We claim that momentum is conserved, ye5f ewpwb y3tv8 vsu b5nt49m86t most moving objects eventually slow down t95n5bu8vyt8mewvf b 43 w6 spand stop. Explain.

When a person jumps from a tree to the ground, what happens tosh4y lqb4: lzpdn(2g0 the momentum of the person upon sdp:2bz (4 lq4nylg0shtriking the ground?

When you release an inflated but untied balloon, why does it ,czp8erx/ 3d i. -mulkfly across the room,/uk d8mpxr -e z.ic3l?

It is said that in ancient times a rich man with a bag of gold coins fx*v47u;xppakgv 1lvn;+ v 6d9jz 3buo roze to death while stranded on a frozen lake. Because the ice was frictionless, he could xu9v7vn; dg4 ;xu *pz+lkv136p ovjabnot push himself 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 out7 i ;8e-rowuet in space and is essentially in a vate 8io7-weu;rcuum?

According to Eq. 7–5, the longer the impact time of an impiumqbc+qa5 w9 sbndc0 +pw/*rl yp:q99fz8v0 ulse, the smaller the force can be for the same 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 infl8 b0*9 ru/z 50da+np vbqf: i9lqw9mcsw qyc+pate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Toj bg6yg8 a:-gvmrks1 9day, though, cars are designed to-sy g6:g9rba8gkj 1 vm have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a kyvrp4dzmqn1 ex 7j (*to 4d83pitched baseball further than a ball tossed in the air by the batto3pen kx1z7v ( y48dq*jr dtm4er?

Is it possible for an object to receive a larger im;oy7f haq3o qx:1ee (npulse from a small force than from a lao1 ohn:e efq(3 ;qxy7arge force? Explain.

A light object and a heavy objeceb2i (dp8ex8i (y wy,at have the same kinetic energy. Which has the greater momentum? Explain(ay8ex d(ew 8bi ,i2yp.

Describe a collision in which all kinetic energy is l frf7 q-m9kum,ost.

At a hydroelectric power plant, water is directed at h5i iv+* g;/s4ypf)ue or a;z6sjyhc5zigh speed against turbine blades on an axle that turns an electric generator. For maximum power generation/js zhyzy;iusf 6 ge)i*o+a5; rv4p5c, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a walnziq g5d 9gr0m:8bn*ik 8:gb .*kgapzl at 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 xkk0*k :w9*9rpugf,vrldxn7 (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Ansx l0 kru7,xw gn* pkrf:kv*d99wer 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 in your ar/uqpn nivl, -y jia.32zl 4s3zms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas thiqd:mycfcedbz(y 5 6.(ub *+ dis is not true for your arm or l*6.mcdf: cdbq+ d eyz5ybi(u(eg?

Show on a diagram how your CM shifts when you change from a wmmz 6r96 1mxhlying position to a sitting m9mmx6h16 z rwposition.

If only an external force can change the momentum pd 9+ j0jac+r8nar7q oof the center of mass of an object, how can the internal force of an engine accelerate a cpan8c++0o qd7arrjj9 ar?

A rocket following a parabolic path through the air suddenly explodes into many xy(k: ow obn448qnr7mpieces. What can you say about the motio(yrkomb 87x:4n 4nqown of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparroj a7g nxnt+/-vw flying with a speed of 8nvgn j/-a+7xt .4 m/s    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier dozlb n/*z3l 1:i a5ivfor 20 s. What is the skier’s change ilao/*z 3bildz5n 1 :vin velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is b4*vpf m-/i-4 -sp3 c qcdbuoohit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time between bat and bd/oc-sppub *ob 34vi fm-q-c 4all 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 with a speed of 8v:g9ppsjl/n 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 boatgsjpn/9v:8l p is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases a8a:yi-7t(rgm 8k fwmx re expelled at a rate of 1500kg/s mi 8x7yw- 8a(:tmkrf gwith a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/st;4 v0;oxl3k ktlnjf)i*+v li on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cllt3jo 0 ;xinkv;* tlv )4+kifornerback running at 5.5m/s in the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on a/62 qdqe ix.etl2lnm6level frictionless track with a constant speed of 18m/s A 5350-kg load,6qq22i/exmlte6d l n. initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar at rest. The iww+m0o-i j0) amnrbd5g) m+ xtwo stick together and move off with a speed of 6m/s What is the mass of the sec)wm +0x r0+w5 am d)-mbiniogjond car?    m/s

  During a Chicago storm, winds can whip horizont8w./wi sp* mw g1xcll.ally at speeds of 100km/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 0.50 m wide. Compare to the typi wx8s.wml/cw*ip. lg 1cal maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of 8.6m/s on arrh9) 8mp o)j vw.ep0a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the or 8hpwm0 )pe.9va) jrtracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particl 2 kl(9o;c9smk vi2w2lq t+qpve in the direction of its velocity, and the remaining nucleus slows to 350m/s If w92ivvcl km2k(sq ; pq92t+ lothe alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and exgz*g4;yuw (.5udb7rze ib9re - -cwu merges cleanly at 1-yzuc9(x7erd w*g-wb g.u 4be zr5u;i70m/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 rocket is traveling at a spz+jl,i 2 ee; giegh(f*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 traveling in outer sk3vr twvvzc .*.+dl(3pnofs/ pace with a velocity of 115m/s To alter its course b3sw*cr+fv (z/3tdvl.o np v. ky 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 sp mn)/ c(y: y1jhk9iaq1d jfc5yeed of 45m/s The golf club was in contact with the ) dc/y(q1yhjknyiamc59f1j: ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8 *f*b3z;cgfbqp. ks ,o.5m/s and comes to rest in a time interval of 8.0 ms. (a) What *.koq,*pfb scb;3fgz is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes a wall at a 45338yj;x)svulb u xhb z, yr09h $^{\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 crashworthiness of new- xlchd3us( 7i automobile models. Cars are tested by smashings-idl(7h 3 ucx them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in 0xa07wjtx.b i 6.75 s by a head-on tackle by a tackler running due 0ti76xx. wb jawest. 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 00:ian 710f eqjwx ld4n.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimxi n: w00lnea7f41qdjate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking the ;qsw :8:sat44j iozag 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 seategszjs: 8t4iqwoa :;4a d position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of collides hecqc ur*xr:y :0*a p/zdad-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and *q: /apyrrcu:x 0zd*c 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/n eewxc 4re4+-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elas4ewe e /xr4c+ntic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfe,;nd7ouvn qzcnv-k; 0 ctly 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 positive direction.Let B represent the ball movin;zqc onu , vn-;7dnk0vg 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 with sxvkwo) ux 9 :yzf;6uiy*bk8:a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are th8ik )9uysk6 zvy o;u*x:fxw:be 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 bjp-: n- b)tzois moving with a speed of 8.5m/s collides head-on -btpnzj)b: -oand elastically 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 park ride collide elasticq .p2./ mwkg q2nq0aagally as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kgwkq /g.qg man.22pq0a 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 sesaoi,2. hr1hjahb 7v +cond ball initially at rest. The second ball moves off b h2i7.+o, 1ahajvrhswith 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 szq*t :u,e, upelides down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom thaqtu u,,pz: *eet 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 object of masoca*om wt-6r. s 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, projectvl cgb elnoj2+58t 82oile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes l+lnot28oc2bg v5e8 jthe 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 travelindwomaww 7ngg8 mb:50 zdd .vvd/d,7j6g 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makezm ov g/ bdg 7j5dm,n:v8dw6waw7dd0 .s 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 kt mulysa9xl 5 c219ub -t4zlfxo(h+)zinetic 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 explosionn nra p78z j9:exvsw)e*i8j+i breaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B rjw+ 8iv:* e nn)i7xpz es98jraepresent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped at a ;x nuo+ma 0pk) v.sh.pred 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 i npkxm.)vs. +u0op;a hmpact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from .: qg:suo,fe*;5eka 9atbg pga height of 1.50 m and rebounds to a height of 1.20 m. Approximately how mans95q t*b:ggp,;eg.ue af oa: ky rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a heyg/uhzqol *(h5 )m- aqad-on collision of two objects is the coefficient of restitution, ea/h*)m 5z uyq-hgql(o, 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 piecetu-euq *gpm y+d7;v /gs, 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 reassem/mv -e7uug +d*g;y pqtbled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at a+,jmof2e hu2 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the ehm2o ,2auj+ ffinal 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 decayo;9*xib hi hyi 5+)cses into a second nucleus, an electron, and a neutrino. The electron*+h5;9icosii x ybh)e 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 mabrmriy 8 +bd)d5bhv b(35 yg*hss $m_\mathrm{A}=0.400$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 mapundo 3pc f6dw+u4.0e1w5 zvhss, each having initial udc+.4fv3wue op01dn6 hw 5zpspeed the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at rightfr a+1m ah56ki 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 a15+6 irfkmah 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) mao+1hcki n xzzc -/) mfuly3ju)odi4-2kes a perfectly elastic collision with another atom at rest. After the izdf)nx4mu3+ i-oy h2o)-1 kl i cju/zcmpact, 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 elastic collisioipgum.a r;5/m n with another atom at rest;/.p rg mm5iau. After 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

  Find the center of mass of the three-mass system shown iy,axz visz-fim, ,l :/n Fig. 7–38. Specify relative to the left-hand 1.00-kglvxm,zy ,,:a-i sz/fi mass.    m

  The distance between a carbon ato3jz0 2w 2mt7qjqt5n (3odk tjtm ($m_{\mathrm{C}}=12\mathrm{u}$) 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 /k9nmrf90 3ga,rooqqm behind the front of the car. How far from the front of rf3qq9 no/g k90oar, mthe car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, i3nwd f jw ai-*j,3xbsf*vb(1h s used as a ferryboat. If three cab3 wn ,d3vf*wjab 1x-*( fijhsrs, 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 +p3d8iasmxv7d)tv( o$l_0$,$2l_0$, 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 0z9 gfsdh-3l8cm7i kl .i(fiwgi-e. qtomato paste (see Fig. 7–40), each of which is a cube of length l. Find the clhg7cl-8i.zi wf qf- k309i is.med( genter of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circu4rd/jxh9 odi bg7 a3q9lar 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 circleb7qxg a 9jd34rd9/ iho, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those ikq0ez7dg 6 llc6aci4* n Table 7–1, and calculate the mass of one of your legs.aid4c e g6zc67 lq0l*k    kg

  Determine the CM of an outstret1deez,s vfu(kq 0;+uwched 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 arm,bwm pb.4nd/s bent at a right angle. Assume that the person is 155 cm /pb .,wd4n smbtall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are h7;zitv5 jm xwd;3s2 u(/n icbyanging vertically, and his trunk and head are horizontal, calculate how faz2sdj5n/7iu; 3bm xyc;wv i (tr 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 o9cuylc a0 p7r:ldh ,x.aym,. 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 fj xmnp 8a8q)-3s5f ibkrictionless 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 up6hy. op 1t0loa0 a9nof 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 t0y6otn0l.9 pu1apo ah ossed, 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 4 ga/as2 -wylg do*3yiezyn 45cylindrical 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. 7–42. If this mallet is tossed, spinning, into the airlgasd* 2- yg 5zwayy3on44e /i, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Examp adcx 8mf.:8:k my(-hav7hpdo xsay1 wfc: l14le 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air anfo p-m3.ex gjp 8(1x,ak5vqu pd 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 happe v-1 j(fpup qpkam ,o8.xx5g3ens if the passenger stops?

  An 0.145-kg baseball pitched horo cng6olr5) 7)vwcw )eizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contaccrogc6)vw)oew l) 7n5 t.    $^{\circ} $

  A rocket of mass m traveling wit (4ohl1dr (scet tww3jc/fing8 *:z:x h 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 Fig. 7eha-ig k k x9of/2 8nusby84:q–43. Relative dimensions are also shown. Shouxg9/84a n o8u2k:qey sb khi-fld the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (in9yzmjty4 ms l;yu :mxqqe 57w(r 7jf:9cluding space suit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-kg spacy(4 ez u9:my7mtjf7mjswrxy ql5; q9: e 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 inprl.sv3aow4j taziy 9 69 ;3gkitially at rest in outer space. They then push each other apart. How far apart are they when a o4jk; ya3i396wtz9 r lp.sgvthe lighter astronaut has moved 12 m?    m

  A ball of mass m makes a 6wju +frs4-rahead-on elastic collision with a second ball (at rest) and rebounds ufrrs- 64a+jw in the opposite direction with a speed 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 casehgx w7+ bee1dys3 +x *y 0ya.1ereob;j 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 he crashed into car B. After the collision, car A sy +g 1w o;0dh1by+e y je7xsr3bxeea.*lid 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 concre4k1m eyts( e-dte steps 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 mts d (4-eye1kthe ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest directly above/nke+y50 d tqmj1fql* it. If the bullet has a mass of 29.1tqnjlfme5* /+yq dk 00 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35- hug9cd,ch18j jl-2vd 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 distanc,ghh9l 2u18-cvjdj dce 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 miad-3avn1c l0o uo3-vass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends1uv on i-0avlocad3-3 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 abouq*xb 02kjmr 6vt $ 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 suddbzp*7 *rmnbzmra (h8 2enly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic ener*bh8bmrp(zan *72rzm gy of the other. What is the ratio of their masses?   

  The force on a bullet e g*l,nm3g px;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,un4k h4.;d sw1 qzwrr $m_A$ = 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 dtw 5 835-cxhk /ata*vtu.hakaecays radioactively into an alpha particle and a smaller nucleus. What will be the skv8 h3tawah ct/ *.a5t5k-axupeed 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 fire4kxkfwd/h:r* ynz4 z2p 2/h dgd 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 down a 30.0mtty130 h ;2d qhgg(5kh enng: $^{\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 i)* )8byu0t zqoz df+wut is to rebound from M, slide up the incline, stop, slide down the incline, and coll) o0bfzu dzw)uq 8y+*tide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. .: d :mt-trx:g-, zdb( uftfezFigure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to, .fzd--xzttu(df:temr:b:g 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