We claim that momentum is conserved, yet most mei0rh ghn4dg iq u(4v 7709xlsoving objects eventually slow downhsxr7g (g iuid l0h9v4q e740n and stop. Explain.

When a person jumps from a tree to the ground, what happensgx ngd fv7ji0;); ,/r4 crmkbh5 vu*nrpbh5*j to the momentum of the personbdpcbx57)hhvig*u 5;*n mr,rg r40j f/j;k nv upon striking the ground?

When you release an inflate* gqw/gxm8k w,d but untied balloon, why does it fly across the room?gw,k*q g w/8mx

It is said that in ancient times a rich man wib12:a-qqo ge: /lr zcith 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. What could he have donob lr:z :a-eg12cq/iqe to save himself had he not been so miserly?

How can a rocket change directip yagf)d8- qwk0 +ni5 /m0dbafon when it is far out in space and is essentially in a vacukf8awdbmy-agi+p0)f5nqd 0 /um?

According to Eq. 7–5, the longer thec+doat0 .f,me impact time of an impulse, the smaller the force can be for the same momentum change, and 0+t mc a,feo.dhence 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 during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisioc:1fwh ib3wq15pjgo3ns. Today, though, cars are designed to have “cr3:o ifbqwwp315 1cjghumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in the air 2xx s15/5oxji sd a9irby the bao55 x1xjrad/s9xi2 si tter?

Is it possible for an object to receive a larger impulse from 6+gkm68htq* ie,yiioa small force than from a large for gyikoe6 *,qi6t8mhi+ce? Explain.

A light object and a heavy obds ;w. u .oxp(6ec;o i84ttcqsject have the same kinetic energy. Which has the greater momentum 4;;.8sxc(w6.o t quoi sptecd? Explain.

Describe a collision inh 3dpq wqkj7(3 which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at hi0uyu )c4q-qg/n bu )yxgh speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should thequ-4y 0unxu cy/b )gq) 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)qta. 5wm7st.j v)bhf(ee i6d 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 from a height h onto a hu ocr.cqw9iy+dce;3 ,ard 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 w i 3.,rycequdo; c9c+ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy6blh s / lh 7r)cxp/4dv,g(bbd load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas thikcvhr79 (eio8s is not true fore ( 9koi8chr7v your arm or leg?

Show on a diagram how your CM shifts when you change from ,gaweh+ dqa).jd.w 3m vho,9na lying position to a sih3w.9 n) ,wghddo .+ja,eaqmv tting position.

If only an external force can change the momentum of the centerv /:.p9bi+c aogp5 rk19mjeo 9j7xjbp of mass of an object, how can the internal force of an eng9 bre vkj oao .gcbp795j +xip9pm/:j1ine accelerate a car?

A rocket following a pa/ 8twz, nyj6ytzqv a iw0c2,-wrabolic path through the air suddenly explodes into many piecewztj0t iy2a q/6-w8 n,,yzc vws. What can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed o/ pik fl7nx/r)f $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What is tb.v(o 7 *ksodfhe skier’s change in velocod*v7.fob(sk ity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive stra 71y+ai/ytidx ight back toward the pitcher at 52m/s If the contact ty+xa7id 1i/y time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a 9de8bm;4xgagx 4+d j gspeed of 10 m/s Fig. below Calculate the velocity of the boat immediately 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. Ign49d4ag;x de xj+mb gg8ore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that thebw ) e*+,zf5sk31cmsuf; rofk propelling gases are expelled at a rate ok u;zw 5fo)ff es+ bs13mr,k*cf $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movinggntw9g+. -jz,b9ycqjnj/r 9 b 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 frictwpvb1 ti, 77d (v(/wcwpwvrixw1lm9 * + r.jcgionless track with a constant speed of 18m/s A 5350-kg load,in7 wi b19+w/vc*p.gj rt(wvxdc, 1 7lvmpirw(w itially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at(z-e w )ei9avr $15 \; m/s$ 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 wxgs,3p/ca mg(,r;vyyf:.zub k; ioi 1 hip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the f:yzu/.g1ipm g fry; ckbiao v3 s,,(x;orce 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 c8 (r;lqwwnvk.b)3n.nva do;bw ysd8 4ar coasts along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and oydra4w;w bdnn n(3w 8 b.8q vv;k.sl)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 initi krp*e)j, ig,zsb 0da,bkr5;u ally moving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s,0g;z kb,r,*)p jas5rud kieb If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetratesa1*hv.z 9v qlt 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 doe zhav.lqv1 9*ts it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speed o1/a.)cgj 8h( her.ii r 5(gtv(zpub bcf $5.80\times10^3\mathrm{~m/s}$ 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 6l* vi 8l bahx,ghb9g83180 kg is traveling in outer space with a velocity of 115m/s To alter its coura8lhbxgv,bi *6hgl98se by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed of 45m/s The golf*u1 :lwm orqg; club was iugrq o:l *m;w1n 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 velocity /b) wcqvw*bw4of 8.5m/s and comes to rest in a tim)bcvww4w/ bq* e interval 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 strikes a wall at a 4xd.vd+7k(9 94lum -tew7va jy1jqtba 5 $^{\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 crashworthin2yzsf; q5f ffhg(c;::hp 4jsj +g(pdyess of new automobile mod2 4f;yqfyh sch;szjp(+p(:g5fd:jfg els. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is sto vt+zi5f gnw(:pped in 0.75 s by a head-on tackle by a tavt : wigz(5+fnckler 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 36-g(ooprjw gdn., imon a tennis ball (mass 0.060 kg) points in the +x direction and is given b6gdw o -roni.( m3g,jpy 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-kxz/gt+ 0xul/x4ugt3b) -6;bs itfq tbg person jump without breaking the lower leg bone of either leg? Ignore air resistance and abl 0u)t/xq /b-;bt +uf i tg3xtx6gz4sssume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with t7uu7*yeluc fw3gat8 c 63u h3a speed of collides head-on with a 0.220-kg ball at rest. u638ytatc 7c g ueuh 7*3u3wflIf 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 sv dm6q +*db-dq- -orj;8g6sgbau(vm o peed 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 theuv6-vobm gm+ as(ddd-6 *oq;8grq jb- 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 a/5 nx 9-u0obwz 0slvko 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 v osl95n0x uo z/bk0w-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 withu s w/g.1nb, huw8fh 0ykv4y1j a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of e hf0,us1.h/jv yu8k yw4bnw g1ach 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.l-ycmxjax g6(zbkvhb61w d) hy-90 ;q220 kg that is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces z- h g;mvwbyay xcl0(kb)69-1hj q6d xbackward 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 mceuy2 hk+y-6dy x) 0ias 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 approyxkd-2emy+ cu y)i0h6 aches 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 bab hm+1ar:oaj,ll makes an elastic head-on collision with a second ball initially at rest. The second ball moves off w1 oar+,hb :jmaith 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 frbh(nf ml v c07v7s n n:pz kwayts/(t;in64y((ictionless 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 floor, where does each cube land? [Hint: Boshnsl bn;vn:ftpm w(y/ (47z(it c 7v(6ayk0nth leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an obje ;3wm7ewzxn.hhv t(z00.g yt z+0 rkusct 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, projectirf 8(mdtq*cvm d4 6jbttl w/./le 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causeb/djmm8w c(tl4ttr f/qd6.* vs the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kq1zz9a(eu d(eg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the penz9u ed(za(1 qedulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction inl t1r 7yii/z/14rkjof kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into tfxlf39ydh/ewfw1/ *f 6nm bl x(p44upwo 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 ehnbf l4 pf9p3ux/l/dx(1*w6f 4wmyfparticle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped at a r/x cu vg lxlp)d107e6+/tixph ed light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represed 0/ll1xc/ixx67uegp p ) vht+nt the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a heighll f:e2)y-dvm t of 1.50 m and rebounds to a height of 1.20 m. Approxid: - fe)vmll2ymately how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticityebc/hckq1 ; fb-ooot-8; vw +5n*l qtu in a head-on collision of two objects is the coefficient of r hqwnuoo 1vbkbf o; +;-*5 t/cl-tqec8estitution, 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 twinam cm846 nlo:q:iwzu n ,, ,c(w8ttfz7xl;co pieces, one with 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 the firecracker explodes, the two blocks separate an,i(:xwt qci8l;8 :,fzznt , cmo amu 67wn4lcnd 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 collides head-on w1t vyeqi-.+ .pl r*nxjith a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each maten i+pq* v.xy 1jl.-rss if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an electron, h.qjn )oy7phqkg *adq w6uz(a * .h/+nand a neutrino. The electron and neutrino are emitted a +(q.gwdho zyq7 p *a/hn6).jku*hnqat 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 jh7sbp.5)pee$m_\mathrm{A}=0.400$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 m 65oso tsmd2tqr*lwc2ou g4, 6ass, each having initial speed the two move off together with speed v/3 What was the ano, o5rc l*4s2 ud66wmqttg os2gle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the origin of - ya5 zcuun.n0an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is movingn-cy.anuu z05 to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elasjaoc1-b;ee /2q t*0jsa qdp+w tic collision with another atom at rest. After the impact, th-1 pjqo +e/te2c;as0daw*bqj e neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision ipv)eil t0b1ula- 2u;dq :dq)with another atom at rest. After the ll)uiv u2)d01tqp d :-baie q;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 th+kp;nf-y;agnrn9*)gdl2 oq st;m 8il ree-mass system shown in Fig. 7–38. Specify relative to the left-nlon;ig 8pdg2m)tq9 * yk+l;sa;f- r nhand 1.00-kg mass.    m

  The distance between a carbon atockhodrtc ( -a;y zj67s5*j5x um ($m_{\mathrm{C}}=12\mathrm{u}$) 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 behinkvm+iu5sy;u *d the front of the car. How far from the front of the car will the CM be when two people sit in the ;s +uukivy*5m front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is usd fh41lgj+9v bq dke2 7b1sps.ed as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of thevbdq jsf2b1k. pg+ 7 l14dseh9 loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides 1dm * 3znef)4dgdiy,2mo*bb r$l_0$,$2l_0$, 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 pa,ys wiv sx2+9g- tt3 x*m5qebdste (see 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 2 5s wxgqmsdtbt3,vi-ey9 *x+can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular platelfj3*kkl * md* of radius 2R has a circular hole 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 th* f*3d kj*lkmle plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and 9.bjsavki3jn5+n 0 q rcalculate the mass of oakns3ji.jqbn v0r5+9 ne of your legs.    kg

  Determine the CM of an outstgb(rctb, be jz. ,e)gp2gsupw( *)lt8retched 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 avecy c30st3 b7rm bent at a right angle. Assume that the person is 155 cm talc evs73 byt3c0l. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his armu da +-w.ecmfm8c g,5gs and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will thisd+.wa58m-g c ,fe mcug CM be outside the body? Use Table 7–1.

The masses of the Eartjb4 h0l7) 1esz+ nw7ifqklwg 1h and 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 jw4qyh88(v 2xq sk2bxv xa70sapart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a unif)vjf kil0dd50 zj7 v3worm 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, awiv30 vdlz5)7 fjjd k0s shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a di9lksqeb5 )ow,* 2 alj3utal gt,hlc.8ameter 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 traje,8hc ksjlt 53g2, lwbaua*t q l9)l.eoctory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7-x ixth6d- 7f0k;4 v9dykd xqm–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 + oj b8 z4ouf fc0h2k0y0lfes0m jjr*-its gondola, of mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and dire*f2fj -4 j+8zl jso khr 0oyufce000bmction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontallvw2*+ef(hy2swd:fava,cz+ 3p - xfh t y at strikes a bat and is popped straight up to a height of 55*+vfhh tx 3wd+f2-2ycp :a,wf zse av(.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travelj(h 5 c wl6)lw2v,ei11jul nlving 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 corner pocket shot shown in 9e nocx.aa/7 u+sz. dgFig. 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 podcea ao .snu+x. z9g7/cket? Give details.

  A 140-kg astronaut (including space suit) ab: 0x u dofve)hou81)kcquires a speed of 2.5m/s by pushing off with his legs b)0 dexfo):uh18ok u vfrom an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 k1*mdq +m,hx laq z/f)s(pgo9 e9zy l9bg, are initially at rest in outer space. They then push each other apart. How far apart are they when thed 9yfq*9h9 ,o xe+z1lm)p lm/gbsqa z( lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (at rest) y iixe(ccu+6(d9ove5 xu/ z,zand rebounds in the opposite direction with a speed equal to one-fourth its /uiy5(cxc9xui(ed6v ,+zeoz 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 z+,twg0 o w1k2*yiccd d 5jn2twitness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction betweedntokd5+0g2cy icz t1 wj2w,*n the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total v (jkfk1w:ewv pg184iyertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a diff wei8w4g kpfv(11 k:yjerent 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 1.4oiya4;0u weeo,,fqpcs9 2j e,0-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the bqj,,p,aeo49s w; oi0ufeyc2e lock rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embeddu:hz3wt46)t 04l ydq8zyg p(tqq - kared in a 1.35-kg block of wood placed on a04-gq)tdtzlry4 qh8pkq6zuw t a:(3y 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 the muzzle speed of the bullet?    m/s

  Two people, one of ma) oa7+y-n+ksg4.q.yj 4jys z jcqrte1ss 75 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 exchange seats. How far and in what direction will the boat move? The bok+n gyj74zrc)s4y+a.o j1 tye.-s jqqat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abouccaxsu s(+i l5 2np,a,(rtb,ft $ 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 bdr;usiskwgc 266cd --edue/ o3 n*eb7y an explosion. One fragment acquires twice the kinetic energy of the other. Whd*b soi/ 2n6e6 r de;7ck d-3w-geuscuat is the ratio of their masses?   

  The force on a bullet is giv v5zaslc9w44+)ctpgaen 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 masses ajn4pfei 93vj oe q:a-jy6g 18$m_A$ = 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 s9oso 7 dw1nt ,i)w3a dm*(-irdqa2zerest decays radioactively into an alpha particle and a smaller nucleus.,draa2*m 9i e7dwz13sw-nqd() s itoo What will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) i 16(nniw sn00w md/ j7hyu(xdqs 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=2.2kzbaqt6x 6+8 blg slides 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 limit on mass m if iy8)0 k9 lmlbuwt is to rebound from M, slide up the incline, stop, slide down the incline, and collide with M m8 k9y)ulb0lw again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the pljdfjc 046omp,f1t rm9bc c 9(qanet Saturn moving in the negative x direction at its orbital speed (with r(rmo6t qcc410j9fb fpd,m jc9 espect 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