We claim that momentum is conserved, yet most mo-nd 2/wyu e 4cu,5ne ovu2tz6uefr5x. ving objects eventually slow down and stop. Explaid4u5 n 2n6u eo u5/fry2eczv.euwt,-x n.

When a person jumps from a tree to the ground, what happens to the momentumpi.jt0mro( zv ))h:mt of the person upon strikzvt(: j0hm )ro).mpt iing the ground?

When you release an inflated but untied balloon, why does it fly acrot2xg4,fvit wl2 gjt90akm8 pzk4c,-rss the room?,t29i a,-zwfktkvl 42 gxcg8t rjmp40

It is said that in ancient t)k pro/*6,jsuxf*ce kimes 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 tsuxje ,k) 6*ok/ c*rfpo 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 essentinv*46ecxq ru(6jv;z e ally in a vacuuv6qnu4e;jvrx6* c(ze m?

According to Eq. 7–5, the longer the impact time of an impulse, the smallo6hocww 1k* d0yht a8:er the force can be for the same momentum change, and hence the smaller the defor86adh oo* w:yk0w1 chtmation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Tp)v(xpcu) nmlebm e1s).u9r 4oday, though, cars are designed to l(e 1)pbpsxve)4uunrc)m. 9m have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseballvcq i4anz3*9l further than a ball tossed in the air by the batte*l 3v9az icqn4r?

Is it possible for an objry 03nyvfo4j7ect to receive a larger impulse from a small force than from a7n4y yor jfv30 large force? Explain.

A light object and a heavy object have the same kineb)m8sb44dav9a38os . wsc dhstic energy. Which has the greater mobda hwa . 4)sms 4vs9bc3d8os8mentum? Explain.

Describe a collision in which all kinetocjrdz* yr in57po(* 6:9m6 vfx, tcaaic energy is lost.

At a hydroelectric power plant, w/kugym7 6*b h, gi2 roou3h1tjater 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 hjb1mu ou2/i tgr*7h63kgo,y that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a waldydt lnk ig3, sar.7o59m .uf.l 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 height h onto a hard steel pt ,pvf yr/n::zlate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b:p,/ynzrt:f v) 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 heavy load in your arms?xz8 vgu)oz( (oz(wk4ezw6vn3 w./g qw

Why is the CM of a 1-m length of /lljero) h+i;h6u k, 0;fsdx fpipe at its mid-point, whereas this is not true for your arsk/6fox ;ljeul) hh+ir ,0f;dm or leg?

Show on a diagram how your CM shifts when you change fromz m2p v)(uorh.f;9-ux o*6byl(myfn j a lying position to a sitting pol6yv(pf-9f(zyox brm. ojh *; mn)u2u sition.

If only an external force ca w g21q8gnk)1mecv;c vn change the momentum of the center of mass of an object, how can the internal force of an engine 1 8g2mcvqngc;we 1v)k accelerate a car?

A rocket following a parabolic path thr s+hkv6hsu 0e33,jo cwough the air suddenly explodes into many pieces. What can you say abohs33u6 0jevshw ,+o kcut the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flyinq3v3-vtonz +n1y .ikbg with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 6wq/zw :9ynur ,5-kg skier for 20 s. What is the skier’s changeq9 yuz/ ,wnwr: in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive straig 4hdw: ygl4 q-gbvu8/iht back toward the pitcherbv/: 4g q wiy8-4hudgl 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 with a speed hs*- n k;xcf6 mjab(9wof 10 m/s Fig. below Calculate the velocity asnwh-(x6 j9 b*mk; fcof 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 on a rocket, given that the propelling )o:hkk; o1hh1r (ycor gases are expelled; )yro11k r oohhhkc(: at a 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 movim0 l)iea w;9:-tmsqy4ur 4a +dcic,jdng 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 oqmivek wj,iht9610dd4pcqu+gr yx pju,;5 9, n alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropk+,x;9ctqm pvueqj6i0g,,ddj 1w 9irp4 y 5 uhped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling2glj24jh jh*dm4:x5qwh vbp. 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 speeds of 5jph+dve, ry* 100km/h If the air strikes a person at the rate of 40kg/s per square meter an5ydp v+h ,r*ejd 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 along with a constant speed of 8.6m/s:l.b :3 hbexfr on a leb:flx. 3rh:ebvel track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits *rc8gc-zj yl. 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*g 8cyc-zlrj. have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrate.uq9u4v 1rbw9lg( hd v,-r yqrs a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, hodb1yq -,4r9 qh.(ruuvwgl9vr w fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling : hhome7:,:wciq 9a q9hwpb8j 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 traveling in outer space with a velocity ofonw.t+w hr/v ez hy53. 115m/s To ay/3n ew.zt. vo5rhhw+lter 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 Thtz90rw h(d8p ue golf club was in contact with the ball forwut80 h9z pd(r $3.5\times10^{-3}$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 ar8rejgy9v i 7(t a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse givyrr7i(9j8 vg een to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=mm b f;a:o8wszfkwlqd8 3: :p;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 eng hzq4 6m9 3w0iozbc(w/yhis8cineer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until w4s09h z /ym iz68 ihcc(bqow3it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is str/xf o ppvbyz02p7z/ t 7mc9w)1 vz*xjopped in 0.75 s by a head-on tackle by a t*r tm9ypwv/f7bjo/ v 1 0xc7x)2zp pzzackler 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 onukc * vt9w/c+:djv2it0 ,;q 0hvoy gce a tennis ball (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 methov c 2oujvc vtec/;* qg hk+0y9wi,0td:ds 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 br( xvuxhhbpn 0zkd-4:3j ci0h;vkv 26n eaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the perkv x :-;inzvkc h40vhju2pdn0hb63x(son moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of 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 spee+z pp3jxy)dx3h9-g)bdwg3 u ud of collides head-on with a 0.220-kg ball at resuwb3 +jg)xyzd d-9hu)pp3 x3 gt. 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, 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, mov1r7 4)ngvthlhb fkuh)h k;f0-ing east with a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, ag hblrnkfk07h) ) vh4u1fh-t;nd 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 m5ez1- o3xv+rjg, s *tq0 sf+tx.kgdicollision. 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?(tgq5esg+xo sv -f ,r k.*30jzdx1mit+ Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed zo d* h+7bjenh42k )qsof 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 perfe4h kebz+ onjh2d)7s*qctly 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 tbnwgdx26ca;,ln x52oz*: ht moving with a speed of 8.5m/s collides head-on and elastically with another ball initialg :62twanc dth ;*z2 oxx5lb,nly 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 ar i-oax o3* 98d:yi:gno 7wdata)97(jfgcr bnn amusement park ride collide elastically as one approaches the other directly from g)a*g3o ( i7r9 a:o7dbyf89d : onwain rcxj-tthe rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s 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 b bca5d) 1jv t(nv*ifsg7.jva-d * wfl0all initially at rest. Tv0)v*i5 dj gc(1* -7dsnjaalf bft.vwhe second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless inclins2vguw q zqfb2 .6:8mje as shown in Fig. 7–35, and elastically strikes another cube at the bottom that i2f.umgwj2:bs6q q8vz s only 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 objedm/ f2 i+gm rij)wp)7nct 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 in a maximum hef 26hid qr,cagnr5.gfpd +9;s ight h of the pendulum equal to 2.6 cm. A second pr gdr6i+rg.af,c9 pq2hdn;s 5f ojectile 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 trav a,ai rb-7w;yfeling 230m/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 verticyw7ib ,rf-aa;al and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction ofmxt t2d- ;ej*n(v*uy b 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 /f;g6fwr xba*5 kii:zobject, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosi x *6 ff5wb/;ia:zkigron, 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 /:z9o3hkgrqhs w-8ht collides into the rear 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 represent9otqhhh/k wr:3 g-z8s the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and reboqf vgc2vg)xd7k5tt -695jz h punds to a height of 1.20 m. Approximately how many76 ct)h xpgvqzkg5jv-59 2fdt rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the cc b 15tz(-l*5zfitc uo9vrs8roefficient of rest c891vb-ozc t 5 s(lrit*5urzfitution, 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 timexwovx98e.zy9+y r xdp t+ha.4s the mass of the other. A depression is made in both faces of the cut, so that a firecracker pxv +o.d +48.y az9hrxyxetw9 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 collides head-on wi pu-l+ s4q9l-5ag* jvxedf k0m hmvc6;th a 10.0-kg obj;l9m-+v0 suaxpqck-lheg6j 4 *m f5dvect moving in the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an electron, and0zn2sx3 *ev5uj vei6zgb kg60 a neutrino. The electron and neutrino are emitted at right angles and have momenta of bk6iz ee*j5g6 uzv0 xvsn30g2 $9.30\times10^{-23}kg\cdot m/s$ 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 m 7f7kvx wk,btv 8uuq7d ;j7o;qass $m_\mathrm{A}=0.400$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 objectsi u4z*q-u*ooe i0 .jgitn s43nqna 0o9 of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their ou z-309t0 eionoqinisg4u .jn4** q ainitial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the ox,zhvlf32c 8 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, bal8o,h3zvc xf2l l 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 elastisb d9 xwm;+5ftc collision with another atom at rest. After the impact, the neon atom tra9b5xmw+tsfd; vels 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 collision witd gypp) :e:m5ex8xsb4h another atom at rest. After the impact, the neon atom travels awa:8 mxgsed yp4bp 5)xe:y 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 m30v ahfny2gpws3*(7 axx+yorbfn f,(ass of the three-mass system shown in Fig. 7–38. Specify relative to the left-hand 1ry 3,ax o7gap 2nn30(w f+f( shvxfy*b.00-kg mass.    m

  The distance between a carbon ato(u nq +m))bte ;llt1hbm ($m_{\mathrm{C}}=12\mathrm{u}$) 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 car. Hct6q-dbzc m0 9hxpd9s,0 6zo3wmo/o zow far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kdxq9wmo6, o3-dho 6c 0tc/sz z zm0p9bg.    m

  A square uniform raft, 18 m ab- ifo7 y0vblyti q)08r86uiby 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, bab 6i0f80i yu8q-r 7ivtyl)oSE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side zcibwyvr9, a1 )f d8/kl8:heos $l_0$,$2l_0$, 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) pallpyvk 8j2+p s; 0p1hi po2qy)kpet has a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontahyj;i82ppy 2k pqvpp1s0 ko+) l 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 o:kf 3fj b jbmseecer*j.j034*f 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: Try subtraction.]:3mb b 4j ef j3*ces0ej*rj.kf   R

  Assume that your proportions are the same as t 0)zwz0k0:wk6 q gpacm9bft c)hose in Table 7–1, and calculate the mass of tp9 k)kf0mqg zwz )acb0:06cwone of your legs.    kg

  Determine the CM of an outstretched arm using Table 7–1. y1gb hd1lu*4t  % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate thel3i* eh7 3eq*k7pulty position of the CM of an arm bent at a right angle. Assume33ty7q7*e hl u liekp* that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position ssde / +q:- brihf+h1wuuch 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 outside th1 u-+ws e +hf:hirbqd/e body? Use Table 7–1.

The masses of the Earth and Moon (*oscw,b apq/kxs i.7 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 stan32k uhtmt ag31d 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 ljnv0q:(;v kpcylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabo q:k0vv p(n;jllic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diamspd coyi/h,w 9po2h41eter 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, dhw,hipyp24 ocs9 o1/into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–wf xn6 u(ugp)514 (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 inrnf/dix (ri,,w; hi f, the air and stationary with rewrixhn ,di (,i;,/r ffspect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball piiyk6-pb uh73l tched horizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4p u637lkb hi-y ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling / l ntx:5r os+ncf(6w4dj8hxgwith 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 shba2m02 fyez 0jyed epz-(f ):nown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will ame)nj 200zd ba- (fyez:eyfp 2lso fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquird7,h alwyt+l80. m j*6oe cxwbes a speed of 2.5m/s by pushing off with his legs from an 1808 7bld6 *cm jw,le+ .hta0xwoy0-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the(a* lzg2 o-2+mrdxeya other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut haley2 (r* adzo +mx-a2gs moved 12 m?    m

  A ball of mass m makes a head-on elastc w.buiau 21 :./xjte4obm3wuic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its or.:uiuu1 m/4j 23ewoxbbwc t. aiginal 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 inmex(e0b0qht6:8bboqw p7y p :volving 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 cayht0b8eb ope:6q (0pw7b: xqm r A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off i45jv mt: m4cr m-7vft2f+f vd +mc;jxthe top of a flight of concrete steps of total vertical height 4.00 m.m mj vtj2;5:df f4 it+m4mcx- fc7vrv+ The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired verticallyc+ r lo:a0*u r*k neybax1ln/epg (-/t into a 1.40-kg block of wood at rest directly above it./(bkp-tc enr**:luno r+0/y g1 aexal 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 bloc lmshx11/xg,7kei. bdk 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 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what wb g .hx/dm1ixl7es, k1as the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mauhpk rg1 p(r- t5sv0q0ss 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m 05pg1v t0s( -rrhqpu kapart 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 ab smo,1 .g3fh:7 3zot eufcth3kout $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart gy2uaa/qc36ke gk hk5cl 6d9) into two fragments by an explosion. One fr6glacgc9ahe )kk /uk625y d3 qagment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formq2x/ jtw(xd*lz2 kps0ula 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 h2d4jtolm1u5xv . gh.9ro ey 6$m_A$ = 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 a8erkzu33uc :u gga(*f smaller nucleus. What will be the speed of*uuuf3z g e:gr 83ack( 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 f cdgid)v r dn0 e.3k:mnm9o;v9ired 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=2.2kgyx lg+s3j dend8v. +18vs+oivl qh5ffo 1*mf: 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), what is the upper limit on mass mlhxmu b 27t;+(d4eecw if it is to rebound from M, slide up the incline, teuexw7(;d c 42bl+mhstop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the p e*et87wwtc(r lanet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s Thee *rc78et(wwt 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