We claim that momentum is conserxy.ibn:.cf) sved, yet most moving objects eventually slow down and stop. Expx:)fy b.in cs.lain.

When a person jumps from a tree b)f69(zze6f 6c(dsdoqa es 5ito the ground, what happens to the momentum of the perso5qzaobe s s9(if6 cd dz6e()f6n upon striking the ground?

When you release an inflated b375rernatpg ,ut untied balloon, why does it fly across the room agn7r, r3pet5?

It is said that in ancient times a rich man wiv z-jboory kbdc63 b,(jk9 z xkp*spr(1ua:7 *th a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. Wbs b-:16kz 3*( 7obj k(vpdak cj9,xorzr y*uphat could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far o)kz iy5zq040x:6unx tsjc8erut in space and is essentially in a va0i8yxk5qx n )zer 40j6:stzc ucuum?

According to Eq. 7–5, the longer the iw pn- b3:k*mp q+wcka5mpact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformatip k5k*ww-am+:qn bc3 pon 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 withstand collisions. r:40b izjxavg ):hj3rToday, though, cars are designed to have “crvgr3j0r:bih xjz4:) a umple 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 f / a,pomr4)sv2 tux)di x,wg(tossed in the air by thp(4f i2tmxosg )ux,, )v/wad re batter?

Is it possible for an object to receive a largericao2j2/)r6w ru nf p7 impulse from a small force than from a lao)fr26 rnjpcw2ua7 /i rge force? Explain.

A light object and a heavyvm w-ls t xaz/),xp86rvc9a7h object have the same kinetic energy. Which has the greater momentum? Explain.- tm/ cap8)wvx6svhr 9x,a7zl

Describe a collision in which all kinetic er xmo n2tu0 )p; bwx6tq7so22cnergy is lost.

At a hydroelectric power plant, water is directed at high speed d8m:w6f3n71l 6emua qkd 4ep 8idc8tcagainst 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 water rm 8ec8up6:a 3l6 mc1 f 4ndi78weddtkqebounds?

A squash ball hits a wall a7xq::osb0 na0oitsb - t 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 n)phup g8)jg8st4 7hsonto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is mhp)4pj 7 8u8st)n sghgomentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a .ca5lm q tsl4y)w :-oxheavy load in your arms?

Why is the CM of a 1-m length of pipe ozl -1(lztl*x1 ouex+ane8m 7at its mid-point, whereas this is not true foxu x(8za1-n7etll 1lz*om+eor your arm or leg?

Show on a diagram how your CM shifts when yom 6y:5p5tfzeq df5 rpxf4;rp7u change from a lying position to a siper47dfp: p5yr 5q f5fx m;6tztting position.

If only an external force c8yimet u9 v9s:an change the momentum of the center of mass of an object, how can the interna9m :vsi8y9teu l force of an engine accelerate a car?

A rocket following a parabolic path through the air -y3qyj ,4rqddsuddenly explodes into many pieces. What can you say about the motion of this sy-qd,y43yrj dq stem of pieces?

  What is the magnitud b n2quabtv1v 25s8dj7e of the momentum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction a+,pyf0;j3*p o ;f6z q;ftc4jhuhybvforce of 25 N acts on a 65-kg skier for 20 s. What is the skier’s change inp;fazyp j3fv o*b ;jtcu6+0h4yqh;f, velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s isuln8 x lum02(ehz*7iwx*(p s d hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact tim ux(h7*m8x wdl(si0ne pu *zl2e between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a shyb jc-yug : 6:;1mo) (bxchhgpeed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the chil:(:cg 6coy1 x-hbh)gmuj yhb;d 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 rockej*o d4 nvc,w,dt, given that the propelling gases are expelledvwc,j*don, 4 d 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 mov(2ytoe x jk,;uing 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 alevvs3qp-8 s7 areel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What rqp7a-v8s es3will be the car’s new speed?    m/s

  A 9300-kg boxcar tra, tj1vk ,0isck9ze) ;ep sg1axveling 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 horizontally at speeds of wf */n: a:g(vxmf3*e7e d xoqxnjt1f:100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume *x3xqxv(fa: : fnmefjg1t7 : nw /doe*the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant kb((17uxx v8io-4qw so*d pfckd4/gu speed of 8.6m/s on a level track. Snow begux /( gs1o4d7up-4o8qvbwkc kx fi(* dins 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 emits an alpha particle in trz0r2)uab882ysyxgc 6rrs 0 v7zm i+vhe 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 )s2 r 8c ayb7z6 zixsgv20+ 80mvryrruof 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230mmyy7i i 6.e5gr o87m0p4 unzwg/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surfa787yog46zi.0 gp um e5rmyiwnce when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is travno8 wiog, e81 o crsv6;-,zslzeling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with 7l) wyaqjrop,,ka ** za velocity of 115m/s To alter * r,ak qz7)*,py joawlits 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 ofmh3 1 cc//gdlft :r8c5)ubf brf the tee at a speed of 45m/s The golf club was in contact withb brm15: )c8 c/dur3/glfhfct 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 on9sl; j72 roqyf 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulo7;9qjn s2ly rse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m 5p1yp 2un7xqs=0.06kg and speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engi bji5z2+cfy:bc3 com /neer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers atm/j y5cficb3:z2b+ o c 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and i6 6tco2kog3u zs stopped in 0.75 s by a head-on tackle by a tackler running dug6 ou6 2kzt3oce 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 kg) 9adm .xo/o3dzdcb6ik)o ;d8g points in the +x direct dg)9;d/dk3dczo 8mbo.x6o iaion 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 (fp8c,ym nnb-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 isnbnp8,mc ( fy-, 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 movpge 0otmyb55,p k mk-.lu o.x/ing east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440/mou m5 t,0plpgyk5.-o x bke.-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 co (6ov0r xmf,/kk6hm:,5mfsj) te ydhfllision with a 0.900-kg puck initially at rest. Assuming a pk thvmr xf,f,d(6omf5j ys 6khe:m /0)erfectly 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 equal mass undergo:po w 7dx:3mxqe m9u9f a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and thodmu:xe79 fwp x mq:93e 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. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collidid9y 6 5fzkpe+es head-on with a 0.090-kg ball initially moving away from it at a speede+idk f6 9yz5p 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 speed of 8c h, /wsj9u)ltls0z;z.5m/s collides head-on and elastically with another ball initially at rest. Afteu0w slc/,)j h9tzszl; rward 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 on4p1m-l*lhj vbd: zk 7ee 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 4.5m/s and car B is moving at 3.7m/s hm*4l1 pkbev:dz-7lj 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 elastieufsy5-ag*hd)d ,x;4fz3w4iav z kk2c head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of tsfkdaez2y,z*- h43fkw)5u;dga xvi 4he 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 cub rdz )(nea(;cse slides down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the fl z((crasd);neoor, 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 y) gcp88joam: an 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 r7d*,e9xl fxlr esults in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as highd * lfxl9e7rx,, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg pendulum h 41mjb brq;2jbanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine tq4bbm ;12r jbjhe vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction 1a1erdt5u3mu 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 obgtr:ud uv*w 81(fm 3mkject, 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 heavier pa 3(1gkm8vrmt*: dfuu wrticle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the r;+fg qff9jo5hl;6m* qows; urear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of ru;h qqfw+5jf9ol;; sfm 6go *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 heigh tl8 rri3(xpjor/. n8zt of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make bei(p nzt3j 8l/.rr rox8fore losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects i) o/z1 y/6ybad0tnm uks the coefficient of re1/nbdy0k) /mo yza6t ustitution, 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 wi la4opx+qf 4:fth three 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 thoxl: f4fa4q+p e 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 collit)iin ar,-89.aa hfl odes head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of 8ana)al ho ft.ii,9-r 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 int *aq2juyjq 5*w dw1z5eo a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momentdzqy **a 5uj2w5q w1eja 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 5(qishpvy( 5sbct64z eskgm 1 1/lg,p $m_\mathrm{A}=0.400$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 eqx 8 9 (-kvus9jr-9fslcgoexs*ual mass, each having initf*os9revsg(s- 8jx9l 9x kc-uial speed the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal m )c vnade 8an0a/kd+.dass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig.0c/ dvana. )e8+da ndk 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 pe32k.vqr a /n nv pnzm/86q9ganother atom at rest. After the impact, the neon n.a/38mpveq v p9 6 qr2knzgn/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) r.ko;l 9m,mezmakes a perfectly elastic collision with another atom at rest. After thlkor z9,;e m.me 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 thregg ;wnia2 ln4;zfn- 92onj wn*n)92lhj;i wm me-mass system shown in Fig. 7–38. Specify relative to the left-hand 1.00-kggwjmn *;o2l n-if h9w2ln9ginn n;4 2wjzam ); mass.    m

  The distance between a carbon atom (y pjl 6d.b;fu2$m_{\mathrm{C}}=12\mathrm{u}$) 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 the car. How far froo4rg+zr p.vdo.dz5 b j5z1 2hom the frz 21o+5. opgrddhjr bzvz45.o ont 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 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m b6-qieo-wd gy()n5c0v4c pg q sy 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 f i s0c -cg(vg65epo-wnqdq) y4erryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesn.-x9+i:t,ig)by r4gc cva/lq p( lci $l_0$,$2l_0$, 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 (segh8)l,r-q*wmajvtw .e Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so tha8jmww*r h qav.g l)-,tt 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 radiu )hz8otqfd9d/t i)yl *s R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the lar*d9hl oqz8dti ) yf/)tger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as w1dhti;1w v1p2zkd*xthose in Table 7–1, and calculate the mass of one of dw1x*k 1wzt2i1 ;vhdp your legs.    kg

  Determine the CM of an outst3gq;u ;j e, ;jvmgn xwv+bu+l7retched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent at a right anj.2hebu u g07cgle. Assume t.7 c gejh20buuhat the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position suchys xuv:;)kl),;iryie that his arms and legs are hanging vertilsv,y; ru):ek;) xyii cally, and his trunk and head are horizontal, 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 Moon are ;kzzuk* ht/a- $5.98\times10^{24}$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 frictionl9 ) m +0gl(dzp5-1ajaucy c,0b/jaztsrpo*dness 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 un1ffe (q0y3hzj 6 fph qi12jco2iform cylindrical 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 followzfj1ef6pfo 2hc12 3yjqh(0q i a parabolic trajectory?    cm

  A mallet consists of a uniform cywz,2*q2 9 ayoiqwc lmjh,9 eq1lindrical 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 follow a parabolic trajectory? hc9ze9m22oi,lqwwqq, 1yj *a    d    d

  (a) Suppose that in Exa c5g:vfcao 0,ijv: j s4ijo7i22ys7kv mple 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 mass M,g+2/- qaiwd5 in rr(u9q xr/xwa:cq;a 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 balloi-+(rxc qqx q/gar;2iawnwa /r9 d:u5on. 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 a y d966kogy7va t16psut strikes a bat and is popped straight up to a height of 55.6 m. If the contacta667yu ykp todv691sg time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling witwdi)3c7awl6 h l u1w4mh 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 corner pocket shot shown in Fig. 7kk2jov d51,el–43. Relative dimensions are also shown. Should the player be worrie vdel,k25 1okjd 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 pu+bf5roq8:an 3hr va6l shing off with his legs from an 5an8 obv:3arfl6 hrq+ 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 anol4usp;-iw u ds3wcgoc:a64t ,s * v.nd the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the light:cuol44d,svc6u tn3p sw ig- owas*; .er astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (at rwnd k:q9 5)fxmxs (4hwest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of kf n5xwh4qdws:mx9( ) 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 az:ip )haizwdk,69iz i3d e+ 1 1rv4jnautomobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied e z:p4zh ddnjw 6i)iraa,iv9+k11iz 3his 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 cornn0w5c., 49ow m 2j(vspu bomncrete 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, (nsw 2om,mjrc4w5n ob9p uv0.what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest dire)ddanm 2 .edse4)vl y7ctly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will add). 4dy27nsev lme )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 wohccxx 1*2c8 liod 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 2cxc1* xi chl8rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass cxxzbcvmb m9 +a+6 2izoz49 o375 kg and the other of mass 60 kg, sit in 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 excz+3x99i 4xbz+mo6bz ocm2avchange 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 wpgnrnu14n;gn j. j5x*dp 0pq:as 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 fkh2n:dzgq 5 f8,ry2uo ragments by an explosion. One fragment acquires twice the kinetic energy of the otheryk:rz2qhfogu,8nd 52 . What is the ratio of their masses?   

  The force on a bullet is v,0*- 8u4:cfq7aggfp shqs c;r i 4ttagiven 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 massespv(z.8p pu+ xrls,/tj $m_A$ = 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 particle and s-qreb:z8p 2c7 i5 q;ibfy) uoa smaller nucleus. What will be the speed of this recoiling nucleus 5;zc )ubp:r7qi bsoe8iq f-2yif 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 fireta ch 5rj32r25dbab l*d at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 3 0/(;(lh4hf yh: mver rd4xzvn0.0 $^{\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. 7–4mra:lziusz-qu 9ae7-v5g ff -up1-i76), what is the upper limit on mass m if it is to rebound from M, slidefg mpis-1zaaqzlie5 u-:u-7 f 7ru9v- 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 effeg+ezb wko:wg k7 (ij- 01ab4anct. Figure 7–47 shows the planet Saturn moving in the negative x direction a(z kia70eo-k4w :+b jgg1naw bt 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