We claim that momentum is conserved, yet most moving objects eventual 47+-tu, k yx7)7 xprw,bg lzgvej.tbrly slow down and stop. Explaitxwjtyxp lu77+,ekg7). g bz,-rbvr4n.

When a person jumps froeli opmw g;w5 qm/g901m a tree to the ground, what happens to the momentum of t/; w1o g 9qmmw0e5gilphe person upon striking the ground?

When you release an inflated but untied balloon, why does it fly 9u2r3bkgvq6n5qu qg6 across the room?qr vu96 qguq2b6nkg53

It is said that in ancient times a rich man with a bag of gold coins fp4;vq5* l am3(u,spjd q dzy9jroze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to ,9dp pdau ys(qjzmv3j5* 4;lqsave himself had he not been so miserly?

How can a rocket change direction when it i 4 6tjwfrl8nr3t-:aoas far out in space and is essentially t-alt8o3:4jrf wn r6a in a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller thyso cpdn +0k5o)b8al,e force can be for the sameb +5,oa l)0ncko8ydps 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 of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. To s i+bin*uag0ywedg,48lyy) ( day, though we)4y*dg,80yin b(yula gsi +, cars are designed to have “crumple 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 tossed in the air by,6i)3oz*u ifmb pd1kpgt++ w h1p+f po) idktu6w3 bmgh, +zi* the batter?

Is it possible for an object to receive a z x1pb),/ z,ogyooj+llarger impulse from a small force than from a large force? Explain.jo1) ,g / z,zbxylop+o

A light object and a heavy object have the same kinetic enerf aps:z7ch,k :++ nbopgy. Which has the greater momentum? nac7+ zsb+p :: ,kfhpoExplain.

Describe a collision in which all kinetic energy*+ yqu7e g dqs,ry9(tb is lost.

At a hydroelectric power plant, q:wxu n7; eofh zd6tc6c, )ju 0y7;dgjwater is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to ozhd d7:;jt0gx67qu,ju w ) y;c6nefc a dead stop, or so that the water rebounds?

A squash ball hits a wallcu* toy xg,4u- 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 stw rbg+g*u3wx(mouu l8rq k *7,eel plate (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 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 lr wm,kqg7bwo8r + (g3*u*xuu falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy 3*o+;njoe(pdglw, uf load in your arms?

Why is the CM of a 1-m length i q4 mnn , 2trqnc9f;5sdb6c(rof pipe at its mid-point, whereas this is not true for your arm or le 6;csqi 4n(n 2df q5c9rb,mnrtg?

Show on a diagram how your CM shifts when you change from a lyxzgnrn ;)s.o 7ing position to a .nz)nr7;o sgxsitting position.

If only an external force can change the momentum ofa/r sn, y4h7tz the center of mass of an object, how can the internal force of an engine accelerate7,shn t z/4yra a car?

A rocket following a parabolics) st(0)bvlm 0 g 7:tivbrop9af-ag;ruib s18 path through the air suddenly explodes into many pieces. What can you say af7;:0is-9trs1v)b osa)0 v8patiu brgb(mgl bout the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying wi,fy-i:4. o lbfpscnckury8 h9v3 0r+xth a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 253bb0trymzge5p p;.w 7 N acts on a 65-kg skier for 20 s. What is the skier’s cpp e by0b7;.m3w grtz5hange in velocity?    m/s

  A 0.145-kg baseball pitched at 39 p(om*whl)j88 dt6z7vi 9bzap m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact 7 8tvo9zwj ppzhl68)(bda*im 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-y .i0ptsg q;l9q1y ar.kg package out horizontally with a speed of 10 m/s Fig. belowtlqraqp9y gs1y..i0; Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exert:-asj-g)-u6; xbpx )mw zhwca ed on a rocket, given that the propelling gases are expelled at a rate wb6 xa;z)hm - uag:w)s--xcp jof $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving atftiswhh4jwkd- , (i19 $4.1 \; m/s$ 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 travlxqty;z k (h.hoi,r ik0kq kq/ ,ep,6/els alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new sp(/, kqi/ qxrqzykikp;, ko,h t.60lh eeed?    m/s

  A 9300-kg boxcar travpimsa pgsxoo-4z/+mqh 16+:(l r1a2moy8pp keling 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 100km/h If th;j x /zv+ymd3je 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 mjzjvx/yd;3 +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 (i6 gt7 qo;yl6ei(ly g,cb.q j8.6m/s on a level track. Snow begins to .yli 7l bt;6og jy(ce (qg,6iqfall 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 init 85yaub ) e(s*bxo7ed5ekxd )jially moving at 420m/s emits an alpha particle in the direction of its velocity,57ee (exo*)b)ds 5ukba jdy8 x 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 have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg bloc8i3r t cs2vzyj.vtt vms2c3: ,k of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emergmt.t3 v 2: 3jrc, cysz8svit2ves?    m/s

  A 975-kg two-stage rocket is traveling at a 0;rvlxq c 8 bl53st qu0jqqb-,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 i/oqq0,s*omhi ;no cg hl4)ud; n outer space with a velocity of 115m/dg ol;hnci4oqm/uho0;)* s,qs 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 0.0bek2ie: 1fqpt 48 s.fu5ox9ta45 kg is hit off the tee at a speed of 45m/s The golf club was in contat9fie4q k1 5px ue.tb2a8:osf ct with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail qrh- 29m i7vs -u*snazat a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to t2v*z7s9 ar- h nmui-sqhe nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s striknag3k61 nxi 5jes 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 craps ,mjj 0 4o71ty/7r :kkq.onqc,chsk.q ip-tshworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mi k op,7 j qc10r joty.4ckq. ks:-h,/p7tqnmsass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in 0.75 s+skm, p;kc- 9bm fuq5r by a head-on tackle by a tackler running dq+ cm9,fk-sb;mrpku 5ue 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 kg) points in the +x direco;o3 eb pv:dl 1mtfr1-nt, gs*tion and is p,lvtb*dt ofomg3sn-1;:r1egiven by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking the lower leg v+jn /ero5e ;ra:t m-+(ud0p 2r tujkwbone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to thor+akj;rut/d:jwn5urmv e t -+e0( 2pe 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) w3a)ac*j3 j cawith a speed of collides head-o aaj)*3cajwc 3n with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, 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 eaoio2gpy x2 xto 2:: g6x,p)lgsst 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 afgx2o ox y)xpt,o:g26 p2gi: lster 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 perfec; dgn(0re5 elytly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what e5eg; r(l0ydn will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of e.9rlsz2 wxw9 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed a zw9e9lwxsr. 2nd 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 moving with a speed of 8.5m/s collides head-9 tf;r/jwkmk3 on and elastically with another ball initially at rest. Afterwf tr/mkk3jw;9 ard 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 w ,bobi4 b6b/nsg* ni:ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass ow bs/ *n:n4,bgbibi6 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 balgk1ou nkob: oh)ogw72/5v y -jl initially at rest. The second bal:bjugo nyo o-o/g)1h2wv5kk7 l 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 sin7ucfea -fy od-0p*i(t(.o down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only sfp*ui0y 7((-i eo .onadt -cfone-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 object of mass m. riocx( +,o2 tihqnz el/(c0x(2skkl$_A$ 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 rl-aom9/ ( 8q y-wedda)uekws;esults in a maximum height h of the pendulum equal to 2.6( uokqad de- 9/eas- )myww;8l cm. A second projectile 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 ti5t.q kmpi;e f-+9oayraveling 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulu+mqe9 -a o.i;i ty5fkpm 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 oxdb(p5q3j nf ;f 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 breaksgbx,jacab be9 + 7 j,*mve7d7x 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 particle, and B represent the lighter par+eb,j jdb7 ,ecag7ax x*mb79vticle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the re5.:l :t8dhrc gpyu;fhar end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and :dr;yfh8g :uhc.t5 pl B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of ec2mbet s o c:md-ek je.,)-d:1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make-edj,-2 bstm ke: ec)mde:c. o before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects m8i3iv* kd. csr 1e4cs5h*i dais the coefficient of rek5v. *m4h diidi*c18c3esasr stitution, 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 piecepmc 82vm zdyfio4u) 0 37*u9ffq,mz vrs, one with 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 slide apart. What is the ratio of di2 fzrf m yp c*f3ui9087mv )dqzvmo4,ustances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on with a 10dgf1x.74kzke qo -2y /qy:cbc.0-kg object moving in the -x direction at 4m/s Find the final velocit4g-z7cx1qd kyf /2kocqye b.:y 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 electronx8n hkfw:t0l, 8rasf hd-((r+as *pd o, and a neutrino. The electron and neutrino are emitted at right angles an-(8xpo0a+ r8f l,thnkfdah rdss : *(wd 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 mji*,b a*3aadj)b; yp$m_\mathrm{A}=0.400$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 collisioxxl7/tn 6jf n, .j0 t6+elxudhn between two objects of equal mass, each having initial speed the two move o7x0 ,j xelhn6+/6 .tndxltjfuff together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at rightk27b hd fx wq(hrh)*a* angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is movixwhhqf(k r* )* 2bad7hng 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 perfect/59s 3,bq9ja ak5emohp gh)rt ly elastic collision with another atom at rest. After the impact, the neon atom travels awae 5ak)stb9mp a5,/3qg rhhj 9oy 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 perfectl8v1pfdqt d/b+y elastic collision with another atom at rest. After t fqbvp/+dd1t 8he impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass systed6kp+8ern*xaxv5nsbl : 1 z5f,ji8 ubo x 9ii-m shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg mass.er: s5b8*8,xflndi6-i x91 azj xk ivpuon 5b+    m

  The distance between a carbon atom w,ykhb):a9 vd($m_{\mathrm{C}}=12\mathrm{u}$) 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 t5w j7b5c2lyn-y q5 axau5ao z)he car. How far from the front of tbj za57o5 c a)qyx ulw-an552yhe 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 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 k xb tlr5g3q;uy+ui4q/ g, is used as a ferryboat. If three cars, each of mass 1200 kg ux 5 q/l3uqr;tbyig4+, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side;7w8j53g;ntcw 5m fh5bkgnu81skesi s $l_0$,$2l_0$, 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) pall: hg22gy x,jkwet 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 horizonta2 kxjhyg,2 :gwl plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plat :n5/sesx2kn ze of radius 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of:e2z k 5x/snsn the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as 7w(dj 3scop.p j6i8 nothose in Table 7–1, and calculate the mass of (w nocj pj8io67sdp.3 one of your legs.    kg

  Determine the CM of an outstregi x),0jld1e rtched 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 t2v6qym0qq 8s :cr6f qzhe position of the CM of an arm bent at a right angle. Assume that tqsry6q2zcqm: 60q f8vhe person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and 6,r(d0j*a jk.zki( v rk.bt gqlegs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median lidgj0rt *r ak kbk.6q (jz(.v,ine the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and e fkxgw2l2 ;f3b r)4dhMoon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart ynr .nl;v0x d: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 hea: cdm a),qfb( (m kth2 dr3s-zki1(zrld 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, a1 :,(qr mab -(ilk2 mhzk)3zs (cddfrts 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 trajectory?    cm

  A mallet consists of a uniform cylindrical head of xx.,a jo..o(gt:iq0 jgj0q cymass 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 bottom0jjxitg(,0ygooa cjxq.q. :. of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Exa,9a5hq ubskr00nykhg-s; h l0mple 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and id4:hfnre 1qw(odiw + +ts gondola, 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 roperiq(hwed n +1o:+4wfd 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 str9bn oqioz 1:jpqebyq6t-s 06 w8b -ot)ikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball durbb bo8 1j-q i)6qyt0woz t-:69pqo sneing the contact.    $^{\circ} $

  A rocket of mass m traveling with speedte/ak80k n/rp $v_0$ 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;wuq uy3-sc x 4gp1v;m corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should thesqcvuxu p34;1mywg-; 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) acq8fcez ;srj 8-wuires a speed of 2.5m/s by pushing off withcjwsf-;e8r 8 z 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 other 80 kg, are initially b+z-shp.* e:ix p *mzkat rest in outer space. They then push eachbh*xeis.pp-m +z :*kz 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 ballfcxta tym*/ e/08hfr * (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. Whx rtcmaff*e 08*hyt/ /at is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving an automobil wikud c643k.h+rv 3wde accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) 3.u 3 kkwd4+v6hdircw speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of 2 kch5 pr;+clma flight of concrete steps of total vertical height 4.00 m. T; hc2l5mkc rp+he 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 vertically into a 1.o9f :5 zfuhn,bff0-vt40-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 tfb9n-f, :5vzfh fu0 othe bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood plac1b+ v6jsu*(fohjzcr-w hvfv: 1;fxr (ed 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 impafj(:wu1bvrxo-r(61ffhhv *;c z +jvs ct 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, sitmtchuq ) i 7:(eiu01vy in a rowboat of mass 80 kg. With the boat initially at rest, the two people,i:)me(uu ycqht71 v0i 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 was about ub) i22t1buhh vk qvmn46/qw.$ 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 bro (x:2 tj zw0)2dw:u/lz u)aizcbstl)cken apart into two fragments by an explosion. One fragment acqui wz/:l0:t ))u2xd)c uit2clwabz (szjres twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is gilx+ :kcl fd/o;bg1j -0 xx;nkaven 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 masses h0 ga v;:+qkjde7z,av$m_A$ = 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 ihks),/z:h )+ f ;anp(iyxurwtnto an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particlef ) +yhh/)puxnw;z: (asri,tk is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at anixi 0 o415ql,f*ah oct 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 30.0svk2 4*7yyn.ejjgyxk;*myv4 o f5; qf $^{\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 t u3gza8+ej*gffvd2+r h 82co whe upper limit on mass m if it is to rebound from M, slide3 ow228j*uaf vggh+d fzre8+c up the incline, stop, 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 plane4o j9v1bmp y.low 6qs )e9p* i/pht;qyt Saturn moving in the n p6lyh*wvy ) q9bij .ep9mq;s4top/1 oegative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s