We claim that momentum is conserved, yet most moving objects eventuzl9f -3 1goiy:aw. fqpo c-ls5ho;h6y ally slow down and h-fl qyi.w -p3 cha :6915ysf l;oozogstop. Explain.

When a person jumps from a tree to the ground, wh22umuv (i q/cgat happens to the momentum of the person upon uumg2(/qc2iv striking the ground?

When you release an inflated but untied balloon, why does it fly acro*qbk. 2ygusj mxdy817/sa 8vgss the roomsax8yb2g8jku gd1.s 7y/m*vq?

It is said that in ancient times a rich man with a bag of gol e-)bu -kdoqc)d 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 done to sav -ce- )ukdq)obe himself had he not been so miserly?

How can a rocket changg9mt-*uxt,o:vq)8 triu c(ab ii8 bv: e direction when it is far out in space and is essentially in(m:ivb r9i:cab 8)*ivtg ut ,8x-quot a vacuum?

According to Eq. 7–5, the longer h n q(ez aw 94,nqo,b.+6enhzzthe impact 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 the force acts. On this basis, explain the value of air bags, which are intended to inflate during an auto z n,q9h,b4+e. zea(wqhzn6nomobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to witj( q-unpe9b c.a2 dy3pj*4dxx hstand collisions. Today, though, cars are designed to have “crumple zones” that colla4p d-cq djx* 93exbyapun(j.2 pse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than p jz3 3atme)qfls54;zly (1 yda ball tossed in the air by the batter?td lze py5a;1y(3z)q4s 3 jflm

Is it possible for an object to receive a larger impulse from a small force tid :oh i7cbr:ex8p cp025+ z-dpq+q8q 7qdphhhan from a large force? Explainp:hc8p7ehr 5 :ddz+2+0oi q- dpbqipc78hxqq .

A light object and a heavy object have a na,br):; s:f k3itizthe same kinetic energy. Which has the greater momentum? Exa)t:si;ar : bzkfi 3n,plain.

Describe a collision in which all kinetic energy is lost2o ;s ,5fr9mru:ltjrj .

At a hydroelectric power plant, water is directed at high speed against ti 1,2 dnlmom3iad-b 7surbine blades on an axle that turns an electric g b amlin,d1m-i3o7s2 denerator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a *i(z2wxaj4gy45 $^{\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 1hvsm(fy0wsp r-0l7urql 5n lgr o2; :h onto 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 andhg2rs(m-u oysr:q0;wl0pv7l nrf1 l5 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 heavy load in yorsp3,ejazt jk u ;:66/ 5iprvfur arms?

Why is the CM of a 1-m l34izd myii3pkg ,cw7m n7 3s5oength of pipe at its mid-point, whereas this is not true 53p3mk3 gdo7,7mnyciz4 isi wfor your arm or leg?

Show on a diagram how your CM shifts when you change from a lying position to q:x;f j 6(gegz.janr 308n*t guv hjz(a sitting positir;vuj3a .6 (j*neh 0z8x gq jtg(zn:fgon.

If only an external force can change the momentum of the center of mae: sy/sk02h4 6px1i9g ifdnu h igub8/ss of an object, how can the internal force of ax6sf ubu0/yi49 1 n8p2d /khisih:gegn engine accelerate a car?

A rocket following a parabol5:efqy/i f9 hqsny:5tg tnsjbq78- .oic path through the air suddenly explodes into many pieces. What can you say about the motion giso 8. :qeh- 5 yyj:nq9nqtf7sf5bt /of this system of pieces?

  What is the magnitude of the mome v0 x3zp2j5felntum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-. dov6rjc8 h5fkg skier for 20 s. What is the skier’sf 6rj8vd.co5h change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on 9dq7p 6ugas(y a horizontal line drive straight back t d6sa7 qpy9g(uoward the pitcher at 52m/s If the contact 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 horizontj zf 4fqt2psb)*gm4p/ zw8jy c1u:2jk3g hp 3nally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially atp cjtgjpg3 f42) :ju4bzq/y w81h*n3m2pz ksf rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases arepv4 yo9ws:pu;y9xln g*/bf) z expelled at a lsp*:fgo u)y9 9;/by znpvx w4rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving at.q 9fao7*qdp9 h vct4d vk2t;n $4.1 \; m/s$ 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 frictionkax; z ,liopx6rl3iq)jo7l ) e8g7*drless track with a constant speed of 18m/s A 5350-kg load,ijqplzok8ri lx6 r))* xl;d, a o377igenitially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travel7v lgx/k1pdi y)e 21yiing 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 stor.e,j k*r zr4j-jw tke(m, winds can whip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/wreet, kz4*r j k(j-.js per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railrqns 81ruf.0ygoad car coasts along with a constant speed of 8.6m/s on a level track. Snow b1nsf .8qgr u0yegins 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 moq b su*1tydvzn;2f v6v*40sxlving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the or2 b;uysf* vns4x 0qvz 61*dvltiginal 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 penetrates a 2.0-kg block of wood and emerges ysidy4 rwy4/)rf0jx;cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet / 4ry xry0)dw;4sfijyemerges?    m/s

  A 975-kg two-stage rocket is traveling at a speedoxjl/v1oawptk ,.ohm6mmi 0k)06s: b 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 w0aiv8 wy t2m0jith a velocity of 115m/s To alter its course by 3i0ywt 2vjma805.0 $^{\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 th.z+vcw wigwm.inj ,,5e tee at a speed of 45m/s The golf club was in contact wimzwwng .jiw,,v5 + ci.th 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+bpj uhipu*m e 9z1q8: at a velocity of 8.5m/s and comes to rest in a time i *+puujqm81 9h:zibpenterval 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 oy5 nwok povk5(513b.mk:mjta 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 envmie8h4n b5l (ns /y3l f1f73h amdv/wgineer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mv8aiy/enl3mw(nmdhh/5 v1s 3b4 ff 7lass 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 tol-e9 0kfd g ng+cepu,g+f:f6 q the east and is stopped in 0.75 s by a head-on tackle by a tackler running duuc9l6gefgqnk g+ ,p+fe: -0dfe 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.f om.6yk 3o, )iakhfj1060 kg) points in the +x directionh,o a3iom. ykj f61)kf 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 pz:.f-o.xpy 2e,t 2 96*rjr gxqgblsxcerson 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 ,bzf*gct..ox6:s 92jxr xlq r2 -p ygethe 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 directg bnuu. ahp9t7rm zr024o8g/pion) 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 represert928bazg 4upph m.07nro /gu nt the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-on collision wi2caix;jlj l i,u- 15ovth a 0.900-kg puck initially at rest. Assuming a perfectly elastic coo;l ic,ij1v5l -x2u jallision, 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 un)m3b. 0nhr 6zenrz5) 1niuv: oakh:zi dergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s 16nzz)5n kho zinu:i 0arb3)eh : rv.mand 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, moving with a speed of 2.5m/s collides head-on with ; yv5u xrlz9s6 tqs8n5pqsp1.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 each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B5 .vl51qssyxuqz 6p 98nrtps; 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/szxz xw5 5kpmv3 *wzfj7 4of.k9 collides head-on and elastically with another ball initially a3fx4 pxv7kzmjw 9zo k*5f.wz5t rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride co6pc 2o4i7kvv, 2jf cvfllide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg andoj 6,2fcv civfk4p72v car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a sec8be9jrnkb) -hg9g d v /0zqh-jond ball initially at rest. The second ball moves off with half the original speed of the - 9g nhhjg-q)0j9 /bz8dkebrv 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 skmw *p4c/+6;( sai1hbd cgcu jlides 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 floor,kw dj6*c cscaphmu( 1b/ig+;4 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 an k j4 sqxcye8 l)c-;(jtt6hq7uobject 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, projectilx6zc8iw cnr d 5o ,ffpc:x4x61e 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the p64np ,8xxw c6frxco:d5 fic1zendulum 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 b7bc2 c+xbw.vmrpm59pl6mdb ;uries itself in a 3.6-kg pendulum hanging on a 2.8-m-longpvpmx 725cr6;cmb9 w b +lmd.b string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula fsut7q 3b2(y v:lx.wnfor the fraction 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, initially at rest, i 8a 5a8ek;wm;pwtrga (nto 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 aca 8 kw5(tpewrga8;a;mquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of. b5nya5 +qyob ri.(hy a 2300-kg SUV stopped at a red lighbo5yqnbi( +y. y5a.hrt. 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 represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a heighu h:c 0t)9a9ix 9jcfhdt of 1.20 m. Approximately how many rebounds will the ball m9 9xh j0)dafc tc9ui:hake before losing 90% of its energy?   

A measure of inelasticity in a head-on collision 18dpx vaj vcys8km 3,9of two objects is the coefficient ofja 1kyv8d8m 3,xpv9c s restitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut intom 3qkw9aobu8- two 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 reassemblekoa 8q93bmuw- d 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/sdflvpv;cs1 hnt5n9 , ) collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity ocd,nf 1h 9ntps5v );vlf 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 into a second p95fauodh:y/ u *r3rf zd93xw nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right ayuu*3o:r3d 9f9p5dwh zx fr/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 ma)(wx5 a)qj ae4m4bzea2 xuiq )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 colli *s.33t 9jd hwk8nkdky prr(d*sion between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between theirtsk3 8yr* d .*3ddrhjnkw(k9 p initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at rijo7ediob inv nw3.( 96dm8m 6nght 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. 7–37). What is the final direction of ball dii jnw.mn on9e7(6v do63m8bA 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 w*dr7qv*f xv0 + mqgz83orw 6qnith another atom at rest. After the impact, the neon atom travels away at am qrgo +v0*qd f6z*wrn7v83qx 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 w ,7:c) blty5o v atsx//p4jyosith another atom at rest. After the impact, the neoy :y o7sjv/ 4btos,)cpx/ta5l n atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. Specify rel2p0-l ;cz.v.c i j3cgtkall q:at:- kc23vigc jctl.aqzl;. l p0ive to the left-hand 1.00-kg mass.    m

  The distance between a carbong prv.pk32 ptqki;fu)x- 8h n9 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 fron tdg.wrpz -t9qe/668 wak; h5 q7otuvmt of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has6q5 z98ewh;atwt r.m t6 g-uvdqpk7/o a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6h d4ipz9e+d ,u800 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 ferrdd ,ezu94+hi pyboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides;-v iey -sew* cavd(:ahmdx/ ( $l_0$,$2l_0$, 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 ident2u.ct *e6mu1sk,noa+ u2q5ernr /dfy ical 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 ey 2a+5m.sue1nko*62f u/ ,qrdrunct can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular platge b v2y-gd+ 77mux0rue 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 ciryx-e0 rguu+dm 7b72vg cle, 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 those in Table 7–1qckiv 0j;* lu*hsqpo w,6q5;u , and calculate the mass of one of your legs. 5c uqo0; sivwl* puqjk*q,;h6   kg

  Determine the CM of an outstretched arm using Table 7–f 8j5- yakq7 b hkz/7b5yvaz9w1.   % 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 any y/(kifj 8 xfwqog4(:gle. Assume that the person is/y:x4g8(yjiff( qwko 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is58 u* 2v-ggmeivz.t xg in a position such that his arms 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. W-v5 gt 8gu2g.v imz*exill this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moob izv3i742v; jhf9 twt(8rxgcn 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 7h lx ifk4vjmo9:,r s910.0 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 a uniform cylindrical head il(zd-75,:,uafhwoj) hboje *qqdr bo/0a e: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 pa, bwoo7zqdl)/h r:afq0ibjo du,-*a5:ej e(h rabolic trajectory?    cm

  A mallet consists of a uniform cylind; ; gwpq9krxr9rical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical;wxq r;g9 p9kr 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 Exaazlq51f6r0ovid t8f (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, af: 1skdmlq0 2xre 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 l: mqs0d f1k2xand direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontadn/csu263 v(z7 tqrpblly at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate t2dpcvr3q(sn 6/u tb 7zhe average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveliq-r1oywt-lr.2,m my wz ig4u 1ng 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 Figznrj;9:p v (vypop0 t5. 7–43. Relative dimensions are avpvpot: nr(z5pyj;09 lso shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s blne 4zg/xko nhh8 /t -nk382ijy pushing off with his legs from an 18 nl h3 g/4ni8/xtk2jzenk8 -ho00-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 othfkhw(x ot,8b7z1r)lrw5 l(xb 1fas*zer 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are theyf 8 xxr* bka l1swfwl)o,h (zz7b(r1t5 when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastvq gr+i/si 81bic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original spi+i /vsbg81r qeed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an,y3 mqdv9;s vg expert witness 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 whiledvsvqg3 9y,;m 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 thk;.7hxx+b4 h1uy voxmwc6ya) 0tczy,e top of a flight of concrete steps of total vertical height 4.00 m. The ball hits four times on the 0amty uyhcby 6v4+x );z7w xxokch.,1way down, each time striking 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 vert kl ls1:4vq9vwically into a 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of s91 vwkllv4q: 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wm4bdj8qdp5 o2yz(f q9ood 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 befo 4q(zym d8fpjqd2o5b9 re it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mu;qp.qj7mu;ev- se 3cl0 qpc2ass 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 eas.p2q;cqcp0q - e; u j3vlum7ech other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass waem j) qg,sp: oll:1t+vs 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 fragments by an+a9 mf+z76gowr+ui9zosmy5u 3xs hc1 explosion. One fragment acquires twiceuau9x o5f61m9 mziw zshy3 c o+s7r+g+ the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the j8i*o;rpd(oo :xtzh6 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,u-l:nsksq2 2ii bs.m ci1lp) )m a8in $m_A$ = 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 radioacty*g0erj -ttwd 7v,- ns0kq5e yively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of -0 tdgejw,vnqe y-r*57ty0ksthe 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 fired at an angle u8fd) tt*/*tgxq. tm4*iqn qb 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 30.ko6q5v-wx5 a/g, /vb d+kbw wj0 $^{\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 1 ig82 j*kfozmit is to rebound from M, slide up the incline, stop, slide down the incline, and coli28om f1z* kjglide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 syohb:as0/14x6b .e ky lzx3o shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.63e/0xlx zo.yo1k6bs :a4 ybshkm/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