We claim that momentum is conserved, yet most moving objects ersz9l4l szgu +1bh4 9wventually slow down anz+ 44rulzsshbwg9 1 l9d stop. Explain.

When a person jumps from a tree to the ground, what happens to the kmyr s( g0mxa6qitz;3ibj).)h(0cea momentum of the person iqh63axc .(); izm(grebm0kja0t s)yupon striking the ground?

When you release an inflated but untied balloon, why does it fly across th) nagnv1.4t 5pdq9 / mqtgfkc:e room?gmct4 q)d /:v159 tfna pq.gnk

It is said that in ancient times a rich man with a bag of go;n13c jchg)g rld coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himselfrj ;ch 3gng1c) to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change di*visd +q 0k,zf3 gzde7rection when it is far out in space and is essentially in a vacuum 0+d7z f,kqvd*sz3gei ?

According to Eq. 7–5, thdq44 pc+z 1 gpsz;)ffje longer the impact time of an impulse, the smaller the force can be for the s4scp;qj41pf)gzdz f +ame momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. To;b*a (:*cck4 cq+lmxi g7wegop5 *agfday, though, cars are designed to have “crumple zones” that collapse upon io*akg xwpb*g;5(f ca cq7m:*e4lcg+ impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball furthejs+vj))m.xxal ; jbr 0r than a ball tossed in the air by the battjj.l0jxbs; + vmr))a xer?

Is it possible for an oea5)x) zb*nhly8c)l r bject to receive a larger impulse from a small force than from a large force? Explain cx)lzy8)*) hr5nelb a.

A light object and a heavy object have thwi.; i ,.fohkye same kinetic energy. Which has the greater mome. hif yi;o,k.wntum? Explain.

Describe a collision in which all kinetic energy is lt4e ou*;y dg vw81,0w5kelturost.

At a hydroelectric power plant,(,5eolaj mvuam* 5gh3 water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbin l5(ogmv5m eja*3au h,e 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 at e+/9l7b s i8i,+mk;c.wznt .jhgtk5l xdm(ika 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard sh97*b y;pwudek g/nf yap96a0teel 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) /06p;*k9 ybwhf n 7pdaa9ugy eIf 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 carrying a heavy load in87kyb p kk(;wxjz; )9t)bxedm your arms?

Why is the CM of a 1-m length of pipe at its89jko8ci xl0w mid-point, whereas this is not true for your arm o kioxjw8c809lr leg?

Show on a diagram how your CM shifts when you change from a lyi /n8rtrgf*gl)ci z,.fng position to a sitti,tnc)rz fg 8/.*r lifgng position.

If only an external force can chan0l4rpd/x7wtx nij1k 5ge the momentum of the center of mass of an object, 1xx tdjl ip075wk/nr4 how can the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes into ma pnd0xigf ; gbonk5:zhr;y1y5 c(6xc+ny pieces. Wp(g hcc6 10n5 byx+5y:rzo;kindf;xghat can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparr p;/rps7s1n kjuiap )-ow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for hx hm;y44n*rcqwnox ;rt:8 d;20 s. What is the skier’s cha4 cn*wx dh ;rnxm;t:48yr;hqonge in velocity?    m/s

  A 0.145-kg baseball r7q 5i9la0go5oqw zic/) lj2 o)ea f9dpitched at 39 m/s is hit on a horizontal line drive straight back toward thegqz2)j d0)5fc 9iiwa7/ reoolol9q5a pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg sz px.--.befrk ceu 12package 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 child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance.ubxfp-2.rcsze-. k e1 The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, give 7o2ob(n w3hcm o*bjyka85ccv, y3c9wn that the propelling gases are expelled at a rateb ocy k,n w3j *hoaccom93 v2b(wc5y78 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 movinp pfd:bmgfo*c(atz + 42ex;8v /txug2g at $4.1 \; m/s$ 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 travelsm,4t*3xnbhj,bf c ywjr,6fq2tv f*9x alone on alevel frictionless track with a constant speed of 18m/s A 5350-fvnwb fj ,,b ,3q6m x 2jtyh4t9xc*f*rkg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling a (k rgz+5k*dpho3d si0q(yj b4t $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of 100km/h Ifx+ ).lq deekyro 7(tk4 the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the.y4 rqx7kee+t() dkl o 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 p: bh+ 5lb6fv9,wwf l 4jp;pp dcc/s;awith a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate : fbal/+4vb6jfhpwcdps pl9,w; cp; 5of 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 initially movqrv:b53ub *ucrwb1 n-h -e. kxing at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleu*r bn b chuuqk:v-x-re. 153wbs 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 penetxbu0v) tth/; jrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast b/vt) ;xtjuh0 does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a sp5 mu dlh4)x 2sdc ylkog0uk*2,eed 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 traves-)8 4c;un-7y ozazm 9mpcqpdling in outer space with a velocity of 115m/s To alter its course by 35.0macu7msyo)-9p zc- 8dq ; npz4 $^{\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 hk.5 uj l9del(kg is hit off the tee at a speed of 45m/s The golf club was in contact wiu k59e(l. lhdjth 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 hu3pd04x/knoy9x/aq m /cw 9wvelocity of 8.5m/s and comes to rest in a time interval of 8.0 p0n/ w4dkxou mx hcywq/a 99/3ms. (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+.6 ys25wn(mplofw xt speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the: run*+sl zrk; crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of ma*;lz rk rsun:+ss 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 a.wcu3gn :t : (pmahh8mnd is stopped in 0.75 s by a head-on.nct( u pmwahhm: 8g:3 tackle by a tackler 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 yw*0h bdoa+t bep0fq*e v.z,;(mass 0.060 kg) points in the +x direction and is givene;tf+pwhzboda0ye ** 0b. q,v by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump witbo e)m qd8:psbzvv*z)m: 90qk g 7lfw:hout 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 unidqleqbb97w0 :f):m* k:gzvo)sz8pv mt 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 h /oy9kp*ajl 7 b0(akjmoving east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collisb9o j/0 ljy kh*pkaa7(ion is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-onil/ k+ws+p zexua)f7, 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 after the collisio+ +f)i7e, u kzs/xawlpn?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 elastic he2/m mo+s i.vn7e:ry maad-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in t7:ayminm. /smo r+e v2he 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 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 w9 64tfkiuidt v)u+,x iith a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after theitv6 4udf,9+it)k i ux 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/*-;p v-d pwse f2pj2tds collides head-on and eladwdpp-2stpf e-2 j* v;stically with another 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 pa0 v6-ga ,iv0 hlkgmm,p/dir g9rk ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of kg,/h9 6m00lpiiggvv-adrm , 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a sec wioljr f a*;3kz9o,g; rvpi63ond ball initially at rest. The second ball mojw;*, o pg;ivlk3ri 6 3aozf9rves 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 slide-chfg qr0qzk w u-53o2s 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 905okq -wg 2fq03-rhu cz 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 abo1 7lv(mka id0bbk1 7n 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, projsj 47;k0bofj(l+fj1)y zm(spn.g dyj ectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the penduky.mobp)jdjjj f(( l 07 nf1ysgs;4+zlum 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 pendul 4xjcbf -7vv7yorqn/ qgi;()kum hanging on a 2.8-m-long string, which 7(b;xy-v 7qn )q /4kgvifjrcomakes 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 kinetic energy lost, 8p0w2 8nhqhpfeysr0:1j0ubj;w kt. l $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion break)iu:d byq4bc9s an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were rel:icd4u)yb 9qb eased in the 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 cozgeb7d 23q a8wllides into the rear 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 tir e7b az2wg8d3qes 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 rebounds unvmj00: wt u)to a height of 1.20 m. Approximately how many rebounds will the ball mj:uwvn0 m 0t)uake before losing 90% of its energy?   

A measure of inelasticity in ai w*l;o6fk9 0t hwfby: head-on collision of two objects is the coefficient of restitution, e, definewfo k*t6wiy:9l ;0hfb d 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 bu:7svc sioywaklz85+s3;o) e/.8u xvcex4m 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 lcelcs 8+mae. sw7 ovsvxuz iy8o) 5;/kx4:ub3it. 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 collidep3*otq3crw 0s s head-on with a 10.0-k*q 3ps3tr owc0g object moving in the -x direction at 4m/s Find 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 electron, an(xn* uw+7uhu8 gzb*rzd a neutrino. The electxuzh*(ngrb u7z*8 +wuron 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 m(iv-2v xc-oe aass $m_\mathrm{A}=0.400$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 collisi6ypfdo yp*)o(*ivg l1 :p buy3on 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 initi6)(1yio3ppy vdl*:b ofp* guy al directions?    $^{\circ} $

  Two billiard balls of equal mass move at right anglesoc3m ec;mw4lkf 7 if4+ez3u)t3rnn ;k 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 movin m4kzioeu c3te;3mw) n+nl 4;7kf3cf rg 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 anothet7yyi6txos/ 0z2edny.z-r .x r atom at rest. Axo/zi z.d.rttyn76xy s0 ye-2 fter 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 perfectly elasticw vuaq68rq :y-.sng- ,vok 3c,:px wjt collision with another atom at rest. After the impact, the neon atomq:o 3r kqu,wxtjp:6v nsw,ac-8-y.vg 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. 7–3 uaa35 dm6xlva s08xlrb526d s8. Specify relative to the left-hand 1.00-kg mass d 5sx d0aamlua2v65b3sl r86x.    m

  The distance between a carbon lhft lh1pw:5 -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 the front of thd7 (y2220hsrpga1n0qyb q aeze 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 oz21e0by2qhq0y(pag r2 a7sd n f 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a ferryboatl mh ,0eo2kyyd -:*ebw. If three ca,* -yobh0kmelw edy2: rs, 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 sideyqvm), 8-k lqyt uteft0f- xz69 ,yu/as $l_0$,$2l_0$, 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 ident).b)bd e6cyje nc89tg ical 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 ) dgbec)t9 .cbn 8e6jycrane 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(2mly 1.q(w6zusu0g uwt*xop cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the cent0x12ozu mwpuyl( tqusw.*(g6 er of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as th/b ,fv+.vgjal ose in Table 7–1, and calculate the /.fl,g+j bvav mass of one of your legs.    kg

  Determine the CM of an outstretched arm using Table 7 3a b5.cmyhx.j–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent at a rigl8om )3akmkux,l2ad 8 di )lh6ht angle. Assume that t)umdi 3 8oh8x)ld,k62lla kmahe person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hanging vjc*. k-2fmjc ww h7lk,ertically, 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 body? Use Table 7–1m .kw 2fj c,hjlw7kc*-.

The masses of the Earth an7vhq4eaw, w,m-r tjgu7 )atq /d 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 frictiond9f;3rfnnd5/ii bovv, qq vr0 d1 35mxless 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 ; 1mfn ee/rwn7c3w9j uh7h- f3eju1dzhead of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed,1 u7/3ne hz9mwee1j -;fru 7ncwjfh 3d 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 zh (;9afoetge4p 8/p9c mv a1ca uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500zhea98 ; (m1 optcp94/evfgca 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 (Fig. 7–29)jrf:g59ry/h j ( xo4tk, $m_{II}$=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 8j;b 8gaoalw-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 balag88l o;ja-wb loon. 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 and is popped stravbuuuhew- 1 0,c tf(8tight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the baf-t8hv( te uwuc1b,u 0ll during the contact.    $^{\circ} $

  A rocket of mass m traveling w,0dd2trk p9o zith 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 with the corner pocket shot shown in Fey p0/x;p(lnixx -p g,ig. 7–43. Relative dimensions are also shown. Should the player be worried about thgy x nx,x(- /;ilpe0ppis being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) l6:kb-d og(encr oz+-acquires a speed of 2.5m/s by pushing -b6g z-len(+rod:ok c off with his legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are initial2 63b..q yx2irpuxpar+a boit .*e;kf ly at rest in outer space. They then push each 6qt ruxef .2i.*pkabx2ra.yoi +;p 3bother 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 coll18 wyh9czr dwaxsa0 69ision with a second ball (at rest) and rebounds in the opposite direction with a speedz6w hrd0wa x8cay91s9 equal 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 court case iaut1le-8-x u -fnn: q4bh3 mn2peb)n qnvolving an automobile accident. The accident involved car A of mass 190unue -2xq4qnb pn bem-:83f-l1 )a nht0 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the tos8j/c81*xzenv, xiv(khxnr 4 p of a flight of concrete steps of total vertical height 4.00 m. The bxxnvhs(v8jri8/ k n*z, 41excall hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kgm6h1 sj:l7d-unx/-ncq 6e lya 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 6j al xn/d:h7c-nsu em1-lyq6after the bullet becomes embedded in it?    m

  A 25-g bullet strikes 1yqbedbotk.x4c a qtu jg3) 717pu57h and becomes 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 it comes to rest, what was the muzzle speed of the bullet 1 ugh1eb 3b .dtu7)757joqt 4xcakqyp?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit 7tou; z4w a(9sa 1aqvmw:vy5ain a rowboat of mass 80 kg. With the boat initially at rest, the two pewz9mv(t:74woayv5qu1 a aas ;ople, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abtr wjcxeqe17,nx(8qk( y,g5y out $ 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 fragments by an explosi f,;9uhjq,p jpon. One fragment acquires twice the; hjpq u9,f,jp kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 58oqu11g*jvf vd5gb 1s0 lm 1pd2iv;jm40-( $1.8 \times10^{ 5}$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(mxs qv6idrt1cy d5:,pn,3fp $m_A$ = 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 radiov c 2sdvc:p8c*a xw:1iactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the spva*p1wscx2 i :8d:ccv eed 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)tuy-lvc,3 :4dl9 irj.jo 1yca 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 jtzmfp/17o69gv m u/)5/puqsycr;qb 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), what is the upper limit on mass m if it is to reb,3wfpm-wr 8 2lysu(jhty:*u gound from M, slide up th,ph(j*lt2f8sry3ww: mgu-uy e incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet S6n 8v0 ulxv e2e0k5hu,d may(ruz- 8ouaturn moving in the n0run v6, (lko 2ye8xuavu8z-h0um5 de egative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s