We claim that momentum is conserved, yet most moving objects eventually slow ddlt vonaaw, b3 90i3-zown and stop. Explainan ,t- odlz baiw9v033.

When a person jumps from a tree to the ground, what happens to t :,dlnnrx xj44cy)n2zx 7ak6qi+ )xgzhe momentum of the person upon striking the ground?g n,:z)qzn kacn xx)46jil4x7 2d rxy+

When you release an inflatex)nwd8e ed39 gd but untied balloon, why does it fly across the room?3) gw89dxd ene

It is said that in ancient times a rich man with a bag of gold coins froze tcq-yn, c6+kjf)m. uspo death while stranded on a frozen lake. Because the i6+qf- csjc,y)umk.p n ce 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 outym520gvfz8:ns )9xz jkvh+ ;)cz9llwto,cr j in space and is essentiallyzgjv8;)y x 2zol9fcm 9+cw lrhvkz:n j,0) st5 in a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smalles4wskk1g-.)9dd q z ix*;ken0ez 0n per 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 intzns e *zqp-) ik0n4;dee.gkd9sx1w0 kended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possy 2fhdsdwa,:l,wf+ / tible to withstand collisions. Today, though, cars are designed to have “crumplht ld+d :2fwyawf,s/ ,e zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tos (uz fbvlb85th ;:e)nxb8r q,ysed in the air by the vb ;nuzb5yb tx):q8flr8 eh( ,batter?

Is it possible for an object to receivyxb j +l8us,7(dm.aa se a larger impulse from a small force than from a large forcl,( m adu7jab +8sy.xse? Explain.

A light object and a heavy object havtuz.3t 57kh9pu l0 pkve the same kinetic energy. Which has the greater momentum? Exp .7u 5ztl ph93tu0pkvklain.

Describe a collision in whicv h9zwgzi 0qpp8t+mh:jq03 s h5d- ld*h all kinetic energy is lost.

At a hydroelectric power plan;/tg s. /axd nan;s5dvt, water is directed at high speed against turbine blades on an axle that turns an electr tv;a5n sxagns.dd/;/ ic generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a ofk8jv*b2 *dp wall at a 45 $^{\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 from a height h onto a hard steel plate 1c ,k cazv+xb myslj-o ; 1, t:ok42cbtln66sd(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) If we conok4s:kob;6b, y6s 1lc-12m ,x aldtjvz cc+t nsider 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 backwardwwz :pa:tap+; when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is not truekd 3.gkyz r/j. for you/g jydr3k..k zr arm or leg?

Show on a diagram how your CM shifts when - kex 0.swm+rkyou change from a lying position to a w-exr0 kmk .+ssitting position.

If only an external force can change the m(3ka x d8ldu0uomentum of the center of mass of an object, how can the internal force of an engid3xl (kau8 0udne accelerate a car?

A rocket following a paraboli2ed4fz3cz8 /pist ,d mc path through the air suddenly explodes into many pieces. What can you say about the motion of thied3tfmpd/ icz z8s42,s system of pieces?

  What is the magnitude of the momentum of a 28-g 1v(u ;eygamf hge1p4 5kj 27kpsparrow flying with a speed of 8.4 m/s pu5p;h4gf(kee2 7j1 1kyvmga    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 v:dv-psz;cwv*/ :luuh p2enqo.) zr8s. What is the skier’s change 8up rv;lu/hnd*s q .e: cw-vvzp:2oz )in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive st o 0 y:qn/*5du:ozxsebraight back toward the pitcher at 52m/s If the contact time eb :d:/ qsyzu0on 5*xobetween 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 thr;ra ss7 o5,6co u-x,mf4pv rtcows 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 w,6m 5 x cos;4ru-cptaof,7rsv as 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 velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling g m m4d;q:x 7iba.a0sa0 (hrnjlases are expelled at a rate of 150(nm0m j .i : ;slxqraahbd47a00kg/s with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an apparent breakaway for a tou ktfgmw.i(o 1.chdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direct. m1( i.gwofktion, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictionless tw6hn-5sl 5bz0.tfyq3h l:lx psff6uw7z)m5prack with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will bw 5lhslt)pffply6053-qzh.m7b5z nsw u6f: x e the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s str0-3 ca2htwsp yikes a second boxcar at rest. The two stick together and move off with a speed of 6m/s What is the mass of the 0tcp2as - yw3hsecond car?    m/s

  During a Chicago storm, winds * wynbz.opo m.8h7 h4jcan whip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m widehm48 wy zjpb n..oho7*. 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 on a l kca8b; fa6xq.evel track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, wh6 8q fxk;bc.aaat is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420b(qe2jafh9w/7q.i v+tfw(ad m/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 2tfhv fbdja.w(92aq + 7q/wie(22 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 wo5(mxm+4i abc xhr.*u aryp 34tod and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after th.b54hpir( ax*mxt4ym + a3ucr e bullet emerges?    m/s

  A 975-kg two-stage rocket is t k:gkarm8s* :hc -bgx9raveling 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 agjpf1 e(12n5,gujv 1cv glir. velocity of 115m1n(2rj1l.,j eci1 gf5u v gvgp/s To alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed of3.z- xs-debz evc/khk qir.46 45m/s The golf club was in contacb-zres 3k .x4c/v q.6h-ik dzet 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 naivt:8*x*;i0l;sov-atx q 56sx 0zvgtnkgm / mil at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) Whavmvt:ont-*tas5likm8x x g;* z 06 sgvx0i/;qt 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=0.0--fm qx, krz wuz6l(m76kg and speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge wk2vf7h7 t-/q.;h/gbff g wfoof 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 it is brought to rest. (a) Calculate the average force exq-7h bv ; h2/tgf.fkwwfo 7gf/erted 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 ozf*ph/-yg-s east and is stopped in 0.75 s by a head-on tackle s*-h y/go p-fzby 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 a tennis ball (mass 0.060 k3u* m 6jdm )opyuu.yts+ncu// g) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical meth ny6u)utc3. o/umdpjs/*muy +ods 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 pereidv8c +3s 3a9zfmdyo8( 4tjason jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breakin8mt 3ias4(8ocdea v d3f9zy+j g 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) wioib )i8a-wr2ik7 apoh7p 8clx d5:2hbth a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 757i 8p2ia pkb)2 lcbohao- x8ir:dhw0.440-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-fn6 + qqsuri6j jbz91 with a speed of 3m/s has a head-on collision with a 0.900-kg puck init9 ubj6j +-qsrn16ziq fially 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-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 elaoe1 rrx;/ ow9vstic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positiveoorx;evr/w91 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 balg8s 69)p8l-uchmylu/pl8/ blj tc,s c l, moving 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 elasc8l j)btms/cu 8ulps8cl/ ygl,hp9- 6tic 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 movi,y( ;elun p7yar-ijeths.,(xng with a speed of 8.5m/s collides head-on and elastically with another b (;iyhr(n,7 petjyxu.al es -,all initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park recp: sk; +3sqds:zr0fide 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 passengerdz3s;+ eqrfs:sp :c0k 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 au*3n,4yuqmbah0gk* qfcr j 5u7+1r g n second ball initiaau* cq3 kfh b1y,5njrqg7nmgru*0 u+4lly at rest. The 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 frictionl79w jbq 2byxd1jp 9wh5xtuh )7ess incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 909 xuwtb7jhypb251 qh7j w9d)x 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 o7iid7l q(hd d0 ykbx3*f an object of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, project q d5eo*v)mybh.z; j/tile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile c mby d;h)q zet./5jv*oauses 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 230m/s buries itself in a 3.6-kg pendulum hanging9zcs8 qbvpeywwdn,,(r( sr9sa c 283x on a 2.8-m-long string, which makes the pendulqvxwnb 9rdy,(w 2zpe c 8rasc8(,3s9sum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kineti7kud t*8w b(fxc 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 at rest, in1siz o:u4fe-:g y;rvito two pieces, one of which has 1f1:o iuy:z;4gr ie-s v.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car crb muyx* p3/;nexo(jz u 4.fa)ollides 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,x)a uy(o*n ux.m4e3 zf;p/ brj knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a h8h,nms86 -yv*ml m upneight of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the bml8nmph uv*,8 y6-nmsall make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the cog+riu+ 1d;mw2w8 z + 1wdjzimyefficient of residwi g+ry 1z+m8w2+1wmudj z ;titution, 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 wi-g qljk/o6a aci bx9sfby 39-7th three times the mass of the 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 -7cbk3q o9 bas9-gfjliy/6a xslide 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 collid ec 0qr0km)d6qp. twnj 4fcn19es head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final veloc 0tmp c4d.n 0qjf9cq)6ewkr1nity 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 decayj w.(5y0bg odps into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at rigd5p .jwog(yb0ht 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 massw3b naj+ and3, $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equal mass,s:gd /dw2vgx1ott 4-szs lnh5: /x;am each having initial speed the two move 2ds:gv4/;wgmxdots5st :x/ l hzna -1off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the origin of vyf (q.7g uoe8lyq l((no2 g8zan 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 and what are their two speeds? direction of (e o87gyzulo8(qgq.fny l 2v (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 collisp0x 10.gmok ztion with another atom at rest. After the impact, the neon atom travels away at a 55.6 t0z.0 x1gm pko$^{\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 crk ;g +qw-l9)eh;iq dixtbn.,ollision with another atom at rest. After the impact, the neon9q tdh,;xwkg. ;i)iq lrn +eb- atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass ofzg2rlc nlp p63a.oa; .gxoe.e ep -.9gzvk05t the three-mass system shown in Fig. 7–38. Specify relative toc z63g9z5l.-gke g;nlae.t..0e vrp2oxp o ap the left-hand 1.00-kg mass.    m

  The distance between a carbon4 f8a*jk bk3i*a daje+a+7kbv 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 vpst9 ec65mt )p8va kh 8.wxqv0zq3j,behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the frontpc kzxa,v .)95ew8jtptsq36m8h 0vq v? 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, isc hrn;)pk3*t u;w m)pvk+r :rt used as a ferryboat. If thr k:+)p c ;tnprv)m3ht;ruw*kree cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side2 (g i;r(aiejn5s k3cqom/6 yns $l_0$,$2l_0$, 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) palletq3t uhi*ryle)/ b+eq 6 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 hoebqr+yet/u)h l 36qi*rizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cu/nzd/b8(*fva r4 c rvv)vq( fst 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? [Hv4r az*/b vf(q(n/s)v c vrf8dint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and,v *iv4kb -jdf calculate the mass of one of your legs. vk,*vdi f 4j-b   kg

  Determine the CM of an outstretched )-;fy 7/x*uqsk mraif arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calcucu5 ile,l(cy( late the position of the CM of an arm bent at a right angle. Assume thalcey5ci(ul( , t the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a positr 8pal3/zx p8q;zxo,lion such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s medi 8/ lpx;8l z3xa,qrpozan line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth awm jcy6s( sm43nd Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man si el;c e48fkdat *(h*itand 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 unifff q)b 8ys9.2l+sapn iorm cylindrical 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.9n8plysbqfs2)i+a f that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diamet-5(eq yt7o)n6 gas 5; u2ht-tcm79nhxuwdet p er 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 pd7thg 6y- t 2 ans(n7utp;eqmhw9uce-5ox)5toint that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–c yloojfh+ nq*vih*1 z( b9.h114 (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 stationary withwti /1vj0ad 9i respect to the ground. A passenger, of mass m, then climbt1/vjd iaw 90is 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 horizontally at strike-. g/m1suwms8 wsunn; s a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calcula;m n-1u/wss. uw mgsn8te the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m t*lbba5 w fn ts d8/kky;8yt.9craveling with 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 r lks1enc- izy8as3erd125x*faced with the corner pocket shot shown in Fig. 7–43. Relative dimens12zyrxceed 5ss i18nk 3*la-rions 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 space suit) acquirw; /qn;fzt/gb7oih9tes a speed of 2.5m/s by pushing off with his legs from an 1800fh7gqz;/t w; 9/iotnb -kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are initially at res isho91:(saaq+o z.jji5g5 ngt in outer space. T. 5q:o(5gn+zghjsjoi1a9si ahey then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ba uwy35e:l dq6oll (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. Whal uqy:wo6 3e5dt is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness il wip+5jo(,gc n 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 Bo g5pw, ic+l(j. 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 the top of a flight of concrete si4;b ama9om) hzj6xuafs j3/- 0g /j,flhfv9mteps of total vertical height 4.00 m. The ball m j f /g9h3/jsu f9)0mmah,iaovaz;lb4- xf6jhits 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 vertdyje8dwj+u3 wq3a a .yutf til,3q+5.ically into 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 becomes embedded in it? ju3wuaj+3qi edl da8yft q+5t 3 ..,wy   m

  A 25-g bullet strikes and bxa:jrrw. )muw hw34x,ecomes 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 fric:xxm )uj4. ww3 a,hrwrtion between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the o8+ wribu d/at;bd+i9ether of mass 60 kg, sit in a rowboat of mass 80 kg. With thrtdui + iw b9edb8+;/ae boat initially 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 w e(vg;qq88wrp as 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 apart into two fragmentsjto4s a7;795pzlpv s mb3xly7 by an explosion. Onx77s3ty av74pljbspml5zo 9; e fragment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is giveq *e6vu rrcz,/ub,d :tn 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 massescz*/be wj)+u4)boihd h6 h5(zgy/ssi $m_A$ = 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 int2t-s.qstw3 fvs rbt12o an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the al.q rtbts3sf22w-1v tspha 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 pqvo up*4fv; n/n+a+gtarget) 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 std 4ix;p738gu,c f kmrlides 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 m if it is to rebof : 6(xvbj8tqaund from M, slide up the incline, stop, slide down the incline, and cxvbtfj(aq 8:6 ollide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the pl 9-fj r 2 fdufw0oxf8m3g1/fdtanet Saturn moving in the negative x direcdxg u3f20/8-j fwr9mf otfd f1tion 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