We claim that momentum is conserved, yet most moving objects eventual ;)phehk- +,loaqi1ljly slow down l+,k )hh-1a; jeoilqp and stop. Explain.

When a person jumps from a iqc4f3oa5 oa. tree to the ground, what happens to the momentum of the person upon striking oai c5ao4q .3fthe ground?

When you release an inflatedm*;d na1jk );qv*a tvy but untied balloon, why does it fly across the roomnvqtdym k) j** ;a1;va?

It is said that in ancient times a rich man with a bag of gold coinm*o:p 76 -o(zjhmtqcis froze to death while stranded on a frozen lake :i jt(m mcqp-6*ho7zo. 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 directx.ff p4kb; d.bgsqx/; r .ji7vion when it is far out in space and is essentially in a v7rsdq4b . ./g ;ixkf.vxbfp;jacuum?

According to Eq. 7–5, the longer the impac )zmtf :s.ob.)/dav4b: s:sj 4yd frhzt time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility zh:od)m .yr : f.v: )b4sasdsf jzt4b/of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. eqt+b4c*,(w cql- omaToday, though, cars are designed to have “crumple zones” that collapse upon impact. What aqo,4l(+w-q*bcce m tis the advantage of this new design?

Why can a batter hit a pitched baseball furt pcr7s2;2zi2 mvn;dihher than a ball tossed in the air by t i ;v2;mp2hn2rd7zisc he batter?

Is it possible for an object to receive a larger impulse from a small force 0mz0 6en2de hhrw)yd 4than from a large 4yhzrdewd6 m h n0)20eforce? Explain.

A light object and a heavy object have the shhhadr *i0 co xt-*w+hwtql. (j+( w-iame kinetic energy. Which has the greater momentum? Explain.(hqlw hji*oai+*.t r- cthwd +-xw(h0

Describe a collision in which all kinetic energy ij d4w7v70 zxels lost.

At a hydroelectric power plant, water is direffw x( s7h3-xbp.(zrn cted 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 wp(wb z s-(fnfxx.7r3hater is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a 45 * q hf0q1xl*ry$^{\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 plambq/+esycu0+ te (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum sme+y+/ b0c quof 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-c)kbxs6dske4zr 1+a when carrying a heavy load in your arms?

Why is the CM of a 1-m lengz 1zks i l4-lhl;i os+f.b)v.bth of pipe at its mid-point, whereas this is not true for your ak h4z1 o.;vzs-+.lliifl sb)brm or leg?

Show on a diagram how you8 8l:r dcg; q omz.(4ucoczxauz..q/ pr CM shifts when you change from a lying position to a sitting position.:q. a o/ugclp(x;d8qmzuzz .c8.4oc r

If only an external force can change the momentum of the cgz w :r5v:q1 rifwg uxaue2gu /,a1+5bigg -b;enter of mass of an object, how can the internal force oi2fg;g5 wz:a-ui5wa /e ru1b+g: bxguqr, 1vgf an engine accelerate a car?

A rocket following a parabolic path through the (u3d+i wmy uof w.w-i6 m9qj2wair suddenly explodes into many pieces. What can you say about the motion of this syyiw w 6w.mmw+ -u39du qifj2(ostem of pieces?

  What is the magnitude of the n);evuw2dq 9 gi/f-fsmomentum of a 28-g sparrow flying with a speed of 8 d-i /f2qw9fuv);e ngs.4 m/s    $kg\;m/s$

  A constant friction force of 25 N acpxb 11e6i;f yqmup* b+ts on a 65-kg skier for 20 s. What is the ski+ b16u xyqf*ipmp1be;er’s change in velocity?    m/s

  A 0.145-kg baseball pitc,3y 9fg(ovjx ched at 39 m/s is hit on a horizontal line drive straight back toward the pitccx fv3oj 9(gy,her 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./0rr.b xtgov98gcv 3dsm/i gi ./ xir:40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, avrd0 xi.xr sbrv: 9/ gom8/gi/ic.t3gssuming 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 velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propellidg:d)k7myk nt0w; n ,4kk re05zuz,pnng gases are expelled at a rate of 1500kg/s with a speem; k nkzkn ,5 wkuyrp00,: zge4d)d7ntd 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 touchdof+ r9 ah9( y+nuyqiaa48ci p.xwn is tackled from behind. When he was tackled by an 85-kg cornerback ru qan+ hxay.fip9(y+4 rua 9c8inning 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 travels alone on alevel frictionless track with a c:l5luk0awc: bonstant speed of 18m/s A 5350-kg wlu 0:bcl: ak5load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second b)m;imix4 xkklk,w3 bb:( vmw ulk779goxcar at rest. The two stick toget) kv( uw4wgkbbl9: 3 ik; m77xmkxli,mher and move off with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds c.leh7qydw /h/i 4i7 rlan 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 to7 ly/hwd 4e7h /il.rqi 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 constantdwq/6oc/3o co cpcu 7lbf),2m speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with tccopu,/o)2c63qmlb /co fd w7he tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s em: lw;ph cjn 5xf5b,3t;bf5)yu t. ksmsits 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 m;5f :uf.)lm5knwj b,b3h 5 txsy;tcs pass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kgz9 t:1n .b+ uqnsr.vpt block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hi. uzq9+pt1s.n: br vntt, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speey9 u, jha.mm:nbcxt+4 .eu-isgi i 2j,d 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 travelingzzma q e jy3q( c+;0;unz/6xwv in outer space with a velocity of 115m/s To alter w/qvz(xyjmz;ua3z+ q e0 c6;nits 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 w17v e rx3-pyc1gia2 xThe golf club was in contact wy 1rxe-xp c v2ag13i7with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocic +q *v-(5rw 2*suox kmvbhco6k/mp -sty of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is thku+-( s/hvcm 6o2pc-bo s m*kx*qr5 wve impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and sppn-zpvz0j;p 3eed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crasvnv*c /:rqj(/nx nhl; hworthiness 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 exerted on the car by the bj q r(:lv/nc;x*hnv/ narrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is runni 9 a3k31v)fqx,a zwnpw xcl3x-ng at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Calcxlnpw qcvfx)33a3xw1 k ,-9azulate
(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 (mas3d8)czq*dezqhoei0 *y0 2 )h-vjv vwqs 0.060 kg) points in the +x direction and is given by the*)yvd2v vj-e q8 oi 0)qq *3dehzch0zw 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 757 cwh9xpl/2vm -kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strengpx 2l9hcvm7w/th (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed ofv av/l fr66fx1r1t 7+cwul0rc collides head-on 0u 61ff /rwr7 xvtvrlac+6lc1with 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, 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 ebw-by2a1.mt xuv/kb ) ast 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 oftk-xbm2y u v) wb/b.1a 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 elasf-+ks, w vatc4tic 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 directionsat+,v4wf kc- 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 of 2.5m/s coll6ap6k o dd0f0klkch-9ides 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 theloadk0 kc 9h k0f6p-6d 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 isb/l ,lpo6+i* hz wznkyoc.8 l4ae /r-z moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces blpw khen. c+ a*8lol z 6broy4z/,i/-zackward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as one appryav0dd+ ;/iw s:gygz u1b/jni61nb;boaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving subng11biga v;ni bz://6dy+dy0wj; 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 t 4glgrt42+i9icg9xl5u+ i jna second ball initially at resnr gt +5g u ll4xiitc4gi9j+29t. 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 slidt) ush4mxsa,6 es down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one- ,ms)x4 u6ahtshalf 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 mkhf /*;z 0)tcq aitjt4$_A$ 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 height h t2l:2mnwa* 8cdh(sfgof the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing tnsgd(:8h*2at2ml f wcwice 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 bw73q*d6fxzr1f*4 g7rotjbl i uries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulumxg *t3iq bl 4fz1frwj*o 76d7r’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction o;9i9 8oct dlqkf 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 breaks1ldj 2x ldgvcf88x *0uk2,rka an object, 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 explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier d *kalxdj 1c,882lx frku2gv0particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped at m f ohjxsa;h;u6c:x0be0u2 -ua 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 representba h02x;uxe :m 0-6c;ho sfjuu the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds7ly/z0.. iq alg 3uorthdq,8w2 zg ov1 to a height of 1.20 m. Approximately how many rebounds will the ball make befora1dhro, u ./70vlw.o3gqztgl zy i82qe losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two ocp+6rf8 awd( kbjects is the coefficient of(r8 +kpafd6 cw restitution, 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 5ry3e)6z nch jcsvp38 with three times the mass of the other. A depression is made in both faces of the cut, so thatyccrj38p3 6z) ehv 5ns a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on wfqw 2m5v0,32 g2p4jdt gi czmvefzh7pm..gp,ith a 10.0-kg object moving in the -x direction at 4m/s Find the finalv.gv c,jzdm0fiw 2h2g pm t,q3 p. z2f47g5epm 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, a 9;xg6xn9 xaro1hkh rq2p 44jxnd a neutrino. The electron and neutrin pkh9 hnx xajr41ogrx49xq6 ;2o are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of mass;wh-j1. bh fae $m_\mathrm{A}=0.400$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 macifi6 6r89 7y+ v9 geayirsq(tss, each having initial speed the two move off together with speed v/3 What was the anglii q+67e avy8yit(sgr 9r9cf6e between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move au/by p i- gq 4skt(1vbcb2xcq8j.lo82t 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 .ub jspc/(v4kx 8cqq1o-2 8blgyti 2bx 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 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 collision with another atom at rexqwxtx:0q7 f+ 8u9c ktst. After the impact, the neon atom travels away at : 09 x +7xkqqt8cxtwfua 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 with anottpwnw 76booj/g)v0 n/her atom at rest. After the impact, the neon an67 ovj//wng t0pwo) btom 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 systeu4imdbj/ so5 .m shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg mass ojs i.m5/bdu4.    m

  The distance between a carbon pd9vt))d *-)-k9 4c d bo:xwqsrw yqcoatom ($m_{\mathrm{C}}=12\mathrm{u}$) 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 105*ulu;c;49 ,qrkx noi x0-kg car is 2.50 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the ca xo,n4qi ul*;u cx9k;rr, and 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 iw+iza/v nw2 96800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg,n +wa/v9w zi2i occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sideszw4y+dxl g4a6.v*go l $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases ofb * w3tqa lnf/tqs608y tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the c8ls bq*ytf3 wt/0qn6arane 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 clsu ovw, g.t8(ut 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 t,w(.s8gtuvo l he plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and my /x1x:glt):mdt8n w46t3g3u zdwbvcalculate the mass of one of)tnxtm:1w /yv4w:6l833z ggxbt dm ud your legs.    kg

  Determine the CM of an outstretchib-k a+yg2n:m ed arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent at a righ ;a:x g-,l l pjyfcfmf::wuzn7 +9/iist angle. Assume tpxy9g7in+;f jmuwla: f/ zs-,:i: cl fhat the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his 6t3u t/fi3hzxfcmf d )0r mi;9arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line t;0fhrcmiu3 fx)d izmf39/ t6the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon a6gk ;z)misvozv1.i-cre $5.98\times10^{24}$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 10.0o.vnb8t23* vq.hgw: dv(f j 5-p;kgimflr3 w m m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical he6 g,8pxjbef4wv3w hs,ad 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 parabolic trajecw3pf 8g,jbh v,x6ews 4tory?    cm

  A mallet consists of a uniform cylindrm9jf*r6glrdo c0q + .xical 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 handlef xr lco+rmj0g.*q 69d is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. -i9,v c3r v g-tu zndad1d*9iw7–29), $m_{II}$=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 gol1k.v nt+ ja wny+o;(:cg5b swndola, of mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to th:t(awjvg + 1k yno.wl+b;nsc5e 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 stri74-na5p53yhdp4y bydvu sab; kes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, a4p 55 y7bp;uadnd v4b3hy -yscalculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speed16 rn cxal4zs9 $v_0$ 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 shownzs6e(0wms j w6 pksplmj a1 og5;,ku11 in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a jso k6me1a(0, ms5wzukgjsw6 1l;p1p“scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acqun)e4fnkft1:n 4 zky p-ires a speed of 2.5m/s by pushing off wp-4nnkf1nf:zy e) k4t ith his legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the dgk2-d8ck3wr other 80 kg, are initially at rest in outer space. They the8wk3r2 dgd kc-n 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 elast prdbm8 c-n0vx-ojtclh;3 x17ic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its orimxn c ;blcd0x18v3p-h 7-jotrginal 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 involv+r 6ggit2al e5ing an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 11r 2i +atggel5600 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was 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 steps3bnz - bnyct5 kag*0 n:c;,haz of total vertical height 4.00 m. The ball hits four times on the way dow,c;5 *t-yn:angcakb znbh03zn, 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 vertically into a 1.40-kg block of wood at rest directl- p s ;wqznal96ls5rs-y 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 s;lza s5l69n -qr-spwin it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood placet8vu.gipce(5 dr 6o) sd on g r8 d.po 5cu(s6e)vita 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 was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in ac),. q2qh*pme 9 -ezrkx l:fca rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at oppositl9hrak ecq.:2, mz)xefp*q-c e 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 *-oo6h ov(m eid-9ivbwas 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 fhj oh6nb1w-8pm cz1- apart into two fragments by an explosion. One fragment acquires twice the kinetic energyhw 1jmhof-zn61-pcb 8 of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 580o59u tzcz(4sx3 h8qqa/s gjt,-( $1.8 \times10^{ 5}$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 hmarrvt hm .-4-edu4/:1q5s g()df *pkhulvz $m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha particle and a smzx ( xr3hsw88th:.ery aller nucleus. What will be the speed of this recoiling nucleus if the speed of the8h z. w:hxrx(esr 3y8t 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;m0pf lvm)n hwbd7,r0 at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.dvqx-un9gcetes-- 4m(88y mt 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), wh3y - kzv0v-owzcsb53 hat is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide downb ov -05y3-zscwvk3hz 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 planet Saturn nqqgw0 .z,yp1ew.l(m o+ nrp/r cd4;m moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.mp0+.r 4qcglznmd/nr;,p.wo ye1(w q6km/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