We claim that momentum is conserved, yet most hm24wv2 ft+n imoving objects eventually slow down and+2i4 wnfhv t2m stop. Explain.

When a person jumps from a tree to the ground, w*h(qdk k- 4zaf up5ibu.x-jiu5:j yc7hat happens to the momentum of the per5-4h xj bad-.f5k7uqyiuj*icu k :zp(son upon striking the ground?

When you release an inflated but untied balloon, w oih4nd6j2jc mjf0 z4;hy does it fly across the roomj2hi0jdjf4 z6 nm4o ;c?

It is said that in ancient 6a ,k hjxst13t.xide2times a rich man with a 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. Wh2hx3 stje16,dk tax.iat could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is essentially8+--tfqk didz9 7bqg s in g-8s+fbid-q7 k9q d zta vacuum?

According to Eq. 7–5, the longer the impa9ae.32brzsa yfy 0av 8ct time of an impulse, 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 inflate 9avy f .zba0e8rsy23a during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisionel2gqtpk/7 k,8fo(jh s. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this notjpegk7 k ,(2h8/ qflew design?

Why can a batter hit a pitched baseball fuqjt51 1m ftlm +yzlg/1rther than a ball tossed in the air by tjt11 mlqzfglmt /y +15he batter?

Is it possible for an object to receive a larger impuhj ht3 w2 e3ni7fy3odu-sw 1r1lse from a small force than from a large forc-3itsye3r d1f3 wn o hwjuh271e? Explain.

A light object and a heavy object have the same kinetic energy. Which has the .jnzv+3x- l u9 6 do/myxurmbp .8wka.greaterjpoad+y/vw z 9m n.xu3-l8ru xkbm..6 momentum? Explain.

Describe a collision in which all kinetic energy is vu*/ nm8jdtq 8lost.

At a hydroelectric power plant, water er.4ul vc 6r6zis directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water isvcr .4lu6z6 er brought to a dead stop, or so that the water rebounds?

A squash ball hits a walls;d 9xbi, v- 0om5 grc9 rhkax444dnyd 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 platenxvp sh xb/89, (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 cpsxn,h 98/bvxonsider 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 d nws5yu:jr .2backward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, wher13c1ld wn4lwuf r/r*deas this is not true for your arm d1*c 1/r4f w3uwdrllnor leg?

Show on a diagram how your CM shifts when you c*ihym4m9 2.xcalyum ) fls8 e6hange from a lying position to a sittinu .hlxiym9a8me 2f64y)ls* mcg position.

If only an external force can change the momentum of the center of mass ir1l;cs*jo k, :go7fjof an object, how can the internal force of an engine al1cof jr*,o7:i gk sj;ccelerate a car?

A rocket following a parabolic path tht1h/rzgar1s n+4x )la rough the air suddenly explodes into many pieces. What can ylhag +r a1ts4r )nx1z/ou say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying ww nrl8 e- 65r1 :kpsbu2fau;sqith a speed of 8.4 su1b q;-:l8u6s rpr2k nwfae5m/s    $kg\;m/s$

  A constant friction force of 25 N acts on a 6qv-4,ba qmz n85-kg skier for 20 s. What is the skier’s change in v a, mq4vnb8zq-elocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizo8 jm4o0ab ej605dijcyntal line drive straight back toward the pitcher at 52m/s If the contact time between bat and baj4y85o jm0aidb0 jec6ll is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws vvwpa9* m 1z2da 6.40-kg package out horizontally with a speed of 10 m/s Fig. below Cal2 9vpaw vd1mz*culate 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 propelling kmnq hp0/:ii4 r kq: u0dmp+2hgases are expelled at a rate of 1500kg/s w:0k0hrkpi 2iq 4 h +m/dqpnu:mith a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moviznour+ b0d7. s* .rluc4wko0 png at 4.1m/s on an apparent breakaway for a touchdown is tackled from behind. When he wa n+ruk*cl .p 7s0odrwo.0uz 4bs tackled by an 85-kg cornerback 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 alevel frictionless track with anmr. s 8nu/wy)i7p tk- constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the ca t/7 -.n)kms p8niruwyr. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveli5us46epx5n hfng at 15m/s strikes a second boxcar at rest. The two stick together and move off with a speed of 6m/s What i4nu5f5xps6e h s the mass of the second car?    m/s

  During a Chicago storm, widcqy8or04o n,q:ljt1 q8zys //cj-r n2b dn 0ands can whip horizontally at speeds of 100km/h If the air stryods4jr : 8oln/ bryq10/q,0daczjc q8 -2nt nikes 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 sp,ki o ;s,nw1yteed of 8.6m/s on a level track. Snow begins to fall vertically and fills the c,tyi wn 1s,;koar at a rate of 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 moving at w 6)( nuulhyy3420m/s emits an alpha particle in the direction ofl6)w3u( unyhy its velocity, 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 and emerge3e* 6kigv p n,bsr(j w6fomm1(s cleanly at 170m/s If1 bew 3,m ( kfgp6smj6inv*o(r 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 7gxapgpuz9u8, rg3 f: speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a velocityuu/ryr /wx0ws .q lismr)u( fm 3k6;m5 of 115m/s To alter i6iruxm 0mr l(sru5.km fw;ys)/ u3qw/ts course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed of 45m/s Thev1x00etdso/ ch0o0 lh 3,ugga golf club was in contact with th3oa0, 01l 0eu0chogvg h stdx/e 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 to rest1i.l/)1m b/ :a lkxbrjqsnu)r in a timi:baljk bsm1))r/u1 q/rl x.ne interval of 8.0 ms. (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 speed v=25m/s st/ - rk6gmy/npe/o.sth rikes 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 cr gvjf/;li5+n+ueeq rk5 g q5*iashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculat;v/e jle5rig5uq*fk n g5i+q+ e 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 theyh+3 gw2z+ezlzjkiw/j hx)q 7qu m,roj-(a 5: east and is stopped in 0.75 s by a head-on tqzh+q/,3jl 7ij a)(2grwezx zhkw-+y :omuj5ackle 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 tenn9zqb-ewr 3ed0 is ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 ar0-q dw3ez9 bes 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 the l:jhr oclg5*2cower 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 bonoj*:g2 c 5lchre 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 movi 4dah1+m8sz9 t(rfi lang east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If thems1t(d lf49a8hz + ira collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent 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-o.i h3zoymncov++1 np*n 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 collision?Let A r. z+ nom*h3on cy1p+ivepresent 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 head-on collision.mg,v v8c magvv 3.)v1l 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?(Lvvg)v m almv81v,g.c 3et 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 sp(v0p7p t. qetjeed 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 eatqjv.p(0tp7 e ch ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed h e8es0 :1 dntvht3-dhof 8.5m/s collides head-on anh1vh:8 t0 de 3-dtsnhed 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 elastically as one apqd2 mkozg j( v0xl q8c*0ln;q9proaches 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 car A approaches at 4.5m/s and car B is movinzd02xo lqv gl8n(qj *qc;9m0kg 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 wy p77qc uw*we k.q(jy(ith a second ball initially at rest. The second ball moves off with half the original speed of the first ball.eqky7c(wy. puq*j7 w (
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as shown in uyl+yo hl9oel 7 +;f,aFig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 o,o; y++ul 79yhlfelacm 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 mass 1crwo ce.e.e.g3w6y l 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 resu sv(q7pz +wm8csi*p ck+tj b6xb6 /s,klts in a maximum height h of the pen sxqm+s,i*vpj6p67 skc t /zc (kwb8b+dulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet trave 8t.z)o3qmp wrling 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertic3om8zp.qw ) tral and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinh m p0fo1od-s.etic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into twoyc2tm9 im,/kv x 3fe5s pieces, one of which has 1.5 times the mass of the other. If 7500 J were releasesx9m, tmci/ vky53f2ed 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 collides into the rea 9noany92 nfq ye8lxy60bc*k+d0h qd9r end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculateslh9na+2nfn byx ok6qyy0* qc9d e90d8 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 to a height of 1.z)utbn;8xg.jd3( 9djvbge ((l0 kjml20 m. Approximately how many rebounds will the ball ma9z e ( j8(x(ltdnugb;gv mj0kj. ld)b3ke before losing 90% of its energy?   

A measure of inelasticity in a head-on collisio*dqdsf(oo ax-i,)k 9 qn of two objects is the coefficient of restkdqi)*ox ds q(-o,f9aitution, 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 thgmoi )f l0*bxlqdhne;eq.(8;e mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances hlb)id; o*q. eme(x 8gflnq;0each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s cof b) n .qk.3z 5tff/chdl2peus4s +.hellides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocitu f plcs)en2 f45.eqh/.sktzfdh . +3by 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 m 1danpqo02v 1c3 :jkd-2siqja second nucleus, an electron, and a neutrino. The elj aocpn-ik v1:2dq d1sj0mq32ectron 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 masslpyx9 -0etw;c $m_\mathrm{A}=0.400$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 inelasticlm 9 cahczy;ne :+j -y58yh9zepifg: * collision between two objects of equal mass, each having initial speed the two move off together with speed v/3- 89+;jcemy*zy:g a npefyczih:l5 h9 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at t8th xpz*d7; gphe origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction o;x7 *ptg zd8phf 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 elast9fz6q93juw rd pffm/1ic collision with another atom at rest. After the impact, the zmpf316fd /u frj99w qneon 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 perfectlb 4nfo6xf75ew)y hv9wy elastic collision with another atom at rest. After the impact, t7ovewnw 6h4y5xfb )9fhe 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 m:n 64gxqqq,vb:5 -qxk f-iyudass of the three-mass system shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg mass. q,:5uqnvgdq :iqb-y-xkf6x4    m

  The distance between a cau: w3*+r+pd xgletrg/b9jad)rbon 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 i p3lw4n cgzyn9kf7:4j s 2.50 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m fr y49:kzwjncg3fnl7 4 pom 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 680;co sm;er v-3 g.r3f.+lz jiwlua34tp0 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the lz g;or+i3aw pt4; ..s uc v-3fmj3lerloaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesfvkp o:l /, **bntjpm7 $l_0$,$2l_0$, 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) palletnc2ku hjl4v y*a8)td6 has a load 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 that4 2d vha *jlu68tc)nyk 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 circular hole of radiu duwd o/s1zlex he2+q9-a;u1xs R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate u swd2lex1hx1+oaud-ez ;9q/? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and .9d5y( pr ko3+qyskz )i9p ngscalculate the mass of one of yousnz p5)ry9d kg+ ( ipqs9yk.o3r legs.    kg

  Determine the CM of an outstretched arm using Tabgyt3- wl5nrd3*t :gci le 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 t*qlpo9 3t8jg /emzm5vhe CM of an arm bent at a right angle. Assume thavp m/59tom3 lj*g8qz et the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his c866gjw;rosm n79c cyarms and legs are hanging vertically, a ycw9os 76c6 mj;nc8grnd his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon ar( j 4t3 fjued.5) lodzv(mwvz)e $5.98\times10^{24}$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 8,lt0 qbe6dfw k0c8vj 2n(hyl00-kg man stand 10.0 m apart on 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 mass 2.00 kg and a diamet *u x,r3 qjvl*4eiuln8er 0.0800 m mounted on a uniformi,*l8x jrv unqu el*43 cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mas7r 5mc4nha l7np7y3nr s 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 above the bottom ofcnmlr73h7 py57nnr 4a the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29bwe(;3y kh(en9.f;de tam;jv), $m_{II}$=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 gp-ym:j.0r 6vj k e4mqivz+bk aki-v/m g2+ dr5ondola, of mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth)a+m d-krk 0-kz+jpv6 ei2r q/ 5v.mjb4g:ymv i does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pcovdrx53hlngn x65;agm *5 )ek-s l5ditched horizontally 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 thn c5 kna)-vlh6se;5xx3* dor mggld55e average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m trajrcx ;o5x/e+x veling with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown in Fighh:q(1 t6ww zvx9bw:)py ,zre . 7–43. Relative dimensions are also shown. Shezb q:1z(wphr,: 6) w9wxytvhould 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 (including space suit) a+ 3sksoiw1;) zzgtd cwg/2m +gcquires a speed of 2.5m/s by pushing off wiwm+z/zgksg +123ogcs ) t;wi dth 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 k-nfprh( bu)f- g and the other 80 kg, are initially at rest in outer space. They then push each otbu )(-frh fn-pher apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastictfx3bi2x 9s b;zrzr*4(ss2x6ps p+ fx collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fpr2+(bf ib sx9r3xtx2f6 pz ;sxs zs*4ourth 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 invu,o4fmm8fsc)j3 d6m7ctdejdh+ i6 5a olving an automobile accident. The accident involved c6uf m fca e+)64 cd3d87 ,dmjmosh5tijar 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/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top ofm 7i-g,.gicseyk24jtv . l7qphs7l,w a flight of concrete 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 hh,im egwgt47.7j 7ps.c,lyq vsk l2-ieight on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest directly gem h8:-)gsljy*e (fyabove it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in f:gh8-eym* )ly(s e gjit?    m

  A 25-g bullet strikes and becomes embedded in a 1. + f,eq-:g zq pg-rdl2 bd)u0xpo7neb435-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 bupf: l4 )q-,d7bdb q-g0ur expzen2og+llet?    m/s

  Two people, one of mass 75 kgr(f9prdr25+dp rs1y hq fgm;8 and the other of mass 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 ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boatpffhy9p;d1g+rr28 5 sqr mrd( move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was 9pb7:e-epsc j5 g zsgeqw;84eabout $ 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 *ix/ d wr;z 7uju:yp/obroken apart into two fragments by an explosion. One fragment acquires twiz/ru ;*py/ :dw7ouxji ce the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula ++lbe:rfm *xcp8i u 4hF = 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 vex2lig2gz2jted26i:j, r4 l$m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into and.ka9a uj hb*h4ld 2:e,d*hwm alpha particle and a smaller nucleus. What will be the speed ofhk*hl.,amh4d * w2 au9:bddje this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired ac0c)zc ghe2m u sx15:tt 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 30.03knpkey ) ),73jfon sy $^{\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 thegwk0q++6go (co x4iix upper limit on mass m if it is to rebound o4icwg + 0kxi+(gq xo6from M, slide up the 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 (a 96nzg g4)n gyfcn6xlu2.cyshows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass og 2n fz)(6 cgyc49l6a.nyn xguf 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