We claim that momentum is conserved, yet most movin( -c5mo1f ygdag objects eventually slow down and stop. Ex5y(-o1dmf a gcplain.

When a person jumps from a tree to the grou 0319itw(gs/zqhx jdmdg q7n-nd, what happens to the momentum of the person upon striking the gr wxmqn1id0dh 3g(7q- z/tgsj 9ound?

When you release an inflated but untied balloon, why does it fly across b/n iij3g ydi5)z +,azg +w*iqthe roomi*ng3z+5)ji+a q wgiy,bdz /i ?

It is said that in anl a5 c(quxhb9ee 7teg5/rlxv 2+4o r,zcient times a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless,,olcze u(e /xqxh7 2r45tv +lr9b a5ge he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction w/y1 h abq;mg.ehen it is far out in space and is essentially in a vacuuqa1 by/e.m; ghm?

According to Eq. 7–5, the longer the impact time of an impulse, the smalyz.inmz0fp1+zat6vfff oy37 q-k 2 g(ler 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 automobile collisfzv 7yf1 kn-mzt0ap zfiy+q6o(f2g .3ion and reduce the possibility of fracture or death.

Cars used to be built as rigid kkiq nwy.h*+gluwu vu2 /iq2929 wkv/as possible to withstand collisions. Today, though, cars are designed to have “crumple nvu 2.9 k2iq*uhw2i/wkl wy gku9v+ /qzones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baexj eibcc.r: g;lvg2m ,o*k sv)9d5 1pseball further than a ball tossed in the air by the batte1di,vcg2m j;v :gc.)9ps*erolx 5b ker?

Is it possible for an object to receive a larger5n::+ c rhn9iofife0l impulse from a small force than from a large force? Explaihec5: :90n ifirlfon+n.

A light object and a heavy object have the same kinetic energy. Which has the gryyj- 1q0df lo +wb,9xm1tlg:eeater momentum? Expt9d1 w my1q:oel- f, lygx0b+jlain.

Describe a collision in which all kinetic energy is los -)8-gizgorv (4 myr7m9i w)wbhhxp/at.

At a hydroelectric power plant, water is directed ar(hi a5l38oqq hf 7v5nt high speed against turbine blades on an ir(8553hqal f7 onqhvaxle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall atjr2g)*h w (iing0w* nc 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 auswu(3gezc4h, 3 d f.e height 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 durine u3(fgdes,.z3cwh u4g 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 carryin, w8- vi6esumt3j 1urxzzy. 8wg a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is no + ;epyh)0khig lxjz03t true for your arm or legj3h+xeih 0gykpz ;l)0?

Show on a diagram how your CM shifts when yoj(le(i x bulkx pc2el1c/. ):ju change from a lying position to a sittin.c jexkl b1u 2l/xle )cjp((i:g position.

If only an external for:e*,p uj;7mmv warp4*0ue csbce can change the momentum of the center of mass of an object, how can the internal force of an engine c m,u0spe epb jr4u*:*;w7mav accelerate a car?

A rocket following a parabolic path through the avqij -.4-*l x+ zjyuyy2o-i0rfp *tjm ir suddenly explodes into many pieces. What can you say ayiry p*x-i 4lqf jy.tj-z0o-+ j*u2mvbout the motion of this system of pieces?

  What is the magnitude of the momentum xkfsf(x+fon1k/+ k 5aof 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-kg skier for 2s3+uzjb+a ) ynzxw8*kb tef40 0 s. What is the skier’s change 4*z)z+bb faetjk+ nyw03x8suin velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line dris0sd 0te/s;agve straight back toward the pitcher at 52m/s If the contact time between batg0ea;s0 s /std 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 speed of 1v k n+pzyb):8x*y sj8c0 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it wa8cj nxv*8:skb+y )y pzs 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 exerted on a rocket, given 9,ke9+y z q( a;wtjbrpthat the propelling gases are expelled at a rate o(z ayer ,tbj+w;kqp 99f $1500 \; kg/s$ 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 r1c z8ohsb 6k1o1hpe- $4.1 \; m/s$ 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 frict fq38 nwp 4fp(.bbe0efionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s newb.(b nfqp fpe84f0e3w speed?    m/s

  A 9300-kg boxcar traveling 4:hcdm) cu +x/f5bsnh 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 hor2jtc6 pdi jnf,v yz6;8izontally at speeds of 100km/h If the air str 86d6z jp c,itvfj;n2yikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad c,ih.rj 4:jl mnsg j6lpm: u3c7ar coasts along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after lhpc :ijuj3m m6 j.,glr7:s4n90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s e,q7, o+wpo5o6ub-s :)5g q qc0unrgc+dey knemits 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 original nucleus has a mass of 222 u, what speed does the eck) w6guo:po5r d eq5-n bon,7guq0c qs++, yalpha particle have when it is emitted?    m/s

  A 23-g bullet traveling ckwjlw 2,() sb230m/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface w)2w,cw kslj(b hen hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket x7b ntw*0u/*i( p/p jscpad/his traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 31u95*jn8c l wa t 2v wiq61brxog4l1yz580 kg is traveling in outer space with a velocity of 115m/s To alter itsy5*19 i zotal8cw 2xw4qvj bl1u6gn5r course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the pdm +pq36axg9tee at a speed of 45m/s The golf club was in contact gd6x 93a pqmp+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 av,xu cy g/ot+, nail at a velocity of 8.5m/s and comes to rest in a time interval oy ,gx/uco+, tvf 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 mg((cid /r8hy/) unwal=0.06kg and speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthines vfly;zmtq19fun6r)q62 b sefd5 q 3s(s of new automobile models. 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 im9v2symdftr( q;q fz)65sq31enbuf 6l pact 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 eastvra76z/ lyuqe3 s )cd9 and is stopped in 0.75 s by a head-on tackle by a tackler running due wes yvad 7/quc6r)3z sle9t. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) k 553idj .srbjpoints in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Usesik.jdj 35 rb5 graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump witho valn0:aa r/3 pj a9d,w2a) olwqy3n*uut 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 strength (force per unit area) of bona p0y2au l a wwl9vdo3aq*,/ra :)n3jne 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 a speed of collides yvn0zilt.;hxcl b1 ;7head-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 zx ;v;h1cn.tl7l0bi ythe 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 3mqhig(bz2d/pm)b+ *zcv-:n b v/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and lebi:2 )/*(cvbd-bpzv g+qnzh m t 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 undergt:.yov4gu/)j (hpoxz o a 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 m/s, and call that direction the positive direction.Let B represent the ) ytjp:4h ugo.zvo (x/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 ofds,o1y0fm )4 je qj e ;8iz.f(6+feweuouy td* 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 each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.edu 4q6ydj,;o f ue1s+zo8fm w(. e0y)tie*fj)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving w.e8.hq 2 dpinbijb5-kith a speed of 8.5m/s collides head-on and nbih- .dkbpij82q5.e elastically with another ball initially at 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 amusemenyt 0c)k ljc h-(a7*ctet 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 differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculatcl(0 kcc h*ya ej-t)t7e
(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 collisit/ glr++0psxl: cm: 4o c2wh3p7wnqyeon with a second ball initially at rest. The syol +/n l0c+7xh2t 3:emgr sqwppc4w: econd ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a fricti bf 3o8+nt;7 d-mvqrqnws x9r52rq,koonless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the inclinq7x2;o qr+q58wrrs3odbt v nknmf ,9 -e is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general casedpw .;d7 la6br 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, projectilkb .rd+lw24q zddfor*ooxs( u +:4)qme 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulumr42+m 4dqo k rd( ud)+sq*.: zoolbwxf 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-kg pendulum hankk-,w5ymut67ottr9xk 1s d/ m ging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacemr7 9sm6kw /mu,t5y tkod-t1xkent.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of k,l,crl:dm eg1a y 2afu,j7s1pinetic 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 ) 9dybrec(ca )(tudsz8x5bv 9wg8 ,oc object, initially at rest, into two pieces, one of which has 1.5 times the mass of the othegwz(ryc e, 8s) )cub cdb5a99o(x8vtd r. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of x)+syf3w1c iwe zn8xy) za7:ea 2300-kg SUV stopped at a red light. The bumpers szwx17ay )e x:i cfe3yzwn+8 )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 de2s+nmzz / x 5)xai;kfhrm; )of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make befonsrzxef)da2z;5 ik+) m;mh x/re losing 90% of its energy?   

A measure of inelasticity i+r ai8uu)/yf htt54 uw0q.8hjinsq.o n a head-on collision of two objects is the coefficient of restitution, e, defined asqtiunysh .jq8fh+ w4 ut 5 /u.r)8aoi0$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the mass of t2ncn-hdf u knq/u+w l1q: )y7)p k7 3*fjqqbsthe other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the blockqjws q37h/1u-)d+uq2nfly7cfn tnpb*q k): k 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 i;naic4k7.:3s z jqnepe,m5;asc sx 1qn the +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass if: q ;p1 ,cs ea5jnaz qkss73x:c;e.min4
(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 invb f4 w9 g:g:f2) g1ms:jlr8cumoo*s7wd.h ljto a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have moment7.ovfjjuo rd4 :gw* gg1m :b9:sh2s8flcw lm)a 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 mk/ yihysmd5v; t, f0e1b3(ac yass $m_\mathrm{A}=0.400$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 inelh;tbhf4jm+*pkn89po,u ay045 e8g: ud lriyvastic collision between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial dirv4:8gb he fph+5unjto,au0l*i8kdrmpy y4; 9 ections?    $^{\circ} $

  Two billiard balls of equal mass move 8b 1gr rbqeu6w :0.aqdfauv4/)crr9l at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axisebaa4rrquw g.)bq609l f 1dr 8:vcr/ u (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 elasti 5xqkl;b p3u d h,owgusk:h96.c collision with another atom at rest. After the impact, the neon atom travels away at a 55. 5 q6.;3uk:bkpdswlhg9h,o x u6 $^{\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 coll7.cxxt eq; qq8h ;j5a4snwb9mision with another atom at rest. After the impact, the neon atom travels away at a 55.6 9qqjs;5nbtmwx8e7;h4 acx.q $^{\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 recgsg 5x t *.gns,y( r)2p(n;bvuas2bglativ (;x5.gyg (2sgbg2usca s n*rtv ,pbn)e to the left-hand 1.00-kg mass.    m

  The distance between a carbon atom ()m9r;rvumnw-yq*q)4aa4 rm d $m_{\mathrm{C}}=12\mathrm{u}$) 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 behi):s jtqfireqy*vwaa(x; 558 ond the front of the car. How far from the front of the car will the CM be when two people sit in taw8y5*q;5rvi xf oe)sjqt (:ahe 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, o- ;dwd,x6u *8hcpu 5mo-f voybedp8-xf mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, oc ;--d bw8,o*vp-oxdm u fc65uhyp e8xdcupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides 4w(2sl-eruwcw8h6z rw uq 7f8$l_0$,$2l_0$, 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 pu(fhf rz lf-x5(*uai 4:hd ug*aste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal pla uh 4hr-**5uz f(ilad:x guf(fne, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plgs ub 9 c3;gi;b(ocq)late of radius 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80 sl ;bb(9iq)cgg;c3uo R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportioe b g4jhv y;6kw)f8rn.ns are the same as those in Table 7–1, and calculate the m4e.kgb8 hw)n f rvj6;yass of one of your legs.    kg

  Determine the CM of an b1 vc6igy (*jfrs.q,loutstretched 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 offv,*rvi y+ *g3gamz9n an arm bent at a right angle. Assume that th+y,3rv n*v z*f9iga gme person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a positib /9w8*;ck sboa p3b0ltrp,mqon such that his arms and legs are hanging vertically, and his trunk anl0 kpa; /c8tmsbr,opb 9*3bqwd head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth a/y1y:8i7-id+wjwvqbb h 0n wand Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on q3 v.zjed7d /nncr*/ffrictionless 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 of mass 2.00 kg and a df8)c *y 8mniqgg.v:boiameter 0.0800 my q gi)on v.cg:f*b8m8 mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a unidqicu)4mob myc uwb c((3*4o/form cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mq cc iuy()4owd *3o4b(uc/mbmass 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 7–14 (Fig. 7–2wd)ft jn*59w w9), $m_{II}$=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, are in the air and stationn;;,9 ,kcfldj jp lrnhnnj i 09d(t2y4ary 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 ; yd,cki4; 0nnhr9j dj2ltjp nn9(,flction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and:+(pau ve6b g*nqsa g7.aui5z is popped straight up to a height vzp * 5.au+( 7gegbns:aiqau6 of 55.6 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 traveling l+ebotpp 30uioq: 01rwith 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 show j hp:1nxef45(ycxgk1n in Fig. 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 pocket? Give detail1p4xefx nj:yg(h1k5cs.

  A 140-kg astronaut (including space suit) acquires a speed +, 5ngos6amyjvtv7aqw5; h y77t;adlof 2.5m/s by pushing off with his l any tqt5a 5v7o+6sg,7; hmyv;a dljw7egs 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 60 kg and the other 80 kg, are initially d 58r see/+vwh /*+ vsvowg1cjat rest in outer spacwe vvs/ evr5*c8j1o/s dw+g h+e. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with av0 4pymcsxm*idgd5n-(xe2* z second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original spee nzgv2 pm0c5 *-4edsi*xxd (myd. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an chhk8 -n+-vkwexpert 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 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)v-hcw-k8kn h + speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight ocuod/t**)w: h/ - oat y:ypatsf concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of ta)d ::/ytts *chpu-yw *o/t aohe stairs?

  A bullet is fired vertically into a 1.40-kg block of woodruw s(l q/nc k0ulo54tvud6;) at rest directly above it. If the bullet has a masu uc(ql5 )u0k 6l/r onsvwt4;ds of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and biy- cp(cr 3q9uecomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coeffiyi(c9pq ur3-c cient 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 75 kg and the other offa e 4ok d-w4o5+zjra; 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 ea w-efaz ;oo+5rk d44jnds of the boat 3.2 m apart from each 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 was about v(kln/ cp1j p.$ 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(a;zp5pxep d4 suddenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic enez;ap 5epxd4(p rgy of the other. What is the ratio of their masses?   

  The force on a bullet is giv2d9g7;p u runden 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*phlkr1gof1gz9vy 5 ej6- 2vy $m_A$ = 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 paryb2c( s wza+9qp-wq h foqv((s(5j;ib ticle and a smaller nucleus. What will be the speed of this recoiling;s bc wys(w-iv (2(q(zajfqbqo+ph 59 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) is firedu4 s;..dgo x*zbf7 dtn at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides do /-/pf wpb nr*ql4vm9kwn 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 toamn wqcfh+l16 5j15msqce 4 ;o rebound from M, slide up the incline, stop, slidhcmqnc4 sqljm +a;w51f5e61oe down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the uxnc8r 6 s:9frplanet Saturn moving in the negatnxf8c:9s 6 rruive x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s