We claim that moment iz58l :xvnqhkvful. a162i )ium is conserved, yet most moving objects eventually slow down and: h1 f ix8kqz l6vl.v25iuai)n stop. Explain.

When a person jumps from a tree to the ground, what happens to the momentumbgqwmb ,3 z/;u r+/ wsl8(ybmz of the person upon striking the gu mrsbm; y(zzw/w/ b8b3g,lq+ round?

When you release an inflated but untied balloon, whkpc inz1s4s v*1gis,vs8a 2 5oy does it fly across the room?1v8z noki psa4i,g*s1svsc2 5

It is said that in ancient times a rich man with a t.kmo;eh rwgj:tj )/ g h-7o k6*yptd.bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he hayje.g.g;:d /mjkt) r 6k7o-pt o h*htwve done to save himself had he not been so miserly?

How can a rocket change dire, 4hj ym5nfgx;ction when it is far out in space and is essentially in a vacuu yx5;hg4,mfnjm?

According to Eq. 7–5, the longer the impact time of an impulse, the smallewh bsb0; n mfk4addwk-52f/1jr the force can be for the same momentum change, and hence the smaller the deformation of the object on which th jad40 mfknkhfbws w1;/d-25b e 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 possiblesq) mdgzrns/ we, :f44sd q/l: to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is thw),/d4lenqsgfs /: dm4r: sqze advantage of this new design?

Why can a batter hit a pitched basebxl;5qib 4r/cx fu)s lu 4ses8(all further than a ball tossed in the air by)5e4ci;ussl 8 xrsbqf/u(4xl the batter?

Is it possible for an object to receive a larger impulse from a small force tuz y )b+ se,jio*:ih6)mn( xifhan from a lar*)+,6eh sm:i(z yij )ibxfnouge force? Explain.

A light object and a heavy object have the same kinetic energy. Which has tya w+cn:3wqb9he greater momentum?c+yqa :n9w3wb Explain.

Describe a collision in which all kinetic energy w86h9g(zdoki lhke++/tm ww5is lost.

At a hydroelectric power plant, water is directed at high speed 4 8b;g68jcay itdn5hb against turbine blades on an axle that turns an electric generator. For maxim6n;8g dy c8tj iab5b4hum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall a5n; klp 8q)yvmyy 6bo)t 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 (fsefeck-d k(7 +ixed 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 momendc-s7kfk(+ ee tum 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 in your vpma9j 8xy27f /i ual*arms?

Why is the CM of a 1-m length of pipe at its mid-point7uu9m- ujqsuvb chw6t /( 26cy, whereas this is not true for your m(7bcw c-h9ju/u6s6q2 u ytvu arm or leg?

Show on a diagram how your CM shifts when you change from a lying positiokgfrs7w.1xdm88 x. a mn to a siwgd r.8m1fam .sxk78xtting position.

If only an external force can chang8 13ve ymi8rawnv3 9mej1:ngy e the momentum of the center of mass of an object, how can the internal for arijy8nm39m1 y we3e1n8 gv:vce of an engine accelerate a car?

A rocket following a paa7* 2-s6 qfs ukmrfli5rabolic path through the air suddenly explodes into many pieces. What can you say abo5fqi u 7s- rslk*62afmut the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a spex,,.8ys jre2keon ti11f5or ded of 8.4 do,rr koj18t,1x2ise .f5ynem/s    $kg\;m/s$

  A constant friction force of 25 Nok)tq cn52/cva j** cf acts on a 65-kg skier for 20 s. What is the skier’s chang *nt ajc2*q 5vk)cfoc/e in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s iono c)*jb2l0tyiwi.2s hit on a horizontal line drive straight back toward the pitcher at 52mt n*b)yi i2 2jow.cl0o/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 package o ve:ei5oyf3vyob /r9 .ut horizontally with a speed of 10 m5 3yeo:9e vfovyi./ br/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. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propellw(yidp p,1v ;:*aizuying gases are expelled at a rate o:p;yvy ( uia,w1p z*dif 1500kg/s with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an apparent breakaway for a touchdown f6)y xwz,j1ex is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the samefewzxx)6jy1 , direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels aloneb.fhf0p+6 ( y*voe lu:a 0wuial h9kg5po9q:r on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What wil9gv9w(p : 0oa 65lloqu: .haf 0+ euy*fiprkbhl be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar aul*gy 2cfduh j9 0d z-ylt2m-u:h-i4st rest. The two stick together and move off huy*j u tgy-z-:2 f m90csld4dhul 2i-with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speeds of 100km/hu+ ;bep,fw j.ye+ dp:j If the ap:+wu+j.y dbpe, f; ejir 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 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 constant speed of 8.6m/s on a l q9r*cnk8e z5revel track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/mr 8rzken95q c*in Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits anefm6j 0;5:q lguj6 z)ec o/kgu(z)vxp alpha particle in the direction of its vmpjeqe0u fz z;kg)() l :vxj5ocg6u/6 elocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood nm4kq w+5uq)b and emerges cleanly at 170m/s If the block is stationary on a frictionless sw4)kn5 +qbmuq urface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at vh riyfwi4-)6a 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 31s 0dka6f)e8 f(vvs) qd80 kg is traveling in outer space with a velocity of 115m/s To alter its c 8f s evd0v(ks)f6adq)ourse 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 of 4(qd ;v: : yfbpfl/)- f.qlqbdk5m/s The golf club was in (kl)d -:v lf.bbffqq:dq /y;pcontact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes tm3 us2yl ;g:avhs+mm (o rest in a time interval of 8.0 ms. (a:v;+h(yl am 23umsmsg) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=1 0;swu2e 3vnb2:: gksvjr iba25m/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 crashworthiness od) 9+v9lt dhmlf new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the timel) 9m9dvt+h ld 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 running7myv *sv70qm3 l1yth q at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by* 3ts0m7l7mhqy 1qv yv 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 9v8bmya7ldv: (mass 0.060 kg) points in the +x directi 9:abdm7vvy8l on and is given 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 without breaking aep:;t; s8 s)a p6musdthe 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 is ed ssp ;saumt8) 6;pa:$170\times10^6\mathrm{~N/m^2}$ 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 movi5xt .f 9)mauvgth*)91ffqi o hng east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball afterg q)h 5m19txhu.9i*otf)fafv the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-on collision w z9+jmisqy a-czsh685tz 5 s9iith 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 collision?Let A represent the 0.450jai68s5m s5 qtsz- z+i9zhcy 9-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 yn5s:dte1 s896qh cbrelastic 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 col s q689bchrdnet: y1s5lision?(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 with a speed of 2.5m/s collides head-on with j1- bhl:irw7 sa 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 sil7h r-wbj1: after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of iad/ vf3 o+kg08.5m/s collides head-on and elastically gk/0 3vad +foiwith 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 elastically as one approa:.pl,*.,x pdcu fb pwhm.ksu/ches the 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 ca d u:hxl, .m.bucp,pk/.*fsp wr 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 zr (bb ,efsrr/v3 q6.kwith a second ball initiallybv/ frre( 6kz.3bqsr, at rest. The second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionl+anoew/fp8i8 ess incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its o/p8+wanif8e 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 of6itkecs-frj4:st ( x16wvc*0y o4 ywg 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 resuljjx3jg q4z/c5ts in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as highq3 45xcj j/zjg, $h_2=5.2\mathrm{cm}$ 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/xz*5 1hy ysa* 9(kv 1vfx5kel.aq)tgc s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which a15qs*15)xk9*(zh akfeyvg.l vt xy cmakes 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 th(yzjcw7f :*p:o )xxp de fraction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosio1x9me d (bxn1p)l8lmr 0d8 akgn 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 represent the lighter ela0m8k)9 (mxgd d bx pln81r1particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUqj,z )mgtkf9f67o +rqV 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 sgo79 r+ tq ffzm6jqk),ports 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 to a height of 1.20 m. A(e gn3oris* v7k 2k*wopproxigos* *wkv2 o3n7r(ekimately how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision :vkvk:) tr7 vvof two objects is the coefficient ovv tv7k:v:k r)f 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 pieces, one with three times l v/+72 o naqu7-)hcvhnzd) kxelk;;uthe mass of the other. A depression is made in both faces of the cut, sh7nh /qan-;k2lolu7cd k )z;+xue v)vo that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker 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 5.5+-ekuyx 33w5 a, **dlxa+mu0zr edg mxm/s collides head-on with a 10.0-kg object movinga3*+l w+-dxdeeux y,k5xrz 0 *mmua3g 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 se1k2z5c 5xn5aganil wwqb)+ xz( nh) 9gcond nucleus, an electron, and a neutrino. The electron and neutrino aria(5nbh ))w9+xk a5ql5 z1 gzncwg n2xe 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 ma 2woqfs :,f vgz /m-im26blaw.ss $m_\mathrm{A}=0.400$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 mass, (j2 oubi6y86)/* x81bu mjszpwub vzdeach having initial speed the two movewubpm ) 1u6 86*ozdbxyjj sv b(z28/iu off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the ,/zec )xj17ke eteqo2origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s ank7q)ee jzc1ox2 / ee,td 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 igqg(mz x/p;7mcd5u: atom at rest.ip :mg7(/g5 ucx;mzq d 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

  A neon atom (m=20u) makes a perfectly elastic collision with anotherpv/-zrbjz d(1y04j j w atom at res4djb p1j 0 w-z/r(yjvzt. 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 in Fig. 7qa,y mh6/. u vjd6am5yrk19co–38. Specify relative to the left-hand u91,y6y ov/. 65hqkcmjadmr a 1.00-kg mass.    m

  The distance between a ;)10rls*ubohmo e.ae -h b0 aacarbon 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 the car. Hofflnl7)e u w1ajo,t+,w 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 tajeo1t,)n,f lfu 7 w+lhe 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 used as a ferryboav5bb l4wbo /w(t. If three cars, each of m wl5( vobbb/w4ass 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 sidesgs8. 7i5w6 , ,hhepdm/z oohsq $l_0$,$2l_0$, 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 lo+j so)8 rx:xwlr)2w/wc2o hztad of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pic)tsc)wo jh/zr + xrwxw:282ol k up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a5rwi. k/c e,sz circular hole of radius R cut out of it. The center .,c eszwr5ki/ of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same a efti* g zh8g8l*hs(k5k1 d)iss those in Table 7–1, and calculate thehk *i(k88gzsd fe5ilsgh )1t* mass of one of your legs.    kg

  Determine the CM of an outstretched akqpgjah4 e-4x i e d50jub96;frm 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:yha l1 z7-owayskfz1al1h z8m uy;;3 the CM of an arm bent at a right angle. Assum1zyo;; wyus1l k8- maa 1zah z7y3h:fle that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position sy puh,e. : e3fk+x*tqmuch that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line t*e+.eu y khpt:qm,xf3he CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Ea.xrly q01 8zkyrth 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 bdx5u54 rnjm: frictionless 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 mk0yf-n cil . (d7mx8bgass 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 air, how far a7c-8 fb0k(ilgnyxd m.bove the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diameter 0gge 3og cnzc 8s+2;me5.0800 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 tocmc n2z ge e8sgo;g35+ssed, 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/, jfi5t7w0,ejjkxd k 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, qgmu;m1 t.1n oc*l 9kvof mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happensgt;lvnmcu1 omk 9 q.*1 if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a u1ymi)e ed18dnh5mt 9nua+k -zltzpy 2c5) 3tbat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average1km1a855imtyn9 y htldd3 -u) tncz+z2eu p)e force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with spees- u3v *itkgp(d $v_0$ 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 hn9pva7mh2m 4 shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “m2phh vma79n4scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by lm x*xu+5sag,pushing off with his legs from an 1800-kg space cap+ml ax,* xsu5gsule.
(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 mass5yi hx2kw6/j6 t*qelf 60 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut has movei2wex6/hjt 6lk* y f5qd 12 m?    m

  A ball of mass m makes ko60 ve b:jgu5a head-on elastic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What0: j5vegkb6uo 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 invp9ngvlh.h * oo5as.7 golving 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 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/g.h n vp*57.ohla9o sgh) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of tddo +*m:wyj*low -ami2o4* cootal vertical height 4.00 m. The ball hits four times on 2l4 owoai mwmy*dooj: c *d+-*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-kg bl)r9 iyoo,veg .ock of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes emb)o.gr i,o9e yvedded in it?    m

  A 25-g bullet strikes and becomes embedxzca.qn91o i* ++1 -psjhiqes ded 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 iianc +19+*-e s jzs q.oqxpi1ht comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowboat lo/xxjk8sz,.of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in whjsx lz,o8./xk at 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 wa) cyjbhx) h/ucuf+kp0 **:l nks 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 b-y5+d+ fg: cnj.s4 ,ozn6g*wb dzxvo sroken apart into two fragments by an explosion. Oned+yjzg.szv5 6 -dn,sg w+x:ooc4 *bnf fragment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet iyk:h4y6jw 8 uks 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 massesd(4;6y *qq3ep pn1 ;bzu o i;qwzovl6r $m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively inl ;n- zz+42hw npd.xl4d bkwoto0w /d4to an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particd4-wtolpkb;w+ x4ddo2 n/. nzw4zhl0 le 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 at0vmw8 1k3 bx7od krt-r (kal.y 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 slidew6lajpx v/ ;/jlvjz07s1d dvow .1zf 6s 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 rbncx sbw ocl 78:;+nm/ebound from M, slide up the incline, stop, slide down the incline,+/ bso8l cncn:mbx ;7w 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 pfy;x ;; ezy 4;66vmgj)echixas+a3u hlanet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) os hh iuc;+me 4xyge;;aay)zf 6;jv36xf 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