We claim that momentum is conserved, yet most moving objects eventuall:dmnl i:7nzt : gjc+5gy slow down and sto:c:5j 7i+dt:g nn glzmp. Explain.

When a person jumps from a tree to the ground, what k3 +w1czog 93raox kldbx4d0)happens to the momentum of the person upon striking th3 o43 zkx)og+wdkcalr01bx9d e ground?

When you release an inflated but untied balloon, why does it fly across w:r2 rbs;a8 nythe room?8wra:;ry sb n2

It is said that in ancient times a rich man with a bag of gold coins froze to du:km ;u2a . qw4o0mfeceath while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have don20fawmuu ;k: c.o4 qmee to save himself had he not been so miserly?

How can a rocket change direction whenyun2 5mr 7,qza5z8)4yancoan o: il+j it is far out in space and is essentially in al2qyyjzo45 +n,ai8 5azn7om uc: r)na vacuum?

According to Eq. 7–5, the longer the impact tiyw o00t;olok 0ogs7rc:/7ncmme of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inf0nt/7c k;:rm0oosy7cloo0 gwlate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possiukxjnh uv8 874ble to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is thek78 uh4 v8jxun advantage of this new design?

Why can a batter hit a pitched baseball furthem6x/89l3(b y3duynj 9wpf-r w.ui ikfr than a ball tossed in the air by the batmi pnf/k 83u3j9b-lfi d.x(69uww yyrter?

Is it possible for an ob(iq6za-om 3ez lb3 d a30fkpa0ject to receive a larger impulse from a small force than from a largea dq3-3zplfieoba0(k z63 ma0 force? Explain.

A light object and a heavy object have the0*9e3p eiq e75k5n cuflb b*ch same kinetic energy. Which has the greater momentum? Explaiqik*ee uh9553cn7e0* c p lbbfn.

Describe a collision inlxw8tb,0xap.b *z;77thj c yk which all kinetic energy is lost.

At a hydroelectric power plant,2qt.f 6bk)jp s9 ft9ul water is directed at high speed against turbine blades on an axle that turnsj9 sftp )l9b.2kftu6 q 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 water rebounds?

A squash ball hits a wall eoow m//t.)(qny 2b ucat a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixed to the Earwf+pq /x3 y) 3kmihsl7th), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any pawx)7 3y f/milh+k3sp qrt 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 lean backward wqjjz p*r8x0mq 6q;v fuk+1,z dhen carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-pointx06 ;1lmhdjcxj+x+q w,mslgr 2 lv6s ), whereas this is not true for ys6)hjj,6l0v cm2+w+l1ml;rs q xx g xdour arm or leg?

Show on a diagram how your CM shifts when you change from a lying pa+1txdx rjz2,osition to a sitting position.1jxrdz+,x2a t

If only an external force can change the momentum g,j2 ci7g *s2-ishsgtnn f,pprn6 .h: of the center of mass of an object, how can the internal force of an engi2 grpiinj7s6gn :,n s ,h2hs cpft-.g*ne accelerate a car?

A rocket following a cgxa7*5.unb dparabolic path through the air suddenly explodes into many pieces. What can you say about the moub*7 5 xgacnd.tion of this system of pieces?

  What is the magnitude of the momentum of ala74 jn3+r4 otoj4qsf 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 65-kg skier for 20 s. W(bk1 tf(ry m0chat is the skier’s change in velocitymk f(c1br( y0t?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line driveas xl ,nom,e/fw40w.awu.3o t straight back toward the pitcher at 52m/s If the contact time between bat and bamof xa.sn/w4ouw3 e,t ,0law.ll is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horc40joa i: cdy.izontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was o.dcy ij4: a0cinitially 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 gases ar6rpo.gl1qo9c ldo , c2e expel1 9,lo2d orqc 6poglc.led 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 moving at5:i r -cjnms4g,jr )yu $4.1 \; m/s$ 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 frictionleue1 jlkx xkello y1)bq.).o pr+w6u (1ss track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the 1le xr xko6ql )+).1(u1eu ypljwbk.ocar’s new speed?    m/s

  A 9300-kg boxcar tra)hc) jpug 1))b4rmm, bjjti:qveling 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 bdj vl17ja.u9bdz-/ e1dl+n c can whip horizontally at speeds of 100km/h If the air striu1-za/ 9bvlc.bde 1 n+7jjdl dkes 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 cokd- zp,j .ynbwi euq5m3 )syr)g/w2v,asts along with a constant speed of 8.6m/s on a 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 theu) iqz.jm/r,k)np yde,y5 v2wbsw-3g speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha pql yl *rq*3wk5article 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 ma5q*lr*3 l yqkwss of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates bpfu8q04j. q lvera,jrhsx( ,;0 u4 a5xao +xga 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 .l0a0 su5qof ,j; (x44upqxh+jarax 8,egbrvdoes it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is travelinr o9y8j6dh i5 :h 4ml59sznqr0 k-ficog 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.cb pt0af+o-w s3b ..3napynv outer space with a velocity of 115m/s To alter its course by .vnw.0pt oafsyabb+-cn 3p3.35.0 $^{\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 h+rlf,i tfmv+;h517(ymdokm7 mojvt3 it off the tee at a speed of 45m/s The golf club wa mdorflmi+jmv1 ,v;y m5fo (tk77h+3 ts in contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a veloc2t7tpiad 8(chux2x :5r 8 0zppvp vg(gity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to t2(v5pc:7 2dx8u8t pvax gpgz(r0 ithphe 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 strikes a wall a3voi yjse8(xu9wh b60 -rk.oat 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 engin tn4 win35wvw5h0xm;m eer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at hw 5n0w4mw;n t5vix3m50km/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 wvu) q30f7p2 sonik; ystopped in 0.75 s by a head-on tackle by a tacn 2;p)sifqvy70u k3 owkler 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 0.06 55wwsw g-b8ntbj)v4x0 kg) points in the +x direction and is gt jw5xg5w8w)nv4b-sb iven 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 j6j thh bqo-9:r2fwln ma5g0 h;3edl4tump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking thtf: b l524amj9 gh-do;hlw0qh r 36tnee 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 movingf ska,7-y7l-mcguajyd r7r 26 east (+x direction) with a speed of collides head-on with ar-cj67kd2mf7ua7 y ryag l- s, 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 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 speyzfisc02e 3 3r 11psjned of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B reprejfrn0zpi2y 11s33cs esent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastic head-on collisiogd:: ot)p(8k 9t elzxon. 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 cx dk(t 9g: tolp:oez8)all 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*c9 x-:i9ycd eceta :q of 2.5m/s collides head-on with a 0.090-kg ball initialle: 9iq-dcca:ety9c *x y 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 that2lac k xemj3y-.ez(t6 is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incom3cmzae(j.kx2 t- 6e lying 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 pa- r,hcm.i3 z tlmtd8b5rk ride collide elastically as one approaches 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 in passenger mass. If car A approaches at 4.zr l, 3ttdb5c8 h.m-mi5m/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 seconqhlk+efk rpnrhm)(7 .j)5 s5w d ball initially at rest. The second ball mpkknwlme5rh(s q)jf+5.h) r7oves 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 sp3c ++goxud 7qhown in Fig. 7–35, and elastically strikes anot3 xuc +podg+7qher 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 anp 0 tdk2/qfa,a 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 pendulucajsb,r :b1.m m experiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A seconda sj:bb.c m1r, projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries iln 4 r,-tsz.sxtself in a 3.6-kg pendulum hanging on a 2.8-m-long string, whz,x nlrs4. s-tich 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 x a6rs/o;z gcx3b./imdmk :u1of 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, in+2julf1 -j.bt7 f)3js xntqvgou87r ito two pieces, one of which has 17.f1s u27jn+g jori )qt-b8 fltj3vxu.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 lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collst32b /u/wtjh ides into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The bjw3/ hust2t/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 nwkxbwn lq/6 re5fu+k)y w-/;m and rebounds to a height of 1.20 m. Approximately how m-n)/xq5r kf +l/b6wwekunw;yany rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is theuk .2zy.wtbm(v.i a*53 rxtg c coefficient of restitution, e,m3uvr*ktgc b..5ya tz2 iwx.( 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 timakzsw4s592 z*)tr ,1pk1crcdyxh c0mes the mass of the other. A depression is made in both faces of t csma)w5k0r,c 2txs1cz z*phyk9r1 4 dhe cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collidesjvm k+viv6fx-2ia 3hh6lkz/(r-z/q c head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the f l2a//hiir6 q3v 6mkxz zv (-cf-jhkv+inal 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 f9 6 nabju6gvyke h65(0ube:pat rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emi vhb90e5e6: y6k n(gjupafbu6tted 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 mass ;rf2 l2 pxqdxq)rjgc.,pn2- j$m_\mathrm{A}=0.400$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 mass, epndd -utj22b 9dz1smi -x-xi;ach having initial s-9; sdx1ptd-muj i2xz n-ib 2dpeed 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 7a-m 3lfxw9ynw( (a z kw5vx:gangles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fwlfxma: (yw -xzv57ag 3k9n(wig. 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 ano6eb 4*irapug4 ther atom at rest. After th p*rgb i4a46eue 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 col xmqij74:kp:s lision with another atom at rest. Aft: msq7pxik4j:er 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-mass3yas zsxa6ln*r;4l 3h system shown in Fig. 7–38. Specify relative to the left-hand 336anhx*lr;lys4z as1.00-kg mass.    m

  The distance between a carborrc p0:hvuq-7 n atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of thg5d wvr bo/eg( s6mlmmx x*9;u0sx2.ve car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3m( /6ss2* m5ggw.v0 u xxlovmb9;rxed .90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 1 q lu7igp 933p6nqd,mxn78phy8 m by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded uipq93ygpmn 6l,px hq737dn8ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidee6 xto1rj;i9- iv0 e 8s1 pzatbks3l(ds $l_0$,$2l_0$, 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 loadia2z* (3y tyg r9dhz,t of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the ,(r *ty2z3giydz h ta9horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of 3;q l lt y+,injyd5w1xgs)l ,sradius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the largexj5lwl+ ,y1gqi,t sdnls3 ; )yr circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the + ubzi. 29ogjdh3 xm)zsame as those in Table 7–1, and calculate the )ozd.bjh92+z giu3mx mass of one of your legs.    kg

  Determine the CM of an outvg s zxp0 l/9+awbv5j+stretched 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 positira-p 4c6g3py+dx3j 2bu*v ys uon of the CM of an arm bent at a right angle. A3yxy6u+p p3b4uc -g rvd* s2ajssume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position suz4 f:,3bbcw iach that his arms and legs are hanging vertically, and his trunk and head are hobb3izw4a f :,crizontal, 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 auh* 9- uywqb4stn9c4f7 ep xw7nd 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 apart o+ jio 1k(ix c7qr/uu2un 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 heai/ rqarmtd/v6)jd )c+d 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 ai6 /dr/ miac)+j drqv)tr, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrih .38z.ytmd8nhrd -hm-tiu oux4p4g+cal head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follgdhh u-t8 .m3+4-z.nhm xpduir 4 tyo8ow a parabolic trajectory?    d    d

  (a) Suppose that in Exampleqsvz3 (jkn* lw(cz.dl-rhmp)*r ntj 5h/l73 z 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of ma 5-6pzabim/a hnxp*s z4eor- ,ss M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down5n-asp zb- ei,hmp6 az4r/o *x 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 0.6 (hml.hodk-k v* f o-eyqerstraight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average ho.o0 .d-lkehfk(*vm- eyr6q force on the ball during the contact.    $^{\circ} $

  A rocket of mass m trav annlqj +jpb,w ag65(*eling 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 tha 6+xl6 tc;i4-jf e u ryvhzaa7n:v6d7e corner pocket shot shown in Fig. 7–43. Relative dimensionsy46z;nleh6u+a ar67xi-v tc7afjv : d 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 by pushtizr66x-sk ;d ing off with his legs f zk66t;xrsdi -rom 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 80n ,k3nk* b5loa kg, are initially at rest in outer space. Thn3la k bk*,no5ey then push each 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 fomu(l(33buxball (at rest) and rebounds in th3(ub oxu3fml( e 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 casqgnvu0 k+ cq m;)u23mse involving an automobile accident. The accident involved car A of mass 1900 kg which crashed intoqcs;mq +vg 02u3nku )m 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 ste85nkyn/q+zu3jc 3 gw2 7qdtrrps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a dwyd3qrn j/t +zng35qur ck782ifferent step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 167guv 8dkixn (.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510mkv 76 xn8dg(ui/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 place2 xsml,c6ygmpqv-/1xr jv *n) d 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 dri)-qnxv,yc2 x6jgvsplr/ 1mm *ves the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowboakl,0fkphl+aii6wv 71 t 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 exchan0vaipkiklw ,6+7 fh1lge 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 abob-i iu 2ik)k0llaz/z +ut $ 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 s6( fxky8 nds;suddenly broken apart into two fragments by an explosion. One fra;fs y6nkd( x8sgment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given byq( 0q o8 *zothagr3o9x 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 massesym8xq /2l;k rdcwr6 2p $m_A$ = 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 aai6w t* 4j l(;ecghbw5lpha particle and a smaller nucleus. What will be the sjtwwbecl i (a*4h;65g peed 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) ise,;c kgp-78n(1 r /zitysb8p+drvjse fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slidesvn ukbb6m 17a 6xosy4: 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 lbpxhp9tx9tfp;y7* ( - x 874tmkmppdbimit on mass m if it is to rebound from M, slide up the m xbtxt(p4p9px; 7*b-ym897dkfp thp 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 effect9t6 h(,.tq3u9xq83ksi1us zd ikt eua . Figure 7–47 shows the planet Saturn moving in the negative x direction at i8ie,( 39uhkukx3 tqst9tz1i.d6 as uq ts 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