We claim that momentum is conserved, yet most movisess6 -7tdop 3g v+yuji/d0i3ng objects eventually slow down and stepis6 3/y0sgv uj od7isdt-3 +op. Explain.

When a person jumps from a tree to the ground, what happens to tslhn1xad3ypu f27p /tecf9 **he momentum of the person upon striking the ht*9afl /d 3n pc12pyu7e* fsxground?

When you release an inflated but untied balloon, why does it fl5 cprp w.2rsyjxe2.6 qy across the room 5eyrq.jpw 6r c2xps.2?

It is said that in ancdvx/n: e 0ty,.zaxtd4 ient times a rich man with a bag of gold coins froze to death while strande 4tda ,0ynvzxd/:.x ted on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket changj0z9aaj5+q-tm cjk/p:2s y rwe direction when it is far out in space and is essentially in a vacusatcm k5 9a +:r-z0p2ywjjq/jum?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller t xeje4ly2/3w+.w dnm bhe force can be for the same momentum change, and hence the smaller the dl3nd /wj.e+2emxb 4wyeformation 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 possible to wgvwgjf0;0 mn pa72 u0mithstand collisions. Today, though, cars are designed to have “crumple zones” that wfv0 ;u2gmg 00mj7pna collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pil-nrgy yn: 7-ytched baseball further than a ball tossed in the air by-:r lyy ny-n7g the batter?

Is it possible for an object to receiv ) shw,;-exidne a larger impulse from a small force than from a large forc-)wdn; hi ,sxee? Explain.

A light object and a heavy object have the same kinets:n 7g*klmzn8 7vr n1vhh-:wd ic energy. Which has the greater momentum? E h1:7wkhvn r z*d8g7v ns-n:mlxplain.

Describe a collision in which all kgw8e hft/c8a,yk wq*: inetic energy is lost.

At a hydroelectric power plant, water is directed at high speed againstostchnnh )5 :kf9e+wnz6e0 (i turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is broughthknwo)esn 60ezit9(:+n c5 fh to a dead stop, or so that the water rebounds?

A squash ball hits a wall a x:5tje:u. agjt 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 s.)-8 u7sbu7g dmmjax nteel 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 fallsa n7jxbs)d8 mm u.ug7- and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy lu/jyqafo zlzf3 41eh351 dri;oad in your arms?

Why is the CM of a 1-m length of pipe at its04 yrsckyfhi09ghk 40a4e- vz mid-point, whereas this is not true for your arm or lh4k ycezf0-kyr v4009g i ahs4eg?

Show on a diagram how your CM shifts when yorbo (;z2zg 3tyu change from a lying position to a sitting positiong ozrb 3;t(z2y.

If only an external force can change the momentum of the center of qxpan)- y m)d;fxl/07 auv xr/mass of an object, how can the internal force of an engine accelera)- xalyur7q axdmnf) pvx/; 0/te a car?

A rocket following a parabolic path through the air suddene fu ndq)*rd m7bwk1la.8s-+yly explodes into many 1rmf7.w) d8dqky*n e u+-sbal pieces. What can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow fl 0c81rwo,usp eying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What is xx;0r7ot;1kw1n, y0 yl( zzedooy-tu the skier0;1xxz z1t-(oy d ou,yn70kety wor ;l’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 n 1yo u+q)znc)m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time between bat and ball i 1q+ ocn)nyu)zs $3\times10^{-3}$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 of 10 l7s.z p(gc* ra3ftw w.m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The ma 7cw.zglt(rs .f3pwa*ss 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 w0uhj tje8+s7 the propelling gases are expelled at a h8 t sjj+ew07urate 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 mov 5zr0/ 8hkdrs12xkydw ing 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 t*6bms0pt( mnppi.9 ng ravels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto0m. gs*bmpni tpnp96( the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar trahkx i0ksy -g8p+ :8gziveling 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, winds can whip h/ bu 2+akmqcj2orizontally 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 2ujqac /bk+2 ma 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 il;l ,eld8m4r7o* swp,d yuc3ptt(: b with a constant speed of 8.6m/s on a level track. Snow beginldi ymb8,ow3*rt;c4,pl le tp:(sud7 s to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s em00qb;te fglg3 om,l s:its an alpha particle in the direction of itsemolfsq 0;l, 3tg0:gb velocity, and the remaining 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 penetrates a 2.0-kg block og-ndie 7uf keb v6m5d*i+l+: s*ep ij5f wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast di s7*eei5jg6ubn* v5+e+ lidd - kpmf:oes it move after the bullet emerges?    m/s

  A 975-kg two-stage rocmz; /d9gqqxzs 66mk; xzri *w/ket 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 wit,n.n2wybrg:e-kp81yn ov 9w ph a velocity of 115m/s To alte-:9 r bogn y8pyw2wk ,n1nev.pr its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at4 9 tatulxj,1q 7sbnd8t6sgb+ a speed of 45m/s The golf club was in contactsjan61u 79xstqlt b,8 b+4tgd 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 va 0auxfzy6q0h z*da 42elocity of 8.5m/s and comes to rest in a time interval 4zx*u0fay6 ada02z qhof 8.0 ms. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s sj: ;ad27cxpqr trikes 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 cras zx f:(rp u9rs2*bncd+hworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new modelr+ 2ns(z *cxr9u:db pf 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 to5ykyzt-e bduw2 v1-mqbmyec6 ( .8t c+ the east and is stopped in 0.75 s by a hea-5w ke1 tz8ymme +cb. tu (dvy2-y6qcbd-on tackle by a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kr6w h) -kfk5rwg) points in the +x directrwhk f 5)r6kw-ion and is 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 height can a 75-kg person jump without breakdd ( ffo+m/gasar ,06 s)uqrp(ing 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 standing to the seate( fgadr /dm6,o p(+r)fq0ussad 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)qd 7 jbab;0w1 gr00zmpb g)c/r with a speed of collides head-on with a 0.220-kg ball at rest. If the collisirz j r/b0bggwmad )0;qc70p1 bon 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 eas9 jp/ 72datkv*,rgars t with a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at r7grr*akd, 2s 9vpj/ta est. 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 puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of eq 0b wo+,1wv0 mnagqvty ih gp(l)/w-t9ual mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) vwtwot9w a1in(0l b p)q /v gvg-0hym,+'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving l,0vu5 nkotzlmyt 0/:with a 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 a per /yzt0vl t0k5uonm: ,lfectly 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:cnkqkvwqdr*x78w0 p 4 +)tx q with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward pt q7x*q 0xwkq84k+ cwdv n:r)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 one apfaksl8 s2;*m,y6m + thyusu+,qg8gk aproaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences iyaahmsly8 *; gssk6fut, 82+m,q guk+n 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 se; ewr)z7m y3al+;kcrjcond ball initially w7 e)yam lrc;j rk3z;+at rest. The second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as shown;sh; 7yr* aehq in Fig. 7–35, ;s; ae7 q*hhryand 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 moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of mas)z/)x1-bmxhuvq vry9 s 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 re5mnyn r6 d()wdgxni(3sults in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as(gd iw3n(ym65x nrn)d 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 23j:g;tl -i 6ip*+)xsk5ppikrt 0m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and :5+*x6tl ipr gpjkt) siki ;-phorizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the d7 mi +76bsf 7frzght9fraction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into two pieces, on :d.nk 6kogc,cq58i)m1eju9asw t lv*e of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the 5k u gj1 cmtawl )*q8dv6.es9n:iok,clighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kgbb dr -jb1+g9rlwh2- df;uhh7 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 the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the Sh bdb;rg7r9l- j hb1fw-u2h+dUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds,fs;rsi t +zu+ to a height of 1.20 m. Approximately how many rebounds will the ball ma z ,sutifs;++rke before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of t ekgz+4n8:bjlwo objects is the coefficient of restitutio8:ejg b4z+lk nn, 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 thrnv 6b+6n l2o-mb, kq- z.lmrfcm6mkt9ee times the 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 firecracker explodes, the two b2zqo k+6n m9b,.vl6tcf--6mnmklmr 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 tho x2 ub4y(psh-e +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/ 2- xb4syh(upos Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a secont8u+ :ihs (mz nz;3 fnuzc(,r2(qemkcd nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momenta of m(ercct kz,f+( uszm:(n3q z iu;hn82 $9.30\times10^{-23}kg\cdot m/s$ 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 m4ofjhz, fhxvc94c -/f fp)a8a ass $m_\mathrm{A}=0.400$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 collisionyxm-9 p/hndqh a n-7i0g/m/yk between two objects of equal mass, each having ini0p /yimxq/n - hhygd7a9- /knmtial 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 right angles i5rhvc( ; h)h/p5aq-sua;e( 8 cpxjhk and meet at the origin of an x5(;uv8 5cjh paqkcxh /; (ri-psahhe)y coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of 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 res78pk6) 76r ultjoml ngt. After the impact, the neon atom tra krl8 onjt6u7 m7l6p)gvels 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 elastic0tqbuz fiz+,* zcal ,4*vjm+w collision with another atom at rest. After the impact, the neon a ++,vqf0, zi4ca* mwz l*ubztjtom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig.e8acqatodw; f-c 8;:p 7–38. Specify relative tf o:w88-a; ;e cdaqcpto the left-hand 1.00-kg mass.    m

  The distance between a car6cdxen 30ozl ,tmh9;nbon 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 cah8(i +w.qpc9;r0p wg kfedvz2r is 2.50 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from th(ec80 r2. g; z hvfpidp+wk9wqe 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 y 27fsgn b:xggl5w-5r used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, Sy:g25l5r -fg xn7w bgsE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides +osbfjw;8 -x1vb p ar1$l_0$,$2l_0$, 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 tohwj; psx5,g1y4qbby xq 5m3 j6rts08jmato 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 tt3 51hs; 0,b5 gjsjyjp 6mxx qqy8wbr4he crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radiuste/t xt. -d/t luwe dnsd,6b12 R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position wl-x/et e t,ub 6nt2ddds.t 1/of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same aoxze)9 x (ifx3s those in Table 7–1, and calculate the mass oif3xxxz)(9 e of one of your legs.    kg

  Determine the CM of an outstretchefc fkgl 0mt*:ujcjm0z)6 +bu+d arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calcula-+s )yc5j(y gy 57ifcud obe2dte the position of the CM of an arm bent at a right angle. Assume that the person isi- c) dcfy ju+g72y55yd( ebso 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such ttm5qh 98rh*wv hat his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s *hhrmq5t vw8 9median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and ;slf.ppt b4i ku) bj3*Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apxy/x (g 0qwy uc-illn:7i- kc9art 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 hea1kcujk ks7p; c) 22srld 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 t ;lsku7j skr21ck c)p2he bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cyl (:i h6yzuxmv9ltiyp 3/k*yp2indrical 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, 9x( iiy6 3t v2zhpk /ypu*ly:mspinning, 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 jol879r65rao fxew0bExample 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 dax 46o;f b7b55rhgsf, of mass M, 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) does the balloon then6 54b5;gfo rhxbas d7f move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at s c+xw7mz0d/+m ddjjl* trikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during t/jzdmd d+c *0w mj+7xlhe contact.    $^{\circ} $

  A rocket of mass m tkw(sgf o asc713e0+iqraveling 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 playerkjyh)j;,qkxuls 6 /t: is faced with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player beh j,ktyq6/;xu s): jlk 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) -i2b vn.uiq4*5tna,kweh q 0;wi ornztz9;r8 acquires a speed of 2.5m/s by pushing offnvwrr,ha;.ii9 tzqo8 ; wqi5eb n-4k2*unzt0 with his legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kgie mmj7;m9dm6 11gxbgi k0wa(, are initially at rest in outer space. They then push each other apart. How far apart are they when6a;(wgm m1e0 j m7xm 9bkig1di the lighter astronaut has moved 12 m?    m

  A ball of mass m makes k(idn93oo3a(rpqxn9 x : 6hel a head-on elastic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth ko dl(ox9p: r 6ix33 (9qnnaheits original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving kf7vemc/t,l:r+(hm. lw gm c0 an automobile accident. The accident involved car A of mass 1900 kg which crashed i/lrmg 07kv. c+c(:,thmmw felnto stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total ver fa gfj2*d9qw.tical 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 i9jf a*fw.gq2d s the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired verbqqn7x3r85qb tically into a 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed oq3xbqq7 r8n5bf 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 p qq:.d8a mn/ltz*zq4 e*dpqi)laced on a horizontal)z de:anmiqq.*pq/q *d4 t 8lz surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes 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 wridlm 9,o*i-a rowboat of mass 80 kg. With the 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 exc*r-o d,wiiml9 hange 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 dw- m,p tam-/nwas 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 an explosion09.cfvh. gac)hf7 jl,ugs wj2. One fragment acquires twice the kinetic energy of the other. What is the ratio of t.acju9j7 cs).f 0f2h wglgh,vheir masses?   

  The force on a bullet is given by the formula F = 5idy97ankdkglsji9 1n0)/a ; q 80-( $1.8 \times10^{ 5}$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 8nu1t)qrctxbtzv;j fs*: qwc*k4jcq) ix ,(0$m_A$ = 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 kt-q (x1cd ; qesjjsx+c41*ur ssdk9( particle and a smaller nucleus. What will be the speed of this r9qkd+ t4u*cs1x 1 s;k(csjxj-(sqre decoiling 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 bh mlb1c4ba.gs 5op71u z6u .yat 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 down a 30.0 :43cyz4f zxwxce1ir,$^{\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 it is4r z-s4cc n,:,hos f cq xbp2*r-wg-rp to rebound from M, sli- 4 cpsxw -c2hczsq,-f:r,*ob4pn rgr de up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturju r;zn9vomo0my6q 9y3 gx 0:in moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn i 9qoxiyyrv39z0nu6:om0 jm ;gs $5.69 \times10^{ 26}$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