We claim that momentum is conserve.iy d; hj)c(ikl)m0fld, yet most moving objects eventually slow down and stop. Exk)j(c.fl0ymhi ;d)i l plain.

When a person jumps from a tree to thob8c5k da,if *n+nmc4q.njcte*, 5 g se ground, what happens to the momentum of the pe, jd*c .*n8sm +gqe c54f, nacotin5bkrson upon striking the ground?

When you release an inflated but untied balloon, why does it fly across the rog81p/yckmud6f d; m+ oom/ddocu1gmp+8f6 ym;k ?

It is said that in ancient times a rich man with a bag xp:x)vu tf/c 6of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he t:p/c)vux6 xfcould 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 when it is far out in space and is e:(ujh-qbq ;awgz5,v k ssentially i;bq gvq(k -a,z 5:hjuwn a vacuum?

According to Eq. 7–5, the longer the impact time of au +(uvfy8y hd.h-p0jk, -evwjoxuy26 n 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 actsxw -udvu +pu .ej20yv6yjh-fh8(, koy . 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 collisions. Todapaq 2z/6q .5tsq9)jhhf 1bvdl y, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advan s q tb/59zq2aldphqj1f v).h6tage of this new design?

Why can a batter hit a pitched baseball further than r 5)(;ps o3zsrjbwsq8a ball tossed in the air byrb)853(z so psqw rj;s the batter?

Is it possible for an object to receive a larger impulse from a syjsucg0ovo.-38y jly 41 lsv2soh1rw6s5ck5mall force than from a lav4r3klv.s-yjy2jyu 861s0hcg w 5 oolcs 1 5sorge force? Explain.

A light object and a heavy object have the same kip mb .9bp oh+o1ao,md7netic energy. Which has the greatebopdo.,m pb h o1a7+m9r momentum? Explain.

Describe a collision in which allp5dmj38nw )hhetwww w ( 9h1w* kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against+rhls3r cj 07wh.l1fl turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine c+jhrr1llh3l0 sw7.f 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 f9g, )p,ijqb2+dvc9bj imz v9k7u z+ ja 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h ontoawi5a6f qs -wio01p-ux* (gau a hard steel plate (fixed to the Earth), from which itii6(s-fuq-a xw 0*wu paoag15 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 backward when c5bcn8idhopijq ep4 1w0 1;j4parrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is nay:aoycf6q * v.3vs b4ot true for your ars3v*cyb :oa 4 qyfa6.vm or leg?

Show on a diagram how 8lc*ge)p bl22shap- q your CM shifts when you change from a lying position to a sitting eca8 *lp) hqgb-p2sl2position.

If only an external force can change the momentum of the c+jii sny8+tu g*pq pt,:pp83penter of mass of an object, how can the internal force of an engine3p ist p +8pn*pgiyuj,8p t+:q accelerate a car?

A rocket following a parabolic path through the air suddenly exp/gen+k :dyx; olodes into many pieces. What can you say about the motion of this sysn og/e+dxy:k;tem of pieces?

  What is the magnitude of i.7bn9jn h +beh+ue)ethe momentum 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-kg skier o mrl/23z eg3zptb*c7kr)/fw for 20 s. What is the skier’s change in velocokw3zzlg*7rer) b fc2 3/mp/t ity?    m/s

  A 0.145-kg baseball pitched at 39q u*9ai0lsb8ab; ;fjelsx 6q5u )co g:gbbw)9 m/s is hit on a horizontal line drive straight back towar uwagbbq x6l)s g) uj*obe9a;b qi:05; sf8l9cd 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 horizontally wiyo)e30 srhq .wth a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after q0s).ehro wy3, 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 on a rocket, given. 4 *l5qgetrfb. :zsug that the propelling gases are expelled at a rate otgs. efugz5*l4 q rb:.f $1500 \; kg/s$ 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 m*7kthf2j a hdstc/,y6 p9ns; $4.1 \; m/s$ 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 fricgjhg jgwg38(4( 2cfrf tionless track with a constant48 wg3 rfj((hfg jggc2 speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelingcb5jo2hltx*j2 ng2 gzndb45: at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at spu5l huwr1 fj xp (ds:y:34jm7meeds 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 ty3m1 j4yrmhpu w: :(5uxsjl d7fpical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of 8.6m/.- d2z)vji thofgv),as on a level track. Snow begins to fall vertica h)2tgof)-j v ,avdi.zlly and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alph8j +,e(7d- ta kem hklzn2d1nca particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha partic-djtne +kae78c,2 k1 (nhldzmle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and eme1pp 53v9oajuon/f.k.o qcr h5bo+ a(8 hp3bqgrges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it mov .5c8p o h5+3.3 oqkg/pfpqbon j9rvo ba(1auhe after the bullet emerges?    m/s

  A 975-kg two-stage rocket is travelincm5,lm/ :ru;y6wpiou*i9vc:w2dj s n g 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 travelinr15,lg m+ew/qfy wz/z7 lybm6 g in outer space with a velocity of 115m/s To alter its ,ebwz5yy 6fz /r7wmgl+l /1q mcourse by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed of 45m/s The golf f+ggg0df(mdg *uxng 4w.4ws a82fwbr) +lq 9vclu g gwa4(8+l2.9wf4r*q+xgbdsd v0g m) gwfnuf b was 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 velocitfz*ihp9(3cgqgxp38e ife h-6 y of 8.5m/s and comes to rest in a time intervaige 3q 8hepx6 (9g*3ifhzfp-cl 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=po zrd m5,b/d. 15boyi25m/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 crashworthiness of new autp*006veqfvcl t7s z7im5 -wc*bw bp/yomobile 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 averagewbzcp5ps*7f 760mve*y b0 /tvql-wc i 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 rc;3;n7 bnlpp vunning at 4m/s to the east and is stopped in 0.75 s by a head-n7 p l;cb3pvn;on tackle by a tackler 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 9wacg07utdj 5 a tennis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fu9d5 g0caw t7jig. 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 pe,3m) fyfw 9rpd amg(0wrson 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 p pdg0w f3yfmr9)m,w( aosition (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of c(r/ew*+y3ai0tyk2v b.c ca n oollides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what .3ew*ia(bcyv0 rn oy/2katc + will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-ondh ,* o9gz9iqdp ,h2mj 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 B represent the 0.900-9dhg9,m j poizd*qh,2kg 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 perfectlyl 6nh sti*,n;n 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 spni6*,n; h sntleeds 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, m/j-8nxhdq-+hzb; 8 bsgkuds 1oving with a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, /+8bh snx qd1g h bu;-s-jkz8dand let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s collides hhdyls8sw8:v 68/hgfkvk)/r b ead-on and elastically with another ball initially at resvb g lws /fd8kyrvh8:)6s /k8ht. 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 elasyz64+j-ev ,h 8h.dbxpgff 5 hatically 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 mov5y+p4adh egjvxh6z. b -hff8,ing 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 withk3w/0blsh.um:m ;ot a a second ball initially at rest. The second ball moves off with half the original speed of the f/ tblmok whm3: ;a.us0irst 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 frkzi6k7 8qaql d64ylk+ 0iivya;n2s p0ictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is onll y6 ay6pi 4qik27vkqdn li0s;kza80+y one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an o4n7( /g/p)vzmfs itrv vkf-o 9bject of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results inz/62pt ir j) b yc.i:a0mzclh. a maximum height h of the pendulum equal to 2.6 cm. A second proje:/ph z0j..l2cc)i bzy6ir atmctile 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 23bf9wev5c05 )av3x l,fnf a)b1 -gir ex0m/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 the vertical and horizontal components of t5flg)0)ve bnx5f,9cev fr 3a ax-w1ibhe pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energ nz12a5 klk -w(0xwpccy 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, inia kmra4umc+p me+ t 2925ghv,itially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piecem 2rh9a k+vipgtu e m4a+m2,c5 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 (+ 8pu srzt 8wfzcp1 pjxk939aa 2300-kg 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 police officer, knowing that the coefficie zcaku f13pw9ps98 p( +z8xjrtnt 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 height of 1.203t39 m6 pqdplo/kzk 3.blx63qmvzsh4 m. Approximately how many rebounds will the ball pdq/zlk3qm 9so3xz bhvkp 33 46 t.l6mmake before losing 90% of its energy?   

A measure of inelasticity ip- h( uhjb7dr k4fky).n a head-on collision of two objects is the coefficient of restituti(fhh) j4 ybp-.k7ku rdon, 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 i:u zuae,)yh3 snto two pieces, one with three times the mass of the other. A depression is mad:z3shyu,) ue ae in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate 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 5xvz5y9m g,v3z f t3q:n 3uq-zr.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 m53mxngt:9f z z r-qu3z,yvq 3vass 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 de :udyd(;-ermk +km04w f1f2ltsjm, ebcays into a second nucleus, an electron, and a neutrino.2-mb 1 e k;t +l,e0rus:f4kjdywmf(dm The electron 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 marh( k/d74nzwcj57bke ss $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of 5bzmg +pv7qh t50jl1w equal mass, each having initial speed the two move off together with speed v/3 What was the angle5 jvm70q 1tlg 5pbwhz+ between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right an87-qeuz;4cl nxxy 0ru 9dpq2k gles 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 colli 2;kypr dnql9uq ux07xc4 8ez-sion, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elasticr-rk+nmx g4 ; :x86c9fetzb qq collision with another atom at rest. After tr+z r8; ntbf 9xm 4kegqcxq-:6he impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic cohig2kel b)k+-ebv1l x k,v2c-bg 2: zrllision with another atom at rest. After the impact, the neon atom travels away at k)b-gr:v1hbbg el+l,vc2i2xek-zk2 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 7;oy vklk3jg8-mass system shown in Fig. 7–38. Specify relati ;gyjk 8lv37kove to the left-hand 1.00-kg mass.    m

  The distance between a carbon 3c 7ssp3or9gy atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of the cz .nc+48 ;vb)jpifmzf ar. 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 fj+n.pzf8vzcbi4;)m in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is usephkw,*j.-u borai3ww 5 k*wdg49o5rmo j2;hb d as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE-ah rjh2w9,kw5uw j.o;kodb4 rbiw p* o*g53m, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidepy9x-z :z6h:- qvkpk vs $l_0$,$2l_0$, 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 tomac rors0:zv/x;to paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizxv;co srz/:0rontal 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 ho- 7 v3 v8g6s: lo/c yfmjmafm-e(an:jqle of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: efjv:vs-l -3 g/am:yj f(oa687 cmmnq Try subtraction.]   R

  Assume that your propd9yh;i 3bdxn; dg*r)tisxd5krp;d : 3ortions are the same as those in Table 7–1, and calculate the mass of onsrgt bddrk;93hn;)i5 xiyd*p ;d: xd3e of your legs.    kg

  Determine the CM of an outstretched arm using Table 7–1. xrp0zi rz/k/w+ e9du *  % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the positi) c.rh*s 8csd+r- h:mxzh/yjxon of the CM of an arm bent at a right angle. Assumrcc*/ )h.-s+mdx rh8 xjzsy:he that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms l60krs+ntfe b,a6t x)and legs are hanging vertically, and his trunk and e66kbxsr+t ,fatn )l0head 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 and Moon a8sx9lb;+to 8zxco s(9q0fch h ((ba egre $5.98\times10^{24}$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 1fde;)n6q x5 v.k8i t6b fx)n 8j7swerl0.0 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 my ;bif7tqem n-0lk (h-ass 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.q7tfkl( b- -nim0;hey 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diametert-gfs:*;2ly6hzj8 6p sgenyz 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 wgte6g;z - 2syj86*znfysl: phill follow a parabolic trajectory?    d    d

  (a) Suppose that in Examp 3,g5ebh;p bgnle 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 air and fi4ka5(,g yx vu9o 88ja;iiqc stationary with respect to the ground. A passeng,5(oa 9 cia4xgvuk8jf; q8iiy er, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitchou(dc lj+cb 8) fmw:9l 6zemv9ed horizontally at strikes a bat and is popped straight up to a height of 55.6 m. If th9b+)(ecz l :v6w ldmj9mu8 ofce contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling 8xdtjxsd kd 7l+5- 0zpwith 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 cej3 .8ll6utuqx8*jn ue :l6vgorner pocket shot shown in Fig. 7–43. Relative dimension*lnxe6v:6jjq8.u ul l8 3utegs 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 details.

  A 140-kg astronaut (including x3sc3uuco5 dsy5p1dw4* rx2 ahq v66cspace suit) acquires a speed of 2.5m/s by pushing o d odc*c65rxx3qsu5yv h3 wu4ac16 s2pff with his legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg 0;z h syy;wh*o h7ab1)ut*tkn and the other 80 kg, are initially at rest in outer space. They then push each y1nt) o0btyw*ah;;7k*h zsh uother apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makdti;hu2f56ml f9 /0t1qtye uzes a head-on elastic collision with a second ball (at rest) and rt9t 6ume/ hlqu2y0;t 5zfd1fi ebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving ahn *6)nd-w wujn 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 exceedingnujw hd*wn-) 6 the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the toxops1k- db tnj1pj0m0:zy 8u:p of a flight of 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 bounpx0-sp dujn jo 01mt: b1:yz8kce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into aeheo5)/yq ,vz 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 510m/s how high will the block rise after the bullet becv/yho5 ezq e,)omes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood placed oo-a*sn,k xwuh+a 4 /9yxzmwz7n 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 im / + mayu9znx4xwwhzs,kao*7-pact 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 of mass 60 kg, sit in axjc-337wm 080qfydy0 oy xk ;o8/qo:owtu cei rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends oc:yto3jm0ow7x; oec / 8wdx0y8-ofiq0 uk y 3qf 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 aboutrrj2-g/ q0h xj5 xp ev53k;pnq $ 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 sudd2. :7 nveo+ovs1i wasnenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their masses?:vn2e1o+aiwvs 7n.o s   

  The force on a bullet is givenxuylcup6 :7hu/kvj 88 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 massesgwj(n ph4-td 8 $m_A$ = 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 radiopgp 46n+ vxx0oactively into an alpha particle and a smaller nucleus. What will be g 4opxn06xv+ pthe 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 7u3hxu -- 2a*dxogyma) is fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides d9swp75gsrn3e2kj- )kcth+d 03lwvg c own 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 u (ktnfp3 -;;)anprl yppper 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? ;np fk3a;-n p)(l rypt   kg (Let A represent mass m, and B represent mass M.)

  The gravitational slings0 .9 2qrqha3ad;mg y d/nu1zyrhot effect. Figure 7–47 shows the planet Saturn moving i qhyynmzr;/r0a a9 gu2. d3dq1n the negative 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