of an outstre kux+s4w.zs2m stcvc.un/q 7w :6,bsbtched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent at a righ+s ;j;4kcre ezt angle. Assume that the person is 155+;kz;r4e c sje cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a positi(gklbr1va1jn)y)ivee k8 8w0 (9gqre on such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will (a()iev grn1kql8 8e)0 rjk19yewgvb this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon +glmx8lot 9sep38k w;,pr z0 zl*:tu fare $5.98\times10^{24}$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 friction+0eu. ha qp9zwless 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 f,0j * jnw,zjk2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical han,k*, w0jjnz jfdle 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 cylindrical head of mi w*l* 6mj3eqk49mj / zl4gv zrt9uqon/1+jycass 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 handlekmjon 1 jc9uw z+v/im4**ez/3 tjr9ll4yq 6g q is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29),:rbcl.p 9t(b+u:1 (y pvgwrg 07k fgue $m_{II}$=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 airdy9;z qp7 v5n;ett2b0kdlwh7 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) does the balloon then mov7d2htvnd5;t ze;0p7 kl wbq9y e? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a -2dybq-z(hg+ u vr4np:h o/ iobat and is popped straight up to a height of 55.6 m. If the contactvp2 +nrh:/bdzhoogyq (ui-4 - time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling34 nuviww /4xfmxkbuv(t+ma 6;-h.fm 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 qy; t9 cx9n)sj.9dc h0a ga/cwfaced with the corner pocket shot shown in Fig. 7–43. Relative dimensiotwaq/ xcad9; yhn9gcs0 c9j). ns are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s b/ 3.cxo4t5xhy 8 krymoy pushing off with his legs from am 8k.o3c5/y4 r xyxhotn 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 in k +q; 1/yasatfouter space. They then push each other apart. How far apart are they when the k+;q1t/ays a flighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastizii047 uic+5i :cqlj rz2ml wxpa1g) *c collision with a second ball (at rest) and rebounds in the opposite directio *g:l p4 wjrm+c)ziia0 ic1q7l52xuzin with a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case invoxa b ak0, 3gcm-f;k2nq /4ktzplving 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-k3gk2zf ;ac m4k/pb,aq0xnt crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off th*0ffi0 jkwxwlscxxx5, v (2q 9(c-byle top 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 horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is2(x xqlw-icxsw *j5y(xfkc0, 9vf b l0 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 directly abovm7i-nl3 gi x +pef7t8xe 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 becommel7 8gxi7-px +tf i3nes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg 2jagezzupf.n4c92 qv j9z9xf; *6axw 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 im u.z p fq4 j 9z9x9;vxc6waz22*gfjenapact 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 othe7a8vnsw 1av+ hr of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sittwa+8 vah7vn s1ing 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 /mo .tn v9hgn(about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments by g s70rg*k.hvz. q+jvsan9mw(5ai4yqr sv9/l an explosion. One fragment acquires twice the kinetic energy of the other. What is the rasql.vs+g mwr70j9*n v yrz ki(av . 594ag/qshtio of their masses?   

  The force on a bullet is given by .q7a5p ap1yac8ldua6cm19g t 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 : i7a9olcj+*8am/ vkif/qcsw$m_A$ = 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 particlel8-,u4 b;jdsnn ;czwc and a smaller nucj,d;nsb lz;c8n4wu c-leus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired q ht 8i vqh-2xst(wcfn*,.vp*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 d(olo p*7+qa tmq 6y2eeown 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), wh: 9os98vl pm bna,glz;at is the upper limit on mass m if it is to rebound from M, slide up s ,9zb9va;nlpl:g8 omthe incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn movingaj-3uu7 vmz 0a in the negative x direction at its orbital speed (with respect to the Sun) of 9.m7au3-aj vu z06km/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