We claim that momentum is conserved, yet most moving)ddf1wdm1n;djl5 j6v objects eventually slow down and5ndlfd wvjj6)m d;d11 stop. Explain.

When a person jumps from axzm: y.kso,w af :;:6l4iyi/nlvtn4c tree to the ground, what happens to the momentum of the person upon striking the ground:o;l 4 ivlf:sixmzn64ykw.n/act y :,?

When you release an inflat8uda 1ih 9bt(k 7plh2fed but untied balloon, why does it fly across the roomh17b(i 8f92dthkulap ?

It is said that in ancient times a rich man with a -jng9j- (8dhgwu +wqgbag of gold coins froze to death while stranded on a fu8jj(-w9d g+gwqhng-rozen lake. 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 dird o6:z0cod+/qjv1 jjrh p76f6)vjbz fection when it is far out in space and is essentially in a djjd 7 hvz1+or6 0jo )f6pqb6fvj:/czvacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller ta,m pql,gr*:,afh7 umhe force can be for the same momentum change, and hence the smaller the deformation of the object on which the forc,* paf,l,hq ug7:mrmae 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, tho-8) m 5gnxhq )4bbkbhxugh, cars are designed to have “crumple zones” that collapse upon impactbh m5b)g84 bkqxnh)-x . What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossedyv o6n9 ek;ihl ,tx58w in the air by th; x85t,9eilvwhk6n oy e batter?

Is it possible for an object to r.jca ns;rhazygk 0904 eceive a larger impulse from a small force than from a large force? Explaincga sjh.400zy;ankr9.

A light object and a heavy object have the same kinetic energy. Which has the ge+amj(0v3)xagp vdjxw77z7 i reater momentum? Exa(7wz0v 7 )mx3aje7xpg+vj diplain.

Describe a collision in wy;m:yrt:5qn hm1 j/ rchich all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high9n 5a8(og:k bzerwiutt 9p h 29sk2ir 4r*k,rc speed against turbine blades on an axle that turns an electric generator. For maximum power generation, sht9ir tc keh5pr*kkb2 gr, 4o i2w 899(:zunrasould 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 awid9jm50;gxq0 ly1kyi d ,; zwt a 45 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fix5 p d,uh7xlex-ed 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 5uxpl 7h,x-edmomentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to leaep4bav5w;g 4bmroo l;nrd46to 6e7o)n backward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at h 2 y+dkb2wh t+,w,b bb23anlpits mid-point, whereas this is not true for your arm or lby3 pah ,h2w2k,b+d2 n+tbwbleg?

Show on a diagram how your CM shifts when you change s a,wupk0g0mw81 ou t x.5mc3ufrom a lying position to a sitting posi,p w3ua u085toks0 mc1gmu. wxtion.

If only an external force can change the momentum of the center of mass ofy.6 - ghei)e:2ertio/cs kaghxn b -3; an object, how can the internal force of ancnisi6yb-t gh g r2-k)a3:ox.ee; /e h engine accelerate a car?

A rocket following a av*x-wuy0 h b4tfg*rk*/zs6 lparabolic path through the air suddenly explodes into many pieces. What can you say about the motion of this system syr*-t6 f blzgah u** v40xk/wof pieces?

  What is the magnitudvqzvyaog6: db 6mt-2 sux(37 ye of the momentum of a 28-g sparrow flying with a speed of 8.4 m/o2v u z6ds:-37bavtyyxgm6 (qs    $kg\;m/s$

  A constant friction force of 25 N . g 6zu .4o-;6woevisx5czgvfacts on a 65-kg skier for 20 s. What is the skier’s change u g4cx.z o5vezv-wig6fs ;6.oin velocity?    m/s

  A 0.145-kg baseball pitt bvox3et;zu(0w k -+gched at 39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time betwt+vb(xz u ;-0w3ktegoeen bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally wic:7zq bgnaa+:oe dc ww- g2*+wth a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, as :b:gazo7+c ew2qadc*g w+ nw-suming 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:vn6xcfw9-(9t xvb od, given that the propelling gases are expelled at a rate of 1500kg/s with a speed o9dton6v 9 wxcv-f x:b(f $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback movz48k/3iul)1x cpsb la.l6 nswing at 4.1m/s on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutuakz a bw. )1lnx/ul cl4s6pis38l speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frhh paq.;4sj, xs8ti +lictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be l+. 4 ;jtxphash8qs,ithe car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s stri3/0z.q y kup0 bop jterlw/8r6kes a second boxcar at rest. The two stick together and move off with a speed of 6m/s What is the /0e8u.0zq/krb 6 ltjy wppro3 mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speeds of 16lzs3 d81pq mn8ada f400km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.d f3d8q a8 6m4l1szpna50 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 alon)tmzeslq-+i exuh,x717 f 0nrg with a constant 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 the tracks, what is the spq 1zxl)uh,e7x mste7i f-r0 +need of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha kjf*j5f9 phopf*/ q;k particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle hasq h5kop*/*ff;f9j kpj 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 2nd. )f ,)lwx3o1pwopxmd)/ vh30m/s penetrates a 2.0-kg block of wood and emerges cleanly at 1.o)fhxwldmv,onp3))w/ dx1 p70m/s 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 rokkouvtd37jzy02f 9v:eyt wxtl e (825cket is traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer xa3s vyn0wp3r: .p5ebspace with a velocity of 115m/s To alter its course by 35.0 .xy :b 3 s5earwv0n3pp$^{\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/ rval z2rjco2pqt,w7lm )y19o ymp,3,s The golf club was iryolp q p ,2oratvcmm,9,y)lzw213 7jn contact 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 velocitnl64hddwz j o6zx(p*yfjtx 6+nm / 0ur;44swxy of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impuh6w j(zpldx ;j n6+f 0t*rm nw6/zodx44xus4ylse 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 strikes a wall atjjc: m3pk*z ip;y5tz) 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 theak-vwr x, yv32 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 ka -kx3rv, vy2wg 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 amp3l c*zm-*l 3r5 4y2k zjpsjht 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackl* mzry3m* sh lzkj4-j l5pcp23er running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points inm4 ,beq; jh qzcc))le( the +x direction and is given by the graph of Fig. 7–33 as a function of b jh4e)m);qc (ez,l cqtime. 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 personzh+kjgv arp9xbzt1v4lnp :) ud 1),9f 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 faf+z b:)u,1 4jkr1plzhpg9) nd9ax vtvll). 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 movaa)c5 cad *up5ing east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction 5ucdaa pa)5*cof 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 east with a speed of 3m/s has a head-on collision wi6-s) 4,sxvmg mde c2y7v do7xbth a 0.900-kg puck initially at rest. Assuming a perfectly elastic collis6gm) 2s cey7-xod4d,msvx7bvion, 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 undergol*o38 3grlah o a perfectly 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 will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positiv83* aorhl3log e 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 colqfm 2ds nwwq o m:d0,an0+:yikrdy8:9lides head-on with a 0.090-kg ball initially moving awayaof9i0 ydqkd+ w:m0w:nqdm,y8 2rs: n from it at a 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 is moving with a speed of 8.5m/s coll+d2qz.:vhlmp 7 am pd)ides head-on and elastically with another ball initially at rest. Afterward the incoming softd . la+m:dmvpqz7h2p )ball 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 amusemenrk g8/ rd/hy) wxv*+qqt park ride collide elastically as one approaches the other /k*y/8 vhq wrqrg) dx+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 e s-ojh(-h yo*tkqjgp* 2z: cxt.4 s*qezg-f6s lastic head-on collision with a second ball initially at rest. The second ball move.-s-o gs t*y(otgzq cjfq p*4ejhhs *6-xz2k: s off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless inclinej7b -cq7k ql)n as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one7jn-qb clk) q7-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 a7uh,(qdj3jca32 d a wmass 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 n 36 e8i)qwixnexperiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A 3nqxe )i68w nisecond 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 traveling 230m/s buries itself in a 3.6-kg penjc qah8-/xq2 v4zdz0 oa. m 5acouxc+58w /qnydulum 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 peaccj5xv 8wyzqm.o0z 5h/- / naxa c+2qod8uq 4ndulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fractio(y +awau 4fnq6n of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, i;dpf ni; /;hd+5jbsvanto 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 particle.nfa/ jp 5db;;+v;dih s ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rp1elhh lu)j* 5ear 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 bee j51)phllhu *fore 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 B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebon7j 1xus56wcmunds to a height of 1.20 m. Approximately how many rebounds will the ball make bemjn1 x7ucs65w fore losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two obj6qgl ;9-*l 6xdv. ey t 2irq1dtfjlj7yects is the coefficient of restitution, e, defin2g l l.-tqy1txvd 6r;fej6dij7l *9yqed 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 piece83z3q f65 +4z9cuqcrpm q ykiks, 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 explod+qk8 m65c 3fu q9cpqy4ik3r zzes, 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 d7 6g(-s qetutxx9sg 5zirection at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Findt5(sxzue 76sqt9gg - x 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 jx9yi.sq.rtf)ni 0r *6eklr2second nucleus, an electron, and a neutrino. The electron ar9.. r ntskr x yqflie2j6i)*0nd neutrino 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+nps f:(ssvz h9)i ql( $m_\mathrm{A}=0.400$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 colcgbgs+c m9of cy: /c64lision between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their ig6cs :mc94/cb+oc gyf nitial directions?    $^{\circ} $

  Two billiard balls of equal mass move at r+3+ 6bn. aq dqk9rrmogight 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 moving along ra qq9donkgm+3.rb 6+ 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 peg6emid pe5f:1k**ucn rfectly elastic collision with another atom at rest. k fu615g:* *pe enmcdiAfter the 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

  A neon atom (m=20u) makes a perfectlylvxi9 yn rk9oye0;+:l oye gny o4i6:7 elastic collision with another atom at rest. After the impact, oyn +96lvegii; 0xl: 947oyorkeny:y 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 system svc;4 (ets-q 4jlcggb b)k/pu4hown in Fig. 7–38. Specify relative to the left-handl c- s4/u(;)qb4c4gbk jtegvp 1.00-kg mass.    m

  The distance between a carbonif2g*+ntaa4sd(u - tfa;pcam7 2 d( hn atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind them sn 4zbdco2 v)t+w+5iojtj40 front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of )44vtoj 0 w+ mzjbtn2dso5c+ i70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, ig;,;dc.r sjg ds used as a ferryboat. If three cars,dgd;gjcs ;r ,. each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides 3chk4y 2 7anh4m frb.x$l_0$,$2l_0$, 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 ivj/l+.bn flc nb(,2ax dentical cases of 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 crane operator can pick up the xfb llb,ja+n (v2. /ncload without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cc v3jp70k k1klkt9ic3ut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig.c73k1pi 93cl jktkvk0 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proporti r-(.a di6fjs)a l+gx(c8wycfons are the same as those in Table 7–1, and calculate the mada(f+yax6(8.sl-c )w jg c irfss of one of your legs.    kg

  Determine the CM of an outsr 4ak6jkco/g) tretched 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 th)x*-i u6u kmjie CM of an arm bent at a right angle. Ak)iuuimx* -6jssume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that a0ah2gsay 9b g* zgz7-his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the bodyzggg ya*79a 2 za0h-sb? Use Table 7–1.

The masses of the Earth c) scnt8 bb7kp)fe4d; 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 frj0nah* n ts vqu/y-:o21 vmnj:ictionless 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 8qzb wcnu91f8uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted o8cn 9u f8z1wqbn 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 trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg9cg-8nx73gbhvrn dstvh9ne8f8 m j7 m8py p(0 and a diameter 0.0800 m mounted on v8h7jv9pfmg9x8b n-nd 8 g(03nhm ts8 cpeyr7a 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 trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fu lbam88;/ic zig. 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 gondo g8smau fqt 8z-2as)u7/8 djstla, 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 t)mt-ag7 u/sz8duq8 8afsj 2sif the passenger stops?

  An 0.145-kg baseball pitched horizontally at ky3o:;dtzhw o -+16(x wkvrfx 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 d-o t (yfk r+wdk:;6zo1x wv3hxuring the contact.    $^{\circ} $

  A rocket of mass m travem o(p,nb+xcd,p n//sn ling with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is fa3qfs, /3jzb wlced with 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,” in which the cue ball will also fall into w3l zsq3,bj f/a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires+x+i1ne .oiy)7iru23w ik7b:f7oywakbme8 u a speed of 2.5m/s by pushing off with his f:oi13 uu.imxkyboyarwi+7w + bn)7 ei2e 78k 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 xwq*iz: 9,;o 8- u hpaqd3go7 qc;rlmx60 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut hu*mx8 h3xic-oq r z;d :gw7oq,9a l;qpas moved 12 m?    m

  A ball of mass m makes m o*qkc35) ou y8dvhj,a head-on elastic collision with a second ball (at rest) and rebounds in the opposite direction with a speed eq8*vmydo jh 5uo3,cq k)ual to one-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 expert witness in a courtji-l xbo5 lht+8d. d+5 llfa7b case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before hef++xth.bod857j5 ail l-l l bd 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 tuhk,j3vh-72om zr/. n c+vouyhe top of a flight of concrete steps of total vertical height 4.00 m. The ball v zr/,v .ymku 23coj huon+7-hhits 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 verticadv0t-g/c1 vx9 p1zo1ww bv*;, clfsuc lly into a 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it? vs9 l -gbvp1*uzw1,v;c 0c1/ft dco xw   m

  A 25-g bullet strikes and becomes embedded in a 1.35-kby8kl3vt8(9,xfv zen s -9spyg 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 (st8yk39,vlz xv-nsf p8e9 y bthe 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 a rowf )bhhsd8 0)qfonw qv3-oz o-9boat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at oppow )fvo hb9oh-)-dnz q0f3oqs8site 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 abobo:),o f dh6 alo4vj, cac:+qxut $ 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 intc5sxae byk *4h lg c3;l0c78xuo two fragments by an explosion. One fragment acquires ycxc*34bklsg7xcl8 5a 0he;u twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bulle74ktw* ztg*s s bpi8e:t is 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 amb+rqgrv d. rn75d* 5$m_A$ = 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 smalb )cli,/nonvc jrf c;c.6+/f vler nucleuc,frc6v b/ ;+lc jn).icn o/fvs. 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,hljqspw. .0ei7k dg lh5a1/d/9b nyk target) is fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg e7xb6sph,o : y6ja2s08qx 6bb ej.dzu slides down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46+ed5 a 7nw *zhml*,xx8es1kdx (pvn.g ), what is the upper limit on mass m if it is to rebound from M, slide up the incline, stop,(dxe.hw * ,vx n pdzm1kls5n7axg+*e8 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 s4,(is,0*jb v p kim )shylai.k4h 1nqshows the planet Saturn moving in the negative x direction at its orbital speed (withks)4 mh,s *(vlnq ksay10ih 4,ijpb.i 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