We claim that momentum is conserved, yet mos;+wl fv6 ajy8xux9 9nwt moving objects eventually slow down and stop. Exp9u +6wywx;xan j98fv llain.

When a person jumps from a tree to the ground, what hap0bgp;n*3 ia(o) yutuqpens to the momentum of the 3yt bup)nu*aq i0 ;go(person upon striking the ground?

When you release an inflated but untied balloon, why does it 2sv kp4v7v5 i8qnwou+fly across the room?uv 725wip+v nv8ko4qs

It is said that in ancient times a rich7vfmbyh2 yz58kb x) /,t4ryhr8zdsk9xm49t p man with 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 donez t45by 87r/h4xdfskymhmp,y89t)9bzk2xr v to save himself had he not been so miserly?

How can a rocket change direction when it ,(e q*2/y1ydra- vfbgj1bie nis far out in space and is essentially * jb/ rg(nede11y2,bv ai-yfqin a vacuum?

According to Eq. 7–5, the longer the impact: n 35qq1malbs;qq y(b time 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 thna5l b( :qbq sym13qq;e 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,ww6e n g;gk lzs+b+fes 62kn9 withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse u6n w+l2gee6;nwk, sk9 s+bgfzpon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball furt+zenv4q3tm:,1dt v nbhr9 n( gher than a ball tossed in the air by the ba3hv ,tnntne9m1zdbv( :4r+ gqtter?

Is it possible for an obje ea4wvbz yw pc,e)3-/act to receive a larger impulse from a small force than from a large force? Ew)/ w,azv4 3eabc-epyxplain.

A light object and a hea j iu/h8g.y lbj)b/ds1 dor:z1vy object have the same kinetic energy. Which has the greater momentum? Explalby/ s1b) . 18hzjg/d o:rujidin.

Describe a collision in which all kinetic energy is i/p g(+1 ljg t06-ifgxc8idrulost.

At a hydroelectric power plant, w 07jupuk(ok1e vle;j ;,f;w:/hqhnjsater is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, ork7w(j oh e 0;1qujlpes/;hnufk, :vj; so that the water rebounds?

A squash ball hits a waljhhy27,;diwwa,p+9s b rzxb+l 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 hard steel pla jiusw*/) bimbc :sg+)te (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserv b) cigmus*/ s:ibj)w+ed during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when ca- dzii6)x6ckku kx ;2orrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas;t uq3x)b h0vk this is not true u;q vxt )hk30bfor your arm or leg?

Show on a diagram how your t gfhp( camp+f+t0x/iz)+tg7 CM shifts when you change from a lying position to a sittii)pf7txg+cgt0hpm f ( + /taz+ng position.

If only an external force can change the momentum of the 3wqah6d2zv 9oip 6qo;tru9, l center of mass of an object, how can the internal force of an engine accelerateou3t9p6 r z, hdq;l o2aviqw69 a car?

A rocket following a parabolic path through the air suddenly esqw9 i+ 3 kw/q k5amk:ky-s;wzxplodes into many pieces. What can you say about the motqqm;-skw3/9 + ksw :a ikw5kyzion of this system of pieces?

  What is the magnitude of th3dv63aqu mwd; e momentum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction forc 5w,j/ p/8zykwor ibv,e of 25 N acts on a 65-kg skier for 20 s. What is the skier’kb8 pj,wzv w //,oyri5s change in velocity?    m/s

  A 0.145-kg baseball pitsoi:yw /k4pw0 ched at 39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time b0 /: s4pkwiowyetween 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 6.408d /b6vnaza)pvu 6z 1o-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immed/)zozv6 dv6a18bp nuaiately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exert:5b4c wour.w9 khz; 3xiw;a rped on a rocket, given that the propelling gases are expelled at a r x;cwap. 9kio:3bzr4hw ;w ur5ate 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 movinxi1tvch)do1u(yw d69bxe +2vdt 08cpg 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 alevelb7fa d) v.-wwehxl (8no/7:nyyo a-cb frictionless track with a constant speed )vb(a/n7fely o-: yan7w8 -bowh xc.dof 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar tralpr2v t-c4p7q veling 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 100kj3 m,,)ybpdwc klv x3o4n gl3+m/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 the person is 1.50 m high and 0.50 m wide. Compare to the ) l4 ,ng+ycx3wkopdm3l 3,j bvtypical 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 spi.rbrjh; yf2vy; ;5 qs9v peg7eed of 8.6m/s on a lever ;.sbgrvjq;p i9 e;2yvh5 yf7l track. Snow begins 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 par2vs(zz3o49m9 gf* kvsz *1chqyhdvf :ticle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emittesk 2 zz:fv49f vvq*1h39zdoms(hgy* c d?    m/s

  A 23-g bullet traveling 230m;uj r*2xkwti a9.nw3r 1(q:2aqun8bot6 kg sz/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is statigt1u3*2kb q 6o;wrksn ir98(au xwn2taz.:jqonary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at aw; yh;g3 uj0cj 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 iss:r m yg4orjl-97o e9x traveling in outer space with a velocity of 115m/s To alter its course byj79 r os m-4y:rgelox9 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 ajj ir-4 ;i+u7 tcb7gt/aznit 7 speed of 45m/s The golf club was in contact with the b;zt7r7gj7c jti -ni+ aiu b4/tall for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes to rest in auyr2 nratn5s- 4+93u; p +jyjn/f yksa time interval of 8.0 ms. (a)4na5 +jyy 9; nu3pss/n-t yr+j r2fkau 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 :; g7ofj4wek9g fj1o da wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthiness of new aupdow7mma6*i d3 s3wl4 tomobile models. Cars are tested by smashi* mp3 d3a ds4wl7iom6wng 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 stopped in dn7y/k 4yx6p1rlr h11gypjv(0.75 s by a head-on tackle by a tackler running due west. Calculate xr4 1rjph7 g (kv npdy61/lyy1
(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 0n/. gk dqcm42v.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estic/v .kn4m2 gqdmate
(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 can9 d t8bjrlzjx(x2hom+d2::eu . 9nnea a 75-kg person jump 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 the fall). Assume the breaking strenl2h.2bmu8x :etejj9z r9oa :+(nxd n dgth (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 (+xmmbdx0l uvgon577 r 2) 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 th5xvrmo2 l )7ngmbu7d 0e 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has fj lixk;gspd ;.-fa.7a 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 c; fj;7dapig-l.f sk .xollision?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 underga;rynly*vdw5-o e21xnnin . 6 o a perfectly elastic head-on collision. If one ball’s initial speedae;2nyrnn 6w o.i- l5nd1*v xy was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, movie ogpcinp:oyl,0z e(q5(1vx:6srvm 4 ng with a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving awor 1, (0 ycmoqnvexg(li5 p:pev6z:s4ay from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s collides headq4gi0i 2m yruv;: v2tw-on and elastically with another ball initially at rest. Afterward the incoming sofymg tw2 v:i;vq 024riutball 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 lrbe,cj/ /8am amusement park 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,bjeacr/ml 8 / differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collisi5iakx c-,we a6+8tb lhon with a second ball initially at rest. The second ball moves off with half the oriha85 bx+ 6kiwc,ealt -ginal 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 frictionlea6dnx:ldv 4-k ss 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: Both leave the incline moving horizontally.x 6ak-:n4vd ld]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case.ll2ayg9f wz5) s1vj b of 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 results inf (g454oo. nm bat2 oqqlz05vy a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twinot f.50o24 a(qvgzmq54o blyce 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 k)ns (p 60uo:9zc gdjj230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum s)n: (0ugd6j 9opc kszjwing 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 fravj/gyqajtz i6)bmtest82j 5 k(6tge(;.c / nwction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initiallyr ps; t*cb;f4r:vn2zh 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 particle, afzspr btn*;;v h:2cr4nd B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the reajiw4ty. t21x)h8coody q9a5qr end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brak2tyyad.54xo 9 )wqh8cji q1 otes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a rg 2ehrfs8+6m08ito i oo -s9iheight of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ballm0oft8i -sr9s6 +g 8iooi2 erh make before losing 90% of its energy?   

A measure of inelasticity in a hea eworqs f(*wg(y rht:7w2sajp/ / *vj+jv:v/sd-on collision of two objects is the coefficient of restitution, e, defined as/+s*hv q y*vvjwr/o 2wgra st(wj(/jep7f:s: $e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
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, onocggi /vx/13t gz++-f 7t 7 1blaj;mz6qdz sjwe with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker caa3v-t jx7 +dgz jggfoc+i71; swb tml/1q6z/zn 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 collides he/r,*ex1)s, r-dsb c5 ytykfkqad-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity ofs*tc-q yf5,k/yrd)x,k1sbe 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 m *n;fy)t0gm hat rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emittemgm *n0)hf;tyd 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 mal1o+n49 iq )ovpt8rrz ss $m_\mathrm{A}=0.400$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 betwee c,k/ks7b2jwe 1s0 yton two objects of equal mass, each having initial speed the two move off toget7,k j2/cowes ky01sbther with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equ;rs x4k ) jl/nbbrp,n,8)zpveal mass 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 positiv)v;p,rn/b s,z nexj4bp8 l) rke 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 per- , dlorhw 5g6hip0myi02d(kbfectly elastic collision with another atom at rest. After the impact, the neon atom travels awamgd5k2ywpri60h 0b,d -olih( y 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 wit)inz9lw. vc802faz mdh another atom at rest. After the impact, the neon atom travels away.)z wfldc029iza mvn8 at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. Specifyng ,wu6wu o d;zlw7c4icbq/lm, 84wm, relative to the l ,4wwgqn dm,w;uwioml 7l ,c4uz6b/c8eft-hand 1.00-kg mass.    m

  The distance between a hy9x 6njwl;*n carbon 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 ea-j ; opbgy8+.kf-pm+a 6jxkof the car. How far from the front of the car will the CM be when twokepxj8;+ j6gk.m fy-oa -+ bap 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 by 18 m, of mass 6800 kg, is used f :;wd j)va p+ff3b1eyas a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferr) 1 fbf3vd;+y epfaj:wyboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides 96ar;pv53 aiabe re uw*elr;.$l_0$,$2l_0$, 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) palletr2ze9 l2bdf8bvds))3w evjp5 has a load 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 horizontal plane, so that the crane operator can pick up tz2 efpswbr5e9 ld)2v3) v8bdj he load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has avsssk14 8dhkln*15 d o 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. s h5 dv*ks11s 84klodn7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same r bl/bv((:kek as those in Table 7–1, and calculate the mas(vbe rkk/b( :ls of one of your legs.    kg

  Determine the CM of an outstretched a p q-nj5fgdy )3fjhp90rm 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 aniazn 9 4.ks7qp arm bent at a right angle. Assu49 s nikqp.7zame that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hangi2t6ofg t6bla86vv, pl ng vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM 2f v,l6lgtaobp6tv 68 will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon v 2lf;zn,du)sare $5.98\times10^{24}$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 ,k*+t 7 jl5 rqyb:12 peeolx1r/n3x;uqgpoi v 80-kg man stand 10.0 m apart 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 y*;4+:tewnmjgf(ef m (i 2evoa uniform 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, sf:wymtv f gnoe ee(4;+*m(j2i pinning, 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 cylunn d+ /d7c ;5+:pxgmu5p zss*pm rp9vindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical sc5mp+nzr:xdg+d*uvnpp7/p9 s5 ;mu 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?    d    d

  (a) Suppose that in Example 7–14ac r2e1ud1jp3r;mj-h (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, ofzc98mw q7q i whea09i0 mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative c9 me7zqh8i0w aiq9 0wto Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontallym8:xt-dba faqhhz1/qr f8 c29 at strikes a bat and is popped straight up to a height of 55.6 m. If the contact chf- aaz9qm d1h:8 b/rxq8ft2time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travgruf, o8t- fg,2lfrm 9eling 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 Fig.0wew+jtf q i:zw,d/f4(-gh au 7–43. Relative dimensions are also shown. Should the player be worriedtu0d/-h4 z fwq+ag,wwej:f(i about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including usc (s+t7fl* ispace suit) acquires a speed of 2.5m/s by pushing off *fticu+(s l7swith his legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass yauc99ymg x )et78np+ 60 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart ypg9y8m9tn xeuca)+7. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on e4j(4kiv3guu.j k yi) zlastic collision with a second ball (at rest) and reb4k4 gijv.(u ji)3zyu kounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court c - r.xl3cblh)6bmqnh- ase involving an automobile accident. Thrl qbh h.b3mlc6n)x-- e 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 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 concres1q: du ie+ jq964wjaste steps of total vertical height 4.00 m. The ball hits four times on the way down, each time st sa 4 sqj916ijq+:wdueriking the horizontal part of a different 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 1.40-kg block of wood at rest directly avf2tve;m e k;fy +2/j)2wk vpucx4c)nbove it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after ty 2vt 4w)kv 2 kc+enc/mvuef;pfj2x );he bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wool:xqhygn-op3 l(+r m (d placed on a :lhg(q- rmn(3 xlyo+phorizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75b m, om/gzk/+i 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 thez/ /i, kmb+gmo 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 aboui7 k1fatm 6r+kktf: (yt $ 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 c. /du ev/0bgzqxf. 8rinto two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is tvr0 xbfz8/ dc./ugq.ehe ratio of their masses?   

  The force on a bullet is gr pams1 t59l)tk kqjncx 95,l.iven 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 masses27c1 ubaqhp*m;felk 5 $m_A$ = 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 particl 0td)5srxhfp3 ;ju2bu e and a smaller nucleus. What willjpduh ur03t) ;s25fb x 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) . :)kydle q-zcyc6 k 28;arqpris 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 x1chx+c2r+kz5 +1zaywmbk1a 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 it is to rebvwpo;dg*i. sk3 jw9l6d-z9sd nhi2 a*ound from M, slide up the p2d*aiw zk v*-9d9dwsjs3nog. hi;l 6incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–6.o* aqier bvo+k/.u bz/u ff.47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturbfo* o ieu.v. uk//q+.ab6rf zn 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