We claim that momentum is conserved, yet most moving objects eventual)j1t6ly+g9(uddtyaqu;s). g t 7roe b ly slow down and stop. Explaid+g1o9ulesgqd jy6ut; .ra)()7bttyn.

When a person jumps from a tree to the ground, what happens to the momentum o6)zn hawaf8: 7 5fwbiga /*kdof the g*a8hf w:k w7nfbo za)i6d5a/person upon striking the ground?

When you release an inflated but untied balloon, whym e7 imc* 7u9x(3jyckk does it fly across the room7*m7(eyk9 im3 ku cjxc?

It is said that in ancient times a rich man with a bag of goldc m ohblp739uafxn *0us;hq3; coins froze to death wh b07 nfcl3;u musx9h;*3oaqphile 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 not been so miserly?

How can a rocket change direction when it is far out in space and isus6x nkmu,7f- na-uop5f cp() essentially in a vacuum?ac -n6u omuk5-,ufsp7nxf) p(

According to Eq. 7–5, the longer the impact time of an0am 3igy mi,;c impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to infm3gcm i ai,0y;late during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built a)xl7qi)h-ug(l mq +rt+nx. gfs rigid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse uponq+n g x 7i ft-q(lr)x)+lh.ugm impact. What is the advantage of this new design?

Why can a batter hit a pitched ba5ium 3/*kcmeja x2 )syseball further than a ball tossed in the air by the battek5ae/mim)32c sxy *ju r?

Is it possible for an obje4 )6*0q bxnask*dmmurc bzo4*ct to receive a larger impulse from a small force than from a large fonx4q* d*us6)*zrbbmc4 aomk0rce? Explain.

A light object and a heavy object hav e+w6i b:6n/xwrxp 2fpe the same kinetic energy. Which has the greater moment+rnp x:6w fwb2 ixe6/pum? Explain.

Describe a collision in which all kinetic energyy wr ia.dby a0w17b8:t:tcxl3 is lost.

At a hydroelectric powwjb vj/(6irvf81v vz/er plant, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is bv6z1rf jwi vj/vv(8 /brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a 45 l 5wp:lsvvy4/ hy)j.y$^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped fr 8uk c7k2jpcm;om a height h onto a hard steel plate (fixed to the Earth), from which it rebounk8cjkmc;p7 2 uds 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 carrying a head7n5:j b 9igrj9mj/s a:qn:sxvy load in your arms?

Why is the CM of a 1-m length of pipe at its mid- 7a+n+ rtcweu3point, whereas this is not truewra+u3+t 7 cen for your arm or leg?

Show on a diagram how your CM shifts spt2f-.p+ /+0s2efqpf lxh.aa ,oiq gxh2gp9 when you change from a lying position to a sittif2 i.2+sh egsqgfapa0,o .-p+q xlxp9hpft 2/ng position.

If only an external force can change the momentum of the centu 6*lv0mi bekalv1uy0mz 5q7-er of mass of an object, how can the internal for706*yvq i1ub 0m-ke5mulzlav ce of an engine accelerate a car?

A rocket following a parym0toi(x302gm-j kad abolic path through the air suddenly explodes into many pieces. What can you say 0 jd2kgyxma m t(0io-3about the motion of this system of pieces?

  What is the magnitude of the momep slc )xs+4nt7jpz m6 di983yjntum of a 28-g sparrow flying with a speed of 8.47yplp cz dj46st93 )in +8mxjs m/s    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What is the .:0qou u iu9:sbqww5iskier’s 9uu5q:.o :ui0sq iwbw change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is2.qjsff(k ia100(pl x4) nqteymi r4r hit on a horizontal line drive straight back tlqr r. 0tq401i(e k a)fi(4 jymxpf2nsoward 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 throfyh t)n /lrbi4ngi-mk1 f78 2gws a 6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity 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. Ignore1tg7/nbmi r gl84nyi) hk -ff2 water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the pramijgkn)8y; 4xio:u *b( h5vdopelling gases are expelled at a rate of 1500kg/s with a speed (dm; h )u5j :yagibkixn4*v 8oof $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s oneoup4h x*d1h;* v0z yj an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-1h4 ;e o*ph vdz*0xyjukg cornerback running at 5.5m/s in the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travep b(y2vhek, . 6epa ) xeh1r(oo9ywc9els alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, i1(,( yyp2w)eb9hex pv re o oh9.eack6s dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar trav fcjp 54ddz ln)-fe(z+eling at 15m/s strikes a second boxcar at rest. The two stick together and move off with a speed of 6m/s What is the mass of the secon-cz45 +e ljf dpdf)n(zd car?    m/s

  During a Chicago storm, winds can whip horizontally at speeds of 100km/h If th+h 7ka.xhwsin a)j l5*e air strikes a person at the rate of 40kg/s per square nk5x ljh 7*a.isha+w)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 car coasts-u;wn/ 6dewfwxg4ulwnq 2hd hh 0 0.d1 along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rhh-nwdd n.1xq gu;e6 /2wlu 4wwd0fh0ate 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 42o8uugvoz6;vu jaj z53sy8d ,*0m/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, ujvjoz ,;v53*dyo8g uaz6 u8swhat speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/satxx xi-ftm/.t u:f *6a4/pyd penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the bloc4p:x.tmxfutti/6 /y x aad* f-k 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 traveling at a speed of i(rby zsc2a h y9 kw.98i:s5a cc;.qzz$5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outeta 3isr.z(et 2r space with a velocity of 115m/s To alter its coursasrt2zi .t3e (e 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 p a7hem+nv n8 )*r4pgd0.045 kg is hit off the tee at a speed of 45m/s The golf club was in contact with the balm+dern 7g p4 a)pn8h*vl 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 velocitw3im u1yr/*yp2 er )ixy of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is t/ *yi1xp ew m2yriu3r)he 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=n6jlpt. hff+k7n f1z) ack2t(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 engix87wd+-i7;v:djewt/+zly7fx x ailxneer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new modei7xddl -y+ xw/8+7et vxf;a lxji7w: zl of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to t3r2c5o6sita d*rthj; he east and is stopped in 0.75 s by a head-on tackle by a tackler runns65tri tha d2 *r;o3jcing 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 ball (mass 0.060d/*ud5r; 7 fiedjy1zr kg) points in the +x direction and is g;urd di7dzy j*e/1r5 fiven by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breas xq749 z4xfoeking 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 i4oxxe zq79sf4 s, 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 speewb,+dsl, b gq4 l6lz4od of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball,,blsbl 6gzowd4,l 4+q and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-on collision tokhz.p,b98-dx mn9 3r7th scwith 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 pu o-7 rxkhmcb,sh39.98 znptt dck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastic head-on coll,:x96 ukytd67b usf 2bdnc/sv6r(uf qision. 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 aftvbsu fbx6f yk: /dun 6(d9c6rtq2,7user the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with-mgo29mawb i:1s*x lt 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 directi *m9-1:mlxgo 2taiwbs on 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 collid hr;(4 rdujakmn.1ax 3qpg t8,es head-on and elastically with another ball initially at rest. Afterward the in1hxp mjtragnua.k4q(;,8d 3r coming 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 amuseme4 uyz 2gr*y6d1cae8p i4kw *kfbm6vu7nt 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 pass gea7r1 c*6pu4mdyw 4k 6z*i fyvu2b8kenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a second ballmx:4x tqv3d v3 initially at rest. The second ball moves off with half the original speed of ttmv xv d3q:x34he 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 frj0ctb-i :tned bd) v+6ictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-haljt d te+ b0b)-ndi:6vcf 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 object of mass xw,nw :z +t6v;ww3wshm$_A$ 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 in a mf1n ema1q+o-taximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice 1o efm n-aqt+1as 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/o*8i k;sxd*k3g kq zt-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the verticdi qkk ko*/;t s3gz8x*al and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the frat fwm-l(jyux bu208jp g 08ty3ction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially a-sol8 f-k:/)sps bav;ct-a rr t rest, into two pieces, one of which has 1.5 times the mass of the other.vtask:f)r- /s;a-pc-8l b osr 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 reaiv6* , uv: rvy dgv*xscn0.3udr end of a 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 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) : 06 dyvxvgi3v us*d*n,vr.c u$\approx$    m/s

  A ball is dropped from a heim227hvaomke a */r u5b 12czwjght of 1.50 m and rebounds to a height of 1.20 m. Approximately how manjmk12omb 7ha* vur e/ c52waz2y rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision ohubea y:vt;u1p7 v x 8ztug15-f two objects is the coefficient of restitution, e, y5bguu18uvpv7- t tx1a:h;ez 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 times the mass of the ig rg.5yc19:wowands yv 4(r,other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and wg c y(d5so:4n wr .ya,1rvi9gslide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on with a -*vw+ 9potdsq 10.0-kg object moving in the -x direction at 4m/s Find the final velocity 9vto q+- sp*dwof each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays intuwp (gc 2zsq,/o a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at r g,2q/(p zscuwight 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 mass dd.j m :)solaw0ipb6m(5 g6;z-koejo $m_\mathrm{A}=0.400$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 coll*s cdzgaz(iu*d9m 2v-ision 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 d*2 zu s-c*9 adz(idgmvirections?    $^{\circ} $

  Two billiard balls of equgn,c79uze.mj. qbw:7 f2se nral mass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A an7eu w.enmr2.q:,sbnjg7zf9 cd what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic col a/ sxvtg6f n0,x,t*yvlision with another atom at rest. After the impact, the neon atom travels awaynf 6,gv0sv atxy/t,x* 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 perfecttu4q:u6j+ 4yu9mqk x wly elastic collision with another atom at rest. After the impact, the neon atom q +ku 4qwuyxu6tmj94:travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. Specify rel+umj 0o6 0odlwative o0luo0jm6 +d wto the left-hand 1.00-kg mass.    m

  The distance between a p- 3cc es4i8zicarbon 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 frou(fp1hyu 7)vhag4t 3nnt 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, andv4( 7ay)huhf3up nt1g three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg,eul 3h j.b,ye( is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the ej3(, hblu ye.loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sideb+mo gck *)ttk 8h;g.js $l_0$,$2l_0$, 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) palleth94xkp;mfd+ugf 48 dr(ajh 8 q has a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the centud+ghf frhdq8(8 ma;x9k 4p 4jer 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 -je5 +-( mnaiuzhxmkts7*lc 1circular hole of radius R cut out of it. The center of the shs7m leimz-( kc-+jnux*at5 1 maller 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: Try subtraction.]   R

  Assume that your proportions4ve)5jk br,, pf 2incj are the same as those in Table 7–1, and calculate the mass of one of your legje,5r4cfjk in )b2pv,s.    kg

  Determine the CM of an outstretched arm , 5vbibl,um8mea4c m1x:3 kpgusing Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calcspe/u kxu8suhjl)6 oa6 h)u5:( i tm)oulate the position of the CM of an arm bent at a right angle. Assume that the person is 155 cm tall.() ) upj suokha/56 ul8:ou6xis he)mt $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hanging vertoh5clw4 f h4x53gygr0ically, and his trunk and head are horizontal, calculate how far below the torso’s median line thcf4y45w h5g h3xlgro 0e CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Mooneedq/rj9vu.y.slu*z o1 ;i ;u 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 apab 6vayd e/v6 nsl7(w5rrt 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 mass 2.00 kg and a diam1lr30keq 2 zai8 gtb1tpz4+4wxu-fcneter 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 mallfzp- 8 wz4 1tqn+4gkbu1t0r 2l3xi eacet 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 hykf+pu c)d1/8b. ex7vgtm7 6y /hk3cj x ,rvlread of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, huj xceyrhv37,7+vtm1 k/df 8k6g bcp/y rl.)xow 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– acj:bp/n4o7ca jf6i* 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 gondolas- 2y+-y ftlrf, of mass M, are in the air and stationary with respect to the ground. A passenger, of mayryl ff2s-t +-ss 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 pitched horizonta v,yit6pcym+* lly 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 duri+*vm, pty6yi cng the contact.    $^{\circ} $

  A rocket of mass m traveling m dq,kd uekbye-)i w 6:6cx/kh*a-i)wwith 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 a6r z,c;ve2fjshown in Fig. 7–43. Relative dimensions are also shown. Should the playera6c2e fv ;zj,r be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 24yp*1* vhaux9yj kt5 /cb9r u3bx q3pc.5m/s by pushing off with his legs from an 1800-kg space caps 9*9bk t 1ccjyp bruhp35u4*/yx3v aqxule.
(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 othe qs1p2zri3gcoo+x8gh 0lyibu/ 8 5cq-r 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the ligylgqih2 /b sxco15o3rg8-uz0p+c8 i q hter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collisio.kri3w+ xw4/apuoct 0n with a second ball (at rest) and rebounds in the opposite direct/ r+kowxtu i0wp .34caion 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 in0 m.euuvnbbkmk 49 a( 2so0*ctsj(w* m 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 cajsb2amu*kk b om n* e.cvsw09um04 (t(r 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 concrete sipcsit s: *h*f0,w/td- bet8m-kd s0jteps 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, s0 d*0 8-:c *pjdi,tetsik /h ftsbwm-what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically w8-u3bq4; o/i;o vnxo wjv)h rinto a 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomv)o;iqo3wh/ rb ov x-8wun ;j4es embedded in it?    m

  A 25-g bullet strikes nul* r) s(4nump59y s(uhzr+aand becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is ulhn4r +5r)u y(n* 9pmu zs(sa0.25, 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 kgs /c-z4xm 9or nj(sew6+ hw3ra and the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat init3w4-n+ems (z9rhrw a cxo /j6sially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will 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 wasuklz5g, k k9qr h);f4n39flpz about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken aparrr/,n3xv od6nly 4s/b t into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of ,s v /r6n3blxdn/ryo4their masses?   

  The force on a bullet is given by the zpv+:5jl o(u0q olp+uge m) p3formula 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 ()w a 27wqh+omy(3vbe8wyrzc $m_A$ = 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 alphe:dy.wt8m62nkjh whe* g)+vkg go :g,a particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of 8:j+mgg:. 2dht n6veekyg)*whwogk ,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 an 5xb ax 1e m2f4gj4lq-ycmpr46 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=2.2kgw4 m7 czgp3 7ku2a14)dmvic pg slides down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), wgd s0zxx4o1r8 hat is the upper limit on mass m if it is to rebound from M, slide up the incl8 ods104gxzx rine, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot ef8+di8ud5ut m bfect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s Td u8 +bd8tui5mhe 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