We claim that momentum is conserved, yet most p,w lk*5,w *lumot; 7dxxn v,smoving objects eventually slow down and p*l 7w,v5 knxsd;m,lu ox *,wtstop. Explain.

When a person jumps fx br4q5 vkej/3rom a tree to the ground, what happens to the momentum of the person upon striking the gror4xkjv5qeb/ 3und?

When you release an inflated but untied balloon, why does it fly across the roomtpbxerwf0 z9 0g (01gyg0r0( f0 1gpwezxybt9 ?

It is said that in ancient times a rich man with a bag ow8kdgt a9s* 2gf gold coins froze to death while stranded on a frozen lake. Because the ice was 2dsg 8gtw9ka *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 changp/4mhb)f5q e de direction when it is far out in space and is essentially in a vacuumf /)5 h4depbqm?

According to Eq. 7–5, the longer the impact time ofk1*( t1uwl:cuf z,., o)ldgyckerxa- an impulse, the smaller the force can be for the same momez,1 x oyf,d.ut:l *cu) lw kareck(-1gntum 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. Today, icmh hyq.z8m6:jbaf si e s8/ sdkfc6; c8u9/8thoug6h6m8.fd zk qb/8a;mjhcse s u :98sc8 if/cyih, 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 thy,gqy+ d(m i7he air by the battihygd ,+(q7ym er?

Is it possible for an object to receive a larger impulse from a xx9;8fa6v p2ioa :*w m g(4mpkuv xm6xsmall force than from a large force? Exvw6( : m u4xvxfgmik ;a*m9p62x p8xoaplain.

A light object and a heavy object have th0b8up v(kl,gg h 5mq;ze same kinetic energy. Which has the gre8kg; 05(,lvbgu zmqp hater momentum? Explain.

Describe a collision in which all kinetic energy is lsi/ l0.daw2uxg26h0st0ys q eost.

At a hydroelectric power plant, water is dirdk 9 ddplrw;o3sj.:l4 ected at high speed against turbine blades on an axle that turns an electric g:pdsdorwld 39 k;4lj.enerator. 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 wall w 848t alohnyzasyt4n1( 0,fdat 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 hardso1:5xit p4 b(cvb) ei steel 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, durp4s:i(tio1e)xb5c b v ing 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 g:mx:f,pp4ok r qb.p8f5jgb*backward 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*fh) ofzr 2x87 j kts-z*z1tdr true for your aohrz)7tdfsxtz1 f2-kj*8* rz rm or leg?

Show on a diagram how your CM shifts when you change from a lycbyi8/4ge9 kxing position to a sitty9cx geki48b/ing position.

If only an external force can change the momentum of the gz rjq 5)u45fvcenter of mass of an object, how can the internal forc ) gqfj45z5vure of an engine accelerate a car?

A rocket following a parabolic pap *vk-lag2h3oth through the air suddenly explodes into many pieces. What can you slp*kgoh3-a2v ay about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g spar p,z,-ca w3ei. lwk-hvrow flying with a speed of 8.4 m/s-,l-waw3k ,cv. zih ep    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s5.bs wyyc)d.nd 9 pjon// (ns-q y;qyk. What is the skier’s change in v k/jcdsybq(syo p5dn9 y w/nn..- q;)yelocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line driveh* dx63n /m c augo6*bfav)+hf straight back toward the pitcher at 52m/s If tadx3)oacfuhgmb 66 *vh+*fn/ he contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg packa z:pjrro5063; m ij;9gk xf4fwv*rxloge out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially ax ;vwf9;j0mk5 or: jpr*4g 3xfi6rlozt 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 propellih 3o tspl1ppuif( t,//ng gases are expelled at a rate of 1500kg/s with a speed oft,t(s ipop31u/p lf/ h $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback movin5usrxzq54na -(knr2ixi 9gp) g at 4.1m/s on an apparent breakaway for a touchdown is tackled from behind. When he knx92 nsi ipgr5(45zq)ux-arwas tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels aloi3i/)kwuihwdaz59+a- lw2 l d ne on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the+dhz-2 diu ia3/ 5wkw la9wi)l car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar at res9ikw3 ojpf 28hse41izjbqj-q.v5+o p t. The two stick together and move off with a speed of 2b1o5o38 ik-pv94 iq +j.pjj fhqse wz6m/s What is the mass of the second car?    m/s

  During a Chicago storm, w 5 8c+tf+cunppinds can whip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square 8 nfp+5pu+ ctcmeter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along withni)ul +bnhyn6*( (nko a constant speed of 8.6m/s on a level track. Snow begins to fall vb+((hnnk6 nin l)y*uoertically 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 inegq2; 6bg. oclitially moving at 420m/s emits an alpha particle in the direction of its velocity, and q. 6ge;2cbgolthe 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 block of wood and eme 5tdo4 u,vf5seq )ocz0rges cleanly at 170m/scoo)tq d0s,5eu 4z vf5 If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speed ofy5lf3;rj 9s:97:s qxhz 9x lysg8gjqb $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a velochnmz) k subi81;ra m:6ity of 115m/s )1m;8:rnsz hamk 6bui 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 kgforp +7l zjz. oq2.uq3l 24lga is hit off the tee at a speed of 45m/s The golf club was in cjo3+l r2q 7p..az4olq 2gu flzontact 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 at a velocity of 8.5m/3hf gdh yi5 s(1rgb*.bs and comes to rest in a time interval of h35 r.ydgibh(gs*1b f8.0 ms. (a) What 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=0.06kg and speed v=25m/s exxps6 3* gx5tstrikes 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 char7n2mhlhx tdgte.s2 2-ge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on thehs.e2 7h2n-xt2dlmtg 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 by1od;f6 6; xllviuxif03at ix* a head-on tackle by a tackler running due west. Calculate 6lff;6ud o val;tx*x i1i03x i
(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) +cin9awr)ttm*; x5/na8 ffv 0hhvc **d fsi.t points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methodsmfanc;as8h* vrtt )w/ t*n h05d.ifxci f+*v 9 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-kghh5 gmf3u/xc 7rq 0ck/*y 9 1vvw/bz 33yywabb 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 sm* 3kqcyru0/h wyag b91cy/7 3x3zbhv/ vbfw5 trength (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 of co 6 e*: kzrip,m;m b56ekrzg5ldllides 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 aftegirek5 m;,br*d 6z5k:e6 lpmz r 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 east with a speed of 3m/s has a head-on c69hq*.m fcnt0hq+u dw ollision with a 0.900-kg puck inimqun06d*h9hfqw.t + ctially 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 elasti5bkr w1u1q;g ec 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 thatbq5;1euw grk1 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 2.5mfl d:8sr1f3o6i b3b sw/s collides head-on with a 0.090-kg ball initially moving away from it at siw3bolb3 d8fsrf1:6a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that urjl3) 4jnza3lu 0z7ois moving with a speed of 8.5m/s collides head-on and elastically with znu7 lral uojj)4303zanother ball 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 ride co. dbix y6md3s29rt1hd0f ;x9.n ecbdiute; 9mllide elastically as one approaches the oteu6 b.iedd; myxcmdi2b39x.n9 r; 9s10h tdtfher 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 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 coll6q1 st;ul)7 zebg-se rision with a second ball initially at rest. The second ball moves l-sg) 617eerbt sz ;quoff 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 cubeo)q0 eisqw,t)ry*w n- slides down a frictionless 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 90 cm off the floo,t*0)iwewn) qsyr - qor, 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 ankfd dwot66 r7k)m82z;yla6yi 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, projectile 1 resultsjsp6 nd ;gy.k)n2rfm7 in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing t s;dnj .y7 n6g2mkrp)fwice 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 its2sv r)g3hd+-y/ winxpelf in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determg+phnxiw )sy2d/v -3 rine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lost, vnjkj*n8+4q ya(ha p9$(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an objecbw 9m7 .tkcr.ft, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in thew m. bc9tkr7f. explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rea:+faf;(uj 2agpy+y u qr 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 speedu;u p(+qa+ j ffg:y2ya 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 fro*f voq mi-w88lm a height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebouv m-ifwlo q8*8nds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a hep 4sb fj ecxwi-z cbn ihn9g:/u+*hxi 88l38/rad-on collision of two objects is the coefficient of restitutiocbic: ir3*4w+ u8hn8j8 nh /sg/xzpefb - xi9ln, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three t+ z+jdb28n h;o0ekyhximes the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in ieyx+o2+8 zh0;dnj bhkt 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 0mu2j pndu)xc3l) hi,direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Fic ilxu,2j)3p h0u) mndnd the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an elect kmatxaj*v-+)ron, and a neutrino. The electron and neutrino are emittemaat*j- k+ )vxd 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 v7q ft lzlqejf6addmnq;kc11a 364* 5 $m_\mathrm{A}=0.400$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 v qwrew ):yan)(03lj s;bx1gkbetween two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their e yxbv3;qn))j:grka0wls1 (winitial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles andftli.lwdy1td(y6 u yy4tf5/ 2 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 ry24f 5 tt1t.lwiduyl (yydf/6ight 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 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 colliyn12 x njhqen5 (5v(cosion with another atom at rest. After the impact, the neon atom travels awavy(1(n 2c e5ohnjx 5qny at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elas pu i 3pl)+8ruxr85 lgqfc+-fdtic collision with another atom at rest. After the impact, the neon atom travels away at a 55.6i-flr5gu l rp+x) uq38+fd8 pc $^{\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 systkgq4x o4) )jzbem shown in Fig. 7–38. Specify relativ4zb x)q )goj4ke to the left-hand 1.00-kg mass.    m

  The distance between a carbon atoz .--hdxw9p::vjwrap m ($m_{\mathrm{C}}=12\mathrm{u}$) 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 fronh(s 2svp1dv7u t 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 ms h(2vuv71ds p from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is uv*zpkdmjm7892jdq1 h sed as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW cornerp m 2jk*7zm89h1qjddvs, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sideswk0xiejf p;kk(8, f;p $l_0$,$2l_0$, 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) pallmwdg oedldf )a (l*)59et has a load of identical cases of tomato paste (see Fig. 7–40), each of wh9g (le*f md)5ddw alo)ich is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cut ou)m *1n+mpqiwl 4o.r bat 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 ow )pml +1q4iaon*bm.rf mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Tabs/al xb+-rgy3r 9vn0bkdc/ 6kle 7–1, and calculate thadcsvrkb/ -69grn/ lykx3b + 0e mass of one of your legs.    kg

  Determine the CM of an outstretched arm usi,4mkg0 ajbl7,gsn+h dng Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calcul+ cqx6 i(lo-pj,ruy p*ate the position of the CM of an arm bent at a right angle. Asyp*i+(o r,cjxq ul- p6sume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arek-duis:fe3wen, u 0 5ms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far bie,5 d0neu f:-uwesk3elow the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Ears8w88 juqqjy+pb p-f6th and 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 stand 10.0 m apart on frictionless i;8 -nu bnp4lue0bmx3mk3xr. q, fun6 cce.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diameter +,3(uiob b azf0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m,fo+iba , (zu3b 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 trajectory?    cm

  A mallet consists of a4c/u(5 u9 v sipztc,xm uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical hansxiutvc/(cp 5 ,z49m udle 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 trajectory?    d    d

  (a) Suppose that in Example 7–dztje,1 g*ri47cgs)u ooy-r he/t -e-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 its g2(pt c7;lft b8 36ghiu zwy0wsondola, 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 the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens (wtu0l78c2sbhf3 y;p6 gtz wi if the passenger stops?

  An 0.145-kg baseball pitched horizoniji3n f(0qr4ps7bpv .tally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the conta37.i rsi b4v0nj pfpq(ct.    $^{\circ} $

  A rocket of mass m traveling with sphc da*+ 0e/ ,qy(1pajynbjer3eed $v_0$ 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 w - a-rh.xi/ noaemp5bts;6ox 1ith the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,”roebt5xsia1pah ;n/m 6x--. o in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including sph zq4 -gi.;qatj3nzs* ace suit) acquires a speed of 2.5m/s by pushing off g.-zzs q4;ij 3hqna*twith 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, k-ygo (n98pg:(,4 yzy goh o8m ucfgq. (h6blaare initially at rest in outeykg4. lofz6(o:nygqh(gpmh (yag 8b9o -c8u , r space. They 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 c++u5tsq:-a a8ba9yvwx *2 ,qlutze n yollision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one w-u b 8qvys z+,+9 t*xnayule5at:2qa-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an u 27f0ldvp+e ezmi y,8r u;be,lfy4h3expert witness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary care 3y+lu 8 rh; ymvzpdbf,eu0i2e,4l7 f 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) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete sp- e*jttigm* -phgvluwc91 08 teps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions arejp-t *9tm*l 8wphe g1 gvi-u0c perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertic4tf73 8er 1,rfi rjybq7zgw f+ally 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 et 7r3b7jw8r i ,1 fzy+4ferfgqmbedded in it?    m

  A 25-g bullet strikes and becz d49 ijefuh e0jb/77jomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before i0j eu9 jih ez/fb77jd4t 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,3yk:m w3-135zxnrkg wxzq(lz sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opx3(- 5knwkgzlmr3:zyx1z wq3 posite 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 pe; iex7p9q,1vkl*74d rt glrwas 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 frajf5e6fiw /*ii0pa tq/h.-vb qgments by an explosion. One fragment tf-iejq/hp.f6aivqb i0w /*5 acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet isavgpnw rj86 )k0y-o+l given 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 pbyk,k8.r,auy2cy apehk()* $m_A$ = 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 part+s)hmrc*pyz5ffak de yc,+z)1 z z:w7icle and a smaller nucly:z *awefr z1zk)z7,ysmc dp cf h+5)+eus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an anglgja;ax9mnyg f:n6 l xiz +rai,pq1wp:qp6 +26e 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 slid eb :-.uuzpw ttzaae2).)qh7r es 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 e/w 3be4p o;iqit is to rebound from M, slide up the incline, stop, slide down the incline, b 4e;ip/ 3qewoand collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slio)2e o 7agtvk4ngshot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Suv) k7ae4o2 togn) 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