We claim that momentum is conserved, yet most moving objects eventualle r(qe1y;1 jdb(g9ov vy slow down(1 bqr y(gv9d;ove1je and stop. Explain.

When a person jumps from a tree to the ground, what ha:mv;ar*kqoutr;l -5 l ppens to the momentum of the person upon striking thua5l: rq vlor;; -m*kte ground?

When you release an inflated but untiexxbedn u2fxk0b*0f. x+g :m 9ud balloon, why does it fly across the room2.u mxd:9nb0 + xg 0fxkxebu*f?

It is said that in ancient times a rich man with a b zbt j0g7sf ms3a- o/ n(euabi(,:6twmag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himsel oz:t -gs3b(jw6m0eb,s fam/an7 tui( f to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space:h vgrq2rj2; ,ptpm+-- pda8,sxkki x and is essentially in a vacuum? a rg-:ipkx;rpk,stpvqd2 -m+jx 2h8,

According to Eq. 7–5, the longer the impacteontfb9* ys0( time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the obje9yeon ft0*s( bct 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, twird .,r,wbuhr oz,d1/(k6x e.r os/yo:d uk2hough, cars are designed to have “crumple zones” that collapse upon impact. Whou6e k/d,yw k:b. xwus ,d2d1.r,z irrh(/oorat is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in the air xd602g ,r x y:akd.w/nr/3aoahty ng, by the battya/ yn a3 r,h oxwx0r,ndt.d26a ggk/:er?

Is it possible for an object to receive a larger impulse from a small forzvc/cb; .: txl-1f izlce than from a large force? Exp- ;.zflcibv/x zl1t :clain.

A light object and a heavy object have the same kinetic ene9hm q- pp8b9kk7v:ckp rgy. Which has the greater m87p-kb kmc9vk9:pp q homentum? Explain.

Describe a collision in which all kinetic energy is b5ln0 ru0l*qp lost.

At a hydroelectric power plant, water is directed at high speed against turbine 6 cn+,gfr i qqeiefket4pc0+7.m69sr uj 8hp ,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 a dead stop, or so that the water rebouh7se g.kpf68q, 9,qe ir c+ufi6 n+0cpmetr4jnds?

A squash ball hits a wall at a 8t3m ( e5 twl) hg,.mqdcs3qrl45 $^{\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 jy*bx8xc kyvl8);bt ;from a height h onto a hard steel plate (fixed to the Earth), from which it;xy;jv88 cly bk )*bxt 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 falls and sticks to the steel plate.

Why do you tend to lean backward when carriknehw 7z nt7 j/j9hzxv 6(l40ying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, wheree2)wea a90mly8hadq k2s)rg4 as this is not true for your arm or hw2)arska2 0qe y g8)elma9d 4leg?

Show on a diagram how your CM shifts when t90e:tc pg4r(w/+b i5y cj dbtw,8omcyou change from a lying position to a sicg9mtoi+08/e( 4:5rwb p c ytj,wt dbctting position.

If only an external force can change the momentum of the center of mass of an- yz iy*bta6o6 object, how can the internal force of an engine accez6-oatibyy* 6 lerate a car?

A rocket following a parabolic path through the air suddenly explodes into oc/s5o:8sb v8h pesbw30gsd.many pieces. What can you say about thd sghsp5s ev38c os o.0/w8bb:e motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying witq/5hoe xlje:7s.qz 1f h a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction for9dvq xw)j1y*:up)l kg 470zuaokrvf4 ce of 25 N acts on a 65-kg skier for 20 s. What is the skier’s change in velo p0w*vxy uougakz d:l4)rq7) 4fk9j1vcity?    m/s

  A 0.145-kg baseball pitched anzseig/ ,:l.75kofc +9v pxhgt 39 m/s is hit on a horizontal line drive straight back toward the pitche.,k il5onspzvcfh:7 g+ ex/g 9r at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a f1i mjbm/wy450dmgc .6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the chw.m0 1cfj/b45 gmdy imild 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 exerted on a rocket, given that the propelli4;pp:zh9xpz/3b hyqtng gases are expelled at a: hp ;x4hzzbq9tp/3 py rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving ae98:+quuj ennkhei9 (t $4.1 \; m/s$ 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 travels alone oocro787e lbepq2vd n0n: 6kmc1 h+9epn alevel frictionless track with a constant s:h7e qdm7 n8ol0e2p eb+9c1pknr6 co vpeed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelinyg 8v owjd41o6aw6;hdmst0 n w( hxh36g 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 10h ,/u+ v9 lcdg5cbs*oc0km/h If the air strikes a person at the raco dcs*9h c+5 g,ubl/vte of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m 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 constanty)l-,odxybxjg:ni/0 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 t:xi 0n/)by x,ygldjo- racks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus inizk.pf *1nv+j*uy0zl lp0 o-av tially moving at 420m/s emits an alpha particle in the direction of its velocity, and theylk 0 01+u j*.*zpozvv-naflp 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 b bl,;o 5saxr)nlock 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 emsab5 r x,;o)nlerges?    m/s

  A 975-kg two-stage rocket-iv( vajr- n62 rauy 2hav:vr2 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 og-s ,y:py :hhwuter space with a velocity of 115m/s T,hypw:ys g :-ho alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed obqx,bczq ;)4n 55z xtubttm9qn28 j -uf 45m/s The golf club was in ;9b nc82x5b,z4 mqtjuqutz)q tbn 5x -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 strikbej:dc4j6 rx3 h +(tjxes a nail at 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 thcrb :ht(4e x+jd6j3xj e nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and spee b7bup*j8mvb -:ih *yud v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge wzj 5 ah w20:;x )ucxnu3kosyt9wk,fhmf131 x of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new modfa wykjho31n:m;9wux53,) w0f2 zkt 1 sxcxuhel of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the 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 8im(lu . 2sijoqm.wt+in 0.75 s by a head-on tackle by a tackler running due west. Cal8 w2+u. il.ijq smo(mtculate
(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 d) c- zwcqsihvg i5m:zu- 4xn6u1i2y 6oirection and is given by the graph of Fig. 7–3gziqz v c- -165wuy46nxocsh im:u i)23 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 juz*e 8oc. m6erbmp 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 strength (force per unit area) of bone 6o8zbe *cr em.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 onus-rn 7 s p-,h8og(tvf collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent thev rsh,-o(pu-gs7 tn8n 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 eastfaaff1 (t,dtay w 225t 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 aftedtt,5ftfa f 22a1a(wyr 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 eqt ,p mkhuzu+:jtri/0 +ual mass undergo 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 mh+ p 0 +rk/:utj,timuzoving 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 2.5m/s collides head-on witht 1e mmt96gq,fq)4ebe 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 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')t4qe,qmb e9 tf1gme6 $_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s xa655 /o qajsx(+twa kcollides head-on and elastically with another ball initially at rest. Afterward the inco5wkaaqajx s+5 (/x6 toming 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 amusemedq 2yv bqz,)9kqy2.k knt park ride collide elastically as one approaches the 9,k2vkky2zyqbq q. d) other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving 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 /m)q9pq*: vfg8tlfb lmakes an elastic head-on collision with a second ball initially at rest. The second ball moves off tb9 *8):ff q/lqvmgplwith 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 incline as sh/cka- db zi-slzs b89-own in Fig. 7–35, and elastically strikes another cube at the bottom 8/-bsbcl-z iszkd-9a that is only one-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 1cqnfn5 aa+r k9th1o2object 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 results in a max(4cbf6 a.kr yiimum height h of the pendulum equal to 2.6 cm. A second projectile causec ib4r.(yakf6 s 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/st ze b. -zvgik/0:k*qi buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, e*bziitq/z-.k gk 0:vwhich makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinec ed qujrbamx.2 *j4.3tic 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 rs6p hx6wrbz9w7 l6u fz.l3x(z est, 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 acqlp w 6hubf.l zwx67z (39xszr6uire? (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 re0lt 75d;ce*jsl aw:rsar 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 was7rwe ss td:;c5 all*j0 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 rebounds to a height of 1.20 m. A, d dsxx9xy6o8pproximately how many rebounds will the bsx9xx 6od,dy8 all make before losing 90% of its energy?   

A measure of inelasticity i;,s+5abvb y .+r 3fqqovcm x2pn a head-on collision of two objects is the coefficient 3yoc .vxa qvq;mbsprf2 b,5++of restitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two k(my4s+wfwfbp/ 2 o3 sjk/0o lpieces, 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 r/okj 2yp/+mlwsf0w 3sok4 b( feassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides h7yhsgp* v,ypl9p4 0qms/t s:nead-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass s: 9lyv4 qt0/ 7h *pmngppssy,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 secondfrb 2abn1q sj d(s) z)t);ztqi-dhz+9 nucleus, an electron, and a neutrino. The )ab2z+r)zqbdh qst 1j9( fsn)-i z t;delectron and 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 dw:v liv4o c-xse ri jbd( :/vi4,aq0+$m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equal massd0 r k4fo- ofumow6j 72tpkj*;v3uoq0, each having initial speed the two move off together with speed v/3 What was the angle between their 42mf*jup-0v0q rkduftok3 o6o;j7ow initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at ridra)d)x 7 fmzik2kxe*4/ -*p :nkuyq ught angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2r/d4)7dkex2 )*fa iuuz :*-ky pxnqkmm/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with another atom at res l/hrku/knu)u z)65av t. After the impact, the neon atom travels awayha)/ ku5 )ku/ulnr v6z 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 elastic collision with another ato3amqz3)ur :n yp mi/m;m at rest. After the impact m3mr3 /:pzymqa);niu, 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 shown in Fig. 7–38. Specify relb:w or3ilk2j.;2s pslz/fhxv ;95gz y ative to the lef .ol;: hlpi/9sgrz2swzf v;32jx5by k t-hand 1.00-kg mass.    m

  The distance between a carbon at/u9xd1kqswxb .vuo ;;om ($m_{\mathrm{C}}=12\mathrm{u}$) 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 the car. How far frcbq:39bvxj :rom the front of the car will the CM be when two people sit in the fron9: xbqbcr: jv3t 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 kg, is usec e,e5 mqz55 kaefq/d1d as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the C e5ce,q5/q51 akmfd zeM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

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

  A (lightweight) pallet has a load of identical cases of tomato paste (see Fig. xby( 7a q0afso7- r6m7jw-mvy 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the cr7v0as o y mfj7 6bamw7-yqr-x(ane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plf1 - 0c72 /yhwsg9v1zvs4 ruobhbwk8date 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.v1hsvw c 0us d49w8/ bgkbzrh2f7-o1y What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions3,bbyl x3 t9 leg(4hcp are the same as those in Table 7–1, and calculate the mas,p lbcxbl3h39e( y4 gts of one of your legs.    kg

  Determine the CM of an outs - fxmvarqt-ljce(d*we0p0; 5tretched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm6i0xccs6 b 0r hgbhaz+d:u7f0 bent at a right angle. Assume that the person d0chf6b+r7: x0ciu sga6bh0 zis 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is i1uwj.6k :w*y04mids)vl gvk+a y qz gb*6som1n a position such that his arms and legs are hanging vertically, and v6gm6. : og0qay1kwi d)+bj1svs4 zw*km* lyu 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 body? Use Table 7–1.

The masses of the Earth and Moon a*yrty6x)v 6 i ks1ywn4re $5.98\times10^{24}$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 x3x k syhx1g+pus+/* bfrictionless 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 head of mass 2.00 kg and a diameter :xvjpibn(6pf+ a.g8 h 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of thgjavp bn.h8 6 fp(+i:xe handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a unitem2qyu9o2 grzebb- d;74+u): sp fjnform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–47fe ;rpez) o4 2n mjubq-9 +:usgby2dt2. 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 71j 0puzyr3 g2 re5*xyr–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 gondola, of mass M, are in gi0x)-d2ilu+ jc )caui1.-r jfi 3xdlthe air and stationary with respect to the ground. A passenger, o.3xjfui) ug- aj-i2dil d1 )+lcxci0rf 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 if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat axe2i kf4t5k, n(q gw*knd 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 t gnk,f2 x(i5w*t4k ekqhe contact.    $^{\circ} $

  A rocket of mass m traveling w,mu2j,d x 6:dnn: xxjmkmn79t ith 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 faced wiub:x r bdn5r+hh3w 8;8ya;rzdth 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 a pocket? Give 8r3rxb58:badr ;+u;z yhwdh n details.

  A 140-kg astronaut (including smmm0bsfsedl6, 7vs *ocnyzg9z+w; 09pace suit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-kg space ca cbs6fmon*0+dzw gmyv9m;e,zl07s s9 psule.
(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 initiaeht361dqg7b3 t cj,prlly at rest in outer space. They then push each other apart. How far apart are they when tgqd,3retjb6 71c3h pthe lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-zwa c 5vm zzhyp)8wp*3m-9kh5on elastic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original spem z5ch-3 yp)*wv58p9 hmaw zzked. 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 aqj48fn g -w8bin a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes q8bw4jn g8fa-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 stevc bh,/u(5 j1o:xpaqc0.brp jzv+ 7dlps 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 are perfectly elastic, what is the bounce height on the fourth bounce when the ba:/ajc d.bv7v+c0r 1b,zj5pqhoul(xp ll reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest dx6;s9x7qbwo 5:hivh rirectly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how :shh rwq6;xiv x9b7o5high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.s g6iq7rux xo+hu7: 0k35-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 theg0hq+xxo6 7ku sriu7 : 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 lvg4my. z:px3 and the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two pg pmzl:.y4 xv3eople, 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 lkwv3xjd e2wh 0(y,:fwas 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 ap ar7lxecn2wc;r fus fq21*5j9art into two fragments by an explosion. One fragment acquires twice the kinetic fjlc92q nf1ea*w r;x725r scuenergy of the other. What is the ratio of their masses?   

  The force on a bullet iskrwr/ wvrpj kl)kcq):84 :y4t 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 masses8;b7(vo31eigg bv bg.4njn e e)a d0rk $m_A$ = 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 d n*i8 lxphv)k9ecays radioactively into an alpha particle and a smaller nucleus. What win*9klx )h vip8ll 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 a.)qksmf8: bl at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides ;vmatq( f8, mgr pa6d6down 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), wh7 i )amvl0ra aim2:6/,yjnbxd2q ;jonat is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and )byolqm rn;d0j ai2x7mn/2 aavj,i:6 collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn moving 4h2++k crzrlj in the negative x direction at its orbital speed (with respect to the Sun) of 9.6kmr jlck24zr+ h+/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