We claim that momentum is conserved, yet most moving objects eventually sloomnpeg( m:cs 5myk373md;0e4aj sjxc,h3)i s w down and stop. Expla jgyd,c k )s i3e7m5enhj ;3(om4scamm x3:p0sin.

When a person jumps from a tree to the ground, what happe 3+rb*ggti6t)kpezu6 x 6( ushns to the momentum of the person upon striking the gro) k*tb36pus66z iuxth + egg(rund?

When you release an inflated but untied balloon, why dah khm5m:()3 (fbtd lpim v(7boes it fly across the roomm(bml bap7dh)(3fv:mt 5 ih k(?

It is said that in ancient times a+x+ nern+x9 yn rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the icen +rx x+ne+ny9 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 essentialh0z gj*z(y,0ch+wy ;i o-dsorly gd;sc 0oh-wzy0rh+ *iyj,o ( zin a vacuum?

According to Eq. 7–5, the longer the impact time of an impuh qz rblmei;j8w:9m. +8g,)bqie6 a8s wojry9 lse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate dur).qyi6sb ba8jl9:r 8m 8mw9e+r ghej,i q;ozwing an automobile collision and reduce the possibility of fracture or death.

Cars used to be built asg8 bud *9er8 90;o:o ijjecluy(0xjbn rigid as possible to withstand collisions. Today, though, cars are desiue 8 :gj(0ujrlb0e9iob98nod; *jy xcgned 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 ti0)1 xbgvlb+- ti+vhv he air by t+-bli0 x )v iv+1gbthvhe batter?

Is it possible for an object tob .(ahspr+c9z; fn:o iv )0plr receive a larger impulse from a small force than from a large forc. )v(h0an9oi:p;fz crr+b psle? Explain.

A light object and a heavy object have the same kinetic eb/ix.ys mvp;i158 yrvnergy. Which has the great y8v;v 5xi/im1pbysr. er momentum? Explain.

Describe a collision in which all kinetic energy is lost..cv4yb abyo,.r x(wn+qe.lz+r: (ell

At a hydroelectric power plant, water is directed at high(q:n/khc2 ahfe e: w9; wwcri( speed against 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 brought to a dead stop, or so that the i:(wweq2an/e :rkcf;hc 9(h wwater rebounds?

A squash ball hits a waac lw9fdhadx7(v7*o( ll 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 dropped frwd(bymdv/ u8o ngq 6wrx 7sok34y 8.wtz0 dm*7om a height h onto a hard steel plate (fixed to the Earth), from whic8kxr7 .wms dwm yg7qynwtvzd63o04o ub 8/d *(h 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 falls and sticks to the steel plate.

Why do you tend to lea+txbby3s; ja8 n backward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is nrr7*izw w *xmm xa;o):ez+; p+9msdveot true for your a+ zxoexe z;) r*pdmv*9rwsa+i7 : w;mmrm or leg?

Show on a diagram how your CM shifts when you change from a lying position to a vzk,907iu6n7ig hph q sitting76kh7gzn,ih 9i vpq 0u position.

If only an external force can change the momentum of the cent /b ovq; 1; b-otcv9iba5iecm7er of mass of an object,v/9o;bq cvibieo; tm7b5- 1ca how can the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly*0w/ r:f- bm-ezw ttnn.3vgxp *ncxou* 1qo (z explodes into many pieces. What can you say about the motion of this e1o-q(rtm 3: g / xfn px*uwowt0-b*.*vnnzczsystem of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed ofjysgz50 9m7n3 s4raa f $8.4 \; m/s$    $kg \; m/s$

  A constant friction forceh3 0bkagygd)+q7 .r sn of 25 N acts on a 65-kg skier for 20 s. What is the skrnhd3y gksg)q 7+a.0 bier’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line dritc7q s,x64a3s sn;:ckgw9 dnoy la( 6xve straight back toward the pitcher at 52m/s If the contact time4( ad; x6t 3g7qc6ol:,kayx swcn 9sns 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 packaghov/txqrz .7 geo24c:3 nmks7e out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediatelycet:z.m4/7 2oh x rqog n37ksv 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 g 9 c0r7ggri4izq jpm96ases are expe0q96cmz4gi7rjpg9 ri lled 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 movigzpw2 l5p .u+4jgv 6ryng at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless track with a consgvjj.y *+gd 5*gm(mlq0/ dpkstant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto thm.gg+5gvj*d(lm 0* y pksq dj/e car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling nhv7:4w.ch-6 i o84qphgclrnat $15 \; m/s$ 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 hor pnnhsf0k(q-w2ddl n1(o a9,sizontally at speeds of 100km/h If the air 1f 9lw0pd( -,qn2onk asshn( dstrikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 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 alongaohx8c7m uyhro:5j,) with a constant speed of 8.6m/s on a level track. Snow begins tohjrmo oh5y)7:ac 8ux, 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 emits7b91 /1nu xn xrljc/0r cg*bv:mi9rol 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 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha vj/1 cx0 :l/ru7m9nl*r1gbo nbi9rcx particle have when it is emitted?    m/s

  A 23-g bullet travelino6bnsczv) :ji7xw t9: g 230m/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move afteri) zno7 9vcwtj 6s:b:x the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a spevk0q6bd )y l :vo8si4ked 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 i ntcjs6psp j2f)u5 1d8i 9csbih*1w r6s traveling in outer space with a velocity of 115m/s To alter its course by 35 i nr62u61jppchsjs 581ifsd *)9tc bw.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 speed of 45m/s Th/i: b1rtthzai5( mx6o 2dyb6 wao9u +ae golf club was in conta+z5xbh :m(tw 1dy o2tbiuro6 ia6/aa9ct 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/ ayay7a19e9mxr0 hesi 0p q,k-s and comes to rest in a time iip0e7y a ,0kqmr s91hax- e9aynterval of 8.0 ms. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strisu gb/jepnl 9/59 ;klokes 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 crashworthinesjg zc )5y6w d7b)d-)ldk azvd(s of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km)dc56vdg)-z bj dl ()k dwa7zy/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 enkz9l) y ar5+ joxben9;vvq r-zd2h(7ast and is stopped in 0.75 s by a head-on +ar-ql5vd7 ebzvkxyho9n (r )zn92j;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 (ma ii-4iz 6b1bh 03q 9zw0pa e21mfaowctss 0.060 kg) points in the +x direction a46w9cp f zwia0atz0 3-hbi1 mo2i1beqnd 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 withoutpj2g 7 z46ef 0e;,yxs9wgjsla breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strefay6sp ;7l02ee swgj9z,x4 gjngth (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 ygtypqjf en2od- .33 0collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed 3 3 pfntjyq0.2gd-ey oand direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-on collision10fnpjz*- zxs with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent t0 fz1x jpsn-*zhe 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 karn ogbl*lrox6/ xkf ;++-t k-8nf9iequal 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 tx;+ bx-8f * kto 9k+r-/l6aong kfnrilhe 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 speednzq r5d2 ck52p of 2.5m/s collides head-on with a 0.090-k2dcr kp2qz5n 5g ball initially moving away from it at 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 is moving with a sp tg49jw)v+iy;yaqo( :1 g dhiw-vn 1uweed of 8.5m/s collides head-on and elastically with yiai1:94gy-) 1oh g( qwj;td uwv +wvnanother 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 o dyra/3wm7;; vgvly0 wne approaches the othe03vadvw;w y;m/ rl7ygr directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball zmo e7ra* gbs+ g,6jr.makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original smg.+jbr re* zgas7 ,o6peed 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 fri c-. wc0iba4 r/.psdwmctionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half -bwc.cmi 4pr /w0ad. sits 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 w 3,-jtca5i s8q(jvbzan 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, projectile 1 resulmgsm4. xrl-5hts in a maximum height h of the pendulum equal to 2.6 cm. A second projectile cau xs mmglh5-4r.ses 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 travel m: 9r7 fld n.+q8s9noffztg)sing 230m/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 od+frfftq 9 8ls.zn7)9gn :smand horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energwcxv;9m) j6 tjs .5gqidan8h ce5t46hy 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 anr e6* divn0le+0rb.nb object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the hen l *ib r+dr.0b6ven0eavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides iina/ofg 94f:umkx/) 3 ht nwn0nto 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 )k49nfu/h3/i ngxt fw om0n :am 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 r; (m;fzjo9 8ovg;kza4m1kzx height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds wzkzoag;v8jo ;m;( mf4 k91zrx ill the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two obje mrn05 rgx(c876 b/tvkmbflg8cts is the coefficiel8bvf8r/7gcb05t6r nmk gx (mnt of restitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three tim 353 :m q9att)l.z. naltgpfxazw*zi;es the mass of the other. A depression is made in both *9lwzp)3m a:z lga ttti.q5 3nzax;.ffaces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate 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 f5sfxj,f; dux;ww rt,5b*;v pdx-j v7in the +x direction at 5.5m/s collides head-on with a 10.0-kg object s5;7 vwjutxr,x d fw-xjd,f;5 pf *v;bmoving in the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest d8;wmlplv +5m ve x4cj+ecays into a second nucleus, an electron, and a neutrino. The ewj+ v8p+5;mlvlmc x4electron and neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of masp thld,,ux+,-.bibpid2 la.ub7+ bxtl-7ktqs $m_\mathrm{A}=0.400$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 two objects of equal vu 3 )u*ar) rfyt1fm:qmass, each having initial speed the two move off together with speed v/3 What was the angle between their initial dirmf *trqu:f)ya3 1)vruections?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at 7xfm5l-hp+z fthe 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-m f+p 57lxhzf 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 wiu :fmyx,b 30b+,tmd kkpx;hg2v/c/ lnth another atom at rest. After the impact, the neon atom tr/2x3 du/g ktm,:0np ;h+cxbkblyfvm ,avels 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 r0qesi- 13 fq8riy 97)oikh/dx7tf hg perfectly elastic collision with another atom at rest. After the impact, the neon atom travels away at a ftsfe7i)-r18h dyqr7g0q ho ik3 9i/x55.6 $^{\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 thng/ tte4f. 6u2dqhe7zree-mass system shown in Fig. 7–38. Specify relative to the lef gz hu7.et4td2neq/ f6t-hand 1.00-kg mass.    m

  The distance between a carbon at+owd+kizexn2 b8pi) 4 om ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m wli /f(,*li)q r)l7vsgf * mbnbehind the front of the car. How far from the front of the car will the CM be when two people sit in the front seatqbi f)flliwv n*(7)sr*, l m/g 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 gy veg*9oxj5) by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, deter jg)ox95y* vegmine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sideseqn i0.l f tkvm0z/(;pg:s8 ;-0rvc i:xjg eee $l_0$,$2l_0$, 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 (se/q6ul*br+-yhs ee y/ ae Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the leyrq /le/ua+*hb y-s6 oad without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular lxy8nnijk /6dt), .eshole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [)xy jsn.ntl,k 6/i8 edHint: Try subtraction.]   R

  Assume that your proportions are the so*3qx jo3 51aee (pzflt jtf69ame as those in Table 7–1, and calculate the 5axfte(6lo 1pz*tjfq3e3 9 ojmass of one of your legs.    kg

  Determine the CM of an outstretched arm ulps jsw) -;(aq6v)jtx sing 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 right ak n-+fi7l*p+oy7 fj mznglkm j+7pinzyf- f+o7l*e. Assume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position 4)dy ts6jwo ;k6as1hy w+ff)fsuch that his arms and legs are hanging vertically, and his trunk and head are horiz hj6tw)kdwfs4 y;6of1s+ f)yaontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Mooi (amjh7id o)1n 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 apart on frictiod5irck.n6xw /lk swj 5.y( wc9nless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diamigjuvh5sz: +p8t7nc* pjg+: x eter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg andgi7jp+::gx zh pvnu sj58 +*ct 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 headobmc s/)) w f6-j/guon 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 tojg f/u-)c/mnso w6b)he air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Exa;qv y5ye,u+/o6u o u oc54ibrpmple 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 gondo gag *zqdvxnk)ah;, ;(la, of mass M, are in the air and stationary with respeckvhxa(dg)a;;*z, q gn t 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 move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is popped strjs5il;(zv baj.u( ig s-yz c14aight 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 cob yz4 (sjuiilc5.1j( g-va;sz ntact.    $^{\circ} $

  A rocket of mass m traves lkk2yin3 .z.u,/y b2ufgqi(ling with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the cn ojsblblx,t ;)v sif*1ko ju.3us m 5/jnx*43orner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pn;x3*m )s.ul *4/f tokbsnvjbj 1 o5l3sxj,ui ocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by pughgl7o wh y27) m,k2ktshing off with his legs from an 18w)l7t 27gy,k 2o mhhgk00-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 t3 aqrq5wd4)fd8uwg n2iv/(fof mass 60 kg and the other 80 kg, are initially at rest in outer space. They then push e 8nw/3q4 fiur2dg(d t5a)w qfvach other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (at restcir6 h/:n f6pj) and rebounds in6i:f/cp hn6j r the opposite direction 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 involving an autol cy7(o;2e: 0dps5-q kh8cam hc 5prgimobile accident. The accident involved car A of mass 1900 kg which crashed into stationcl8eysgd5;rc0a5o7h(c- q h p:2kp miary 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 .q rc,60y0helk5ragr 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 is thq6r.rlh , ac0 5yke0gre 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 aboper6*-jr) kgp ve it. If the bullet has a mass of 29.0 g and a speed of 510m/s how hirppr-g) e6k* jgh will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in ljd fyte/d 4z77;pgi . ts33sya 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was thegesp 774y3 ti/zt yjddsf; l.3 muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a r1wm )y- 0a;ojhjk wmb;owboat of mass 80 kg. With the boat initially at rest, the two p b;y1wow-0majm)hjk ;eople, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abokmdsw g4.m5-e ry/j t*x e,fl3ut $ 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 explos36/e cec9uss:*bsizz p w5c2 sion. One fragment acquires twice the kinetic e2wszb* ce 5scz/6ps3e:s ci u9nergy of the other. What is the ratio of their masses?   

  The force on a bulletl: n7g 7ua nua2r)y2zl is given by the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of massesyne tr7 mxn) my2l4-z7 $m_A$ = 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 id/n2n ntmx4y(tbsjlpf 8 6)2n nto an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus 6y2f8p 4 (tdnb2l mnsx)n/tjnif 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 f(oe h8i npb.*xired 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 slid5mro( qzg1p7 dd2;zqso*a 6gjes 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), what is the upper limi+tao i2oi3ov n wj s8( 2xm7m:*uqffu1t on mass m if it is to rebound from M, slide up the incline, stopo3 (ni qfx*+fiuovju27otmw s2:1a 8m, 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 nurw3rddi g77ojt4x 7z09d-bshows the planet Saturn moving in the negative x direo 97nritw4rdj-g7dbx7 3d0z uction 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