We claim that momentum is conserved, yet m(w/ otz5p 7qvze 6e7jkme/i5host moving objects eventually slow down and stop. eto(jkqhz 55e7e/7/wi p6m zvExplain.

When a person jumps from a tree to the gh9pc2z n pu1go9+;kkoround, what happens to the momentum of the person kp9zck1uohgop9 2 +n; upon striking the ground?

When you release an inflated ht4yus-ng )d n 6dg,n1but untied balloon, why does it fly across the roomutgnsn- dh416 n, y)gd?

It is said that in a,c4iv)z a6 *:v0uhra5u8 qpvv3jpzdvncient times a rich 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 done to save himself had he novzqj*a8p 6a cv hv0u:, 45upvd )r3zvit been so miserly?

How can a rocket change direction wq/ aknuu;2, dh:tcha:fl0. hqhen it is far out in space and is essentially in a vacuuc./ tha:;lqn au0hu2 k,hq :fdm?

According to Eq. 7–5, the longer the impaeogy b+m0-e v*d6wm:kct 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.oe: b w0k-*d+my6megv On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collis2p+4).dok i8 cyeyldnq08fc;z bo yf;ions. Today, though, cars are designed to have “crumple zones” that collapse upon impact8 bz;c4 ) yclnk p2i+0o;qfyd.8df oey. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ballnn,uin kd 44bp3m+5e5e y aex( tossed in the air by the batnx m4e4 5ey ku5(nbn+a3idpe,ter?

Is it possible for an object to receiveoc261 7egwmgm /p*vqp a larger impulse from a small force than from a large fogm7 p o*p26c emqgw1/vrce? Explain.

A light object and a hei gw3yaql9ps20mr3f 0avy object have the same kinetic energy. Which has the greater momentum?q 03yi0ls f29ap3rwgm Explain.

Describe a collision rw) c5u1pd/j 7qh (.kp qzeg4ein which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against tur4ke 7y;) j20b 6lgbdiddl lq+zbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water d0 76kde)ild24 gly;bz+ql bjrebounds?

A squash ball hits a cf y uef11*pz04 x2fvd9b5fgfwall 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 *pav:k4e(wnfmr3)9xl)xs vh height h onto a hard steel plate (fixed to the Earth), from whexx )*vpvs: hm3(4 f)9rkn lawich it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is 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 backwarddsm0:4nt9 t l6vap )ap when carrying a heavy load in your arms?

Why is the CM of a 1-m lens3 tjwv h23k ;/dutmjb0ay*yfacw +9-gth of pipe at its mid-point, whereas this is not true for your arm or leu ay2h*td+k;wyw mb-3 9ja sjc 3vf0/tg?

Show on a diagram how your CM shifts when you change from aaofwkqk)8:t(,k z:y z lying position to a sitting position.w:akykoz8:q( tzfk,)

If only an external force can change the momentum of the eus2/j fk9 8mc;ixur,center of mass of an object, how can the internal force of an engine accelerate a car9emj ;ui/sku8cr 2,xf?

A rocket following a parabolic path through the air suddenly eh b;bfd u/oa2 4rr-r/lxplodes into many pieces. What can you say about the motion of this system of pieces?d/;f lra ur4-bo2b/hr

  What is the magnitude of the momentum of a 28-g sparrow +mf*f;i7i7q (hrfv r fflying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on ahlo,ja l1d.2ek 5sk utpdq.(2 6od5lh 65-kg skier for 20 s. What is the skier’s cha 2h6et5 k 12k .du(hdoo5jqad p.s,lllnge in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizonqw )2 tl9i+bvhtal line drive straight back toward the pitcher at 5iw t)vb9 +qh2l2m/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 6.408owcc0imkw iok4cs7 vh26kk ay y 827,-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velociks6 ,ao8oh07k ccy 2cmv2kik 87iy w4wty of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted opo+ * p(a:a jcqinphqys7;t2ra:37uu-t q,qd n a rocket, given that the propelling gases are expelled at qq:7(,jqa3+u crapsqi yh :unpt;a7 2 -*odtpa rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movinmwr6hvsed 3: 3c;-s0uatsly3.dhc *rg 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 oxw6d pma b6zvp4j2 m6.z,cl6zn alevel frictionless track with a constant speed of 18m/s A 5350w6 jav6lzc mz z4b m6p.x6,dp2-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar trave2p,nup1 c k7)s :x tk-exkdat/ling 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 2uht 4h kvy0 d.l:b7xdhorizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the 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 frictiu:d4yvb7khd x l 2th.0on $\mu\approx1.0$ 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 cons sg1y w.y4rx/xtant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rat s.gywrx/4x 1ye 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 inigh)-h(yt/ iys0aeu q,tially moving 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 original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitsug)qthyi,ey(0 /a-hted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and emerges x5uh(tge, ;ih cleanly at 170mi ,h(eug;xth5/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is travel- nvgz i7g d59.mh gqd3fm)(heing at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is travelingh :n;lqrt1k:65b3zn scylv9c in outer space with a velocity of 115m/zlc1 ht6r;:9s yv3n qlb:5 nkcs To alter its 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 tee at a speed of 45m/s The golp yr)) b3eyc94) zbfa ua7b4fof club was c)o74a bba3yuef)r4py)fb 9z in contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes to rest atb l l1ty8;l-in a time interval of 8.0 ms. (a) What is the impulse given to t; tbllly81a -the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=,)ze g t2kgg9g 7t +csyr9r)gb0.06kg 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 crashw7d n u yu/23e26wqicnnorthiness 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 impact until it is brought to rest. (a) Calculate the average force exertee/cq yinndu63 w7n u22d 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 0.e- lj( 3qv dtt3(9hsz op-l:hc75 s by a head-on tackle by a tackler(z( q-dht3osp3-j:hv tel l9c running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ba *of/)gznr 4qx3 e/ott*kxu3x ll (mass 0.060 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 estiooq 3rx/zgef*n* uk/ )t x3t4xmate
(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-ls ;7zed.3zoy)-r/mkcha)e sm-v /ynkg 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 stre)s7 z3vkm)ncy-hl;srz.d/yo m ee a -/ngth (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 directio:fr6bk f/qcbj j2w:/ vsitd:, n) 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 afte:2vcft/s f/j w:q,6ibbrkdj: r the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has +yjxx42ewue-l u ,j9ba 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 let B2x+-u ue4exb,9j ljwy represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastic head-on c+ l2qtl9d8 qbcxs ir ,4bqp85follision. 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 rer8q8ciq2dt9s5 4qf, bx ll pb+present 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 collid53 xzb9no .8wrdmfjh 6es head-on with a 0.090-kg ball initially moving away from it at a m o.z3x 5n6 wdr8bjhf9speed 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 col4n yyt ;65m d2;tsx)kjqqu os7lides head-on and elasticao5k; 6uysq;s 2dq7nt )tm 4jyxlly 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 amusement park ride collide elastically as one ap(um(x0 /ymou6rv+ bfw proaches 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 movi 6+xfm0vu(m y(w bo/rung 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 jk. rb z8:go0m1 nh+qly8gt6 ksecond ball initially at rest. The second ball mo8h gmj l6+o0ngr8yz b:kt.1k qves 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 cubxmt 2w/*oe e6te slides down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does et/x6*e2 em otwach 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 object 0j.x6aa6bvw8u 0u o2i huyi4m 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, proj c4ba s;wndc-at3ki /(ectile 1 results in a maximum height h of the pendulum eq(i4-caa/nkbsd3w; tc ual to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230r g3ch/de tp)sxn pae8b32-x9m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine tbxget2e - prn ca39p8/shx)3d he vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the 83, 4h7nlup nmhg sdj 8e/zga,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, initinv5ze6m;g t er*l cvm5 (;t4vmally at rest, into two pieces, one ofvgez65cr vm( ;*;tnvm m54lte 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, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-3 b.e:mk5 q abg.zbrg8kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The policeg.qm5z b:8 egkbrb3 a. 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.ph*vg q+*ezsopq l0,wj g084n50 m and rebounds to a height of 1.20 m. Approximately how many reboun4p8* +sez0glv ,w0oqqpj hng*ds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objub4s94 pyshl ;ects is the coefficient of restitut sy494 lbh;psuion, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three time /gy u56-k8t2elp-jmt g/ ccyxs the mass of the other. A depression is made in both faces of g65 cx g e/tu2k-8lpmytyc/j-the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate 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 c r1on,iofjruva lqmv 9 3-w6c.1 n7d;sollides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass-,fvi3 wnv9jlu11 scoad;q7.6rm onr 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 ix+3rpf cy25m lnxb38oes ,vm6v li c)fk87e:into a second nucleus, an electron, and a neutrino. The electrovcyefpr),ovx7lms:cil33n2b xemk8 f +6i 58n and neutrino are emitted 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 maslrz ;7x(t /uwzs $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equal mass, each f oai 2//t0khoho,:;2 otkc qdhaving initial speed the two move off together with speed v/3 Wha0hto oi/;qhfkt:ad, o2/ok c 2t was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angllmnzamf-7 h b(dh.b) 4es 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 Aftermzma ()7 h d4b-f.hnbl the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectu w9v- dtl2 x,x3s.lknly elastic collision with another atom at rest. After the impact, the neon atom travels2.nls-3uk9 twv d,lxx away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastirl k* f2rw4tn;c collision with another atom at rest. After the impact, the nlwr42fk* r; tneon 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 sh i 34;ew4q vkqof:6fc9ddulu -own in Fig. 7–38. Specify relative to the lfuq4wkdiv6c:34ul f9 qe-d;o eft-hand 1.00-kg mass.    m

  The distance between a carbon *:ce*q xktd .p6i adjg:c+4lwatom ($m_{\mathrm{C}}=12\mathrm{u}$) 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 2.50jn3u*a,t dz 2p m behind the front 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 dpntaj *2 u,z3m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raflx(bo i/usi89p14jy en *2ehz /j dd3ft, 18 m by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, dete/ z12x8p3eu /diif nbj4s9*yld(eo hj rmine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides 4 3 zhfdw9b15x buj:ta$l_0$,$2l_0$, 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) pallyj/i x ja 9wy+o8kc6v+i;4fmoet has a load of identical cases of tomato paste (see Fig. 7–408mi 9f/yk wv+jjaxc4+;o6io y), 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 the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cta+xdo a( w5xfp5gb*7ut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of t+ w*axp g5t(b5xa f7dohe center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those5 xk c1 3abr*wahtou5, l85neg in Table 7–1, and calculate the mass of one ab1lkao 5w5,3 ru5 c8hg*tenxof your legs.    kg

  Determine the CM of an outstretched arm using slu zpoz0 *phb0h2 7q(Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an ad,f1zz,ozd8llg. u7d.-e vm arm bent at a right angle. Assume that the person is 1z1uoe7f.v.a z - ,mz l8dldd,g55 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a posh+9c 7ia-o k .6mvfgxr 4ppgr0ition 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. Will this CM be op rr .co04igv+7gp9m6-fx a hkutside the body? Use Table 7–1.

The masses of the Earth .:znpt)ma c sp:9t+ ziand 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 8(dlbhk h-;9 h *6tidrm0-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 a uniform cylindrical head of m2oztr8y i54emass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical hanzeotri5y 2m84 dle 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 uniform cylindrical head of mf4sb6txt/rx9l h 2,m vass 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 foll,2rvhx6tm4l f /txsb9ow a parabolic trajectory?    d    d

  (a) Suppose that in Exam 1nm.*k4aabc u+ m+rczple 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, are in the u+qqa9,doey( hqxuk i 5*u 9 j0kg.spm:e4r4iair and stationary with respect to the ground. A passenger, of mass m, then climbs out a9*.,ioi4q5xeh(u4qdr +0q9ump: ea ky gs ku jnd slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball v, qosnj mk4/.pitched horizontally 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 the average force on the ball during the contact.n,/vjqkmso .4    $^{\circ} $

  A rocket of mass m traveling with speed o,kw2x;lyd;k0ua7fr9f)a o o$v_0$ 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. 7–jhy- v k:l)yzug3 m86m43. 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 -:mmk 8)6vz lg3juh yya pocket? Give details.

  A 140-kg astronaut (including space suit) acqui3c nfxl9i8x:5b7 xc wmres a speed of 2.5m/s by pushing off with his legs from an 1800-kg space cxb5l97x 83mccwi:xf napsule.
(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, areda8n3 rl6pi.v n9j.m f initially at rest in outer space.ri.j3pv l68dmf9a .n n 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 el-nmln* -fmo46lx4o.8plzwo x astic collision with a second ball (at rest) and rebounds in the opposite direction l z -p.4*8olf6oo-lx 4mxnwmn 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 case involving ane u+.vaw+ 90qck+zua s 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. Aftez.c+q sw+9+ v0kueau ar 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 coor97e i8+: lbd/* hq;e xrbbq 9x zcwqydiu.50ncrete 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 arl+oy789qx iui. 9hrcwx5b*d;dq0rb/ qze e: be 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 ac ws bvb/,.4qq/0ogo veqev(-t rest directly above itc4/(v e.eq qqo v-wsbb0/vgo ,. If the bullet has a mass 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 becomes embedded in a 1.35-kg block of wood n y303si6e7 p7ylj6k ko;ulueplaced 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 k;oyk6ey7 inj 7u36esp3l0ulm before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the vzwv3e7v8 q1jother of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people,378v zev vw1jq who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was 6f cjlc2/ y-uwtb* e7km)p;xeabout $ 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 b3e5 ipt irc(ohxx..x4roken apart into two fragments by an explosion. One frao5 cx(etixp4ixrh..3 gment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formull8ou( pgo.5vl.v p ) vp6*1ucmqxxo9ca 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.88-yot papyb $m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha particle and a smalrfx q9)//vwfe ler nvwqf /9e)/ rfxucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at ac+e y ua7z*3lqn angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 3 aduzxgp/9 s420.0 $^{\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), whe 5vp9dx8 qu) 9oew9cd a3)gojat is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide with M again?959 d djgce) o3epaw)vxo u9q8    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot emk :i+wspgz. s23+fsd8sakz32w9gxuffect. Figure 7–47 shows the planet Saturn moving in the negative x direction at +skf ww.x283zsd3+m:ig ka9z2gus ps 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