We claim that momentum is conserved, yet most moving objects eventually sjzwn2t6b4go mb/ 1zp+low down and stop. 1+wbz p6bm4zo2/ tnjg Explain.

When a person jumps from a tree to the ground, what happens twuqsz 1u iz97r l6w82io the momentum of the person uporw78wils zi2 69quzu1n striking the ground?

When you release an inflated but untied balloon, why does it fly across tmj-*bu;, 3p g7hbzwcthe room?gthu3 z -;bj7m*, wbcp

It is said that in ancient times a rich mhmwcpnx1jx 7 x12cu. -an with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice wapw1 cn-1m2 xxj7x.chu s frictionless, he could not 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 out in(n,+hqa3 0gi k pqk4wv space and is essentially i(,wag k3h 4ki0 p+vqqnn a vacuum?

According to Eq. 7–5, the longer the impact time of aa-il)wl c+9n sxos0p6n impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformationxca sw 906on)l+il -ps of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstandrjo 9 d/ tedzzvw mbu,l (;(o+h2.2ahp collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the adva d9oho;zd+2 /pa(,u lv jrebz(wmt2h.ntage of this new design?

Why can a batter hit a pitched baseball further than a ballfi;* pz,tv0a0ra ikp; tossed in the air by the battertpkv;a fzi; p0,*i a0r?

Is it possible for an object to receive a la;q *wu b9-pve/avlt m2rger impulse from a small force than from a large force?*bq w;m9/vu-vp2t al e Explain.

A light object and a heavy object have the same kinetic energ z p;1yw)7a.vkvw bn;asz4:aey. Which has the greater momentum? Explain.ezkby4;a);v1s 7 paavnwzw: .

Describe a collision inp0x7 -t czcx+90: xfamz+ixrm which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at .8 q: rmjem-yphigh speed against turbine blades on an axle that p r.:m e-my8jqturns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wf,p fj; z:1ogmall 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 ont fd: 9y2ie+f i6b n+nyw/ekv0to a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball +:yfnyk/2e eb i6wtfi9v+n0d conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carryi. gu.ntyz9e ey jx8(s0ng a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is n*o)-sa72 ;:vj9eehm nttd8lexn5b ktot true fo*eavo)t7lnn : 8kde ebt 5-t9sjhx;2mr your arm or leg?

Show on a diagram how your CM shifts when you change ipky;7oh7 ce; from a lying position to a sitting pos7;c7k ;ie phyoition.

If only an external force can change the momentum of the2+fs w ko;h6pp center of mass of an objep+wp f sho;26kct, how can the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air -t4p6qfcue -2j axa(9b bz5arj n .zm*suddenly explodes into many pieces. What can you say about the motz 6cqx*- -(4a5te m af2ajunzb9rpbj.ion of this system of pieces?

  What is the magnitude7 fg,s hrjv-o0 of the momentum of a 28-g sparrow flying with a speed of 8.g-v 0,7fhsro j4 m/s    $kg\;m/s$

  A constant friction force of 25 N acts ,anp68.xpnzt+ hj z4xon a 65-kg skier for 20 s. What is the skier’ hxp6z,np xzn +jt8a.4s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horq9ddxa5r:hv2zr9fvs ;xo w 7 5izontal line drive straight back toward the pitcher at 52m/s If the contact time betw h 5;vzrxw:d7dxvq 52or9s9af een 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 packvf :i. hc9 cv0ok2ad+nage out horizontally with a speed of 10 m/s Fig. below Calculateio. :+0 hvfna9 cd2ckv 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, giiktj s usa 66,.jss.aq/qb: i/ven that the propelling gases are expelled at a rate of 1500kg/s with a sp6:bji.k uq,/ sa ajq./6 tsisseed 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 appare2ui+,8pgi nje:vadmp ;qzm)0j4ut6gnt breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual spgm)+iqp:uazd2eij068g ;ujt m, nvp4eed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictionless track with a consrisk-m bs 3y;ucs98d0tant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will bers8cib9sds 0;myk3 u - the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second b5seh /s12 icjqq./le1d3 xntzoxcar at rest. The two stict.dj/ zh ee1is l5csn2q 13xq/k together and move off with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip hvc(/; mu lcj:.uvy gs)orizontally 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 )v gu luscm/y;.c:v( jm 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 consl3b,u vh a *ml9gu*3l iyd+1gx gnk8*ktant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction witbglk ldhm1*kau 3,+vg*9 3nxi g8y*ulh 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 an alpy)+bl,d0 shxe ha particle in the direction of its velocity, an)b he,sld0+x yd 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 adsbip-p ;4;xx 1)er psnd emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet e)i p;sxp14b; rdepxs-merges?    m/s

  A 975-kg two-stage rocket is traveling at a speed otsmc wra/n3 li*12 9usf $5.80\times10^3\mathrm{~m/s}$ 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 )kr8 qxh9aqo 73180 kg is traveling in outer space with a velocity of 115m/s 9oxrqqka78h )To alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at 7lt*+x ka ltk 2.f.yuva speed of 45m/s The golf club was y.*ulxv t7.kt+ f2alk in contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes to re w px(,8fu*h+nixcb6y*bf5vjst in a time interval of 8.0 ms. *uj xp+ w*in6h8c fxby(vb,5 f(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 sx c jmet-:s3g rsjzr2n+:re 01peed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge39gmfakh;l rwg4t +q- of the crashworthiness 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 kgawkrq4g- fmgt l;3h+ 9 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+ h*w1 aie5p;5o-wx2 js yqnvlas-;wx 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler rowa ji5 xw va2+x-;y;* es-sq5nhwl1punning 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 -z j)uq2poev 0tennis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as 2j- 0o)zequpv 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 lower leg,u2 25i lsr:npzm 8 knl+a+jfl 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 (l l 5pl2z iu2,fjs:a+nr+mk8 nthat 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 0.440.0q ktkc 3m,ak kg moving 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 after the collision?Let A reprkt 0m.kak3c ,qesent 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 3v/ wo/, d0 yn8m0utchqm/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the colli0vno 8 /hc0umq w/yd,tsion?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 underg st3sze v)/7 iwiiql50o a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite d/i3swl5s7) iq izv et0irection, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of : b(:qov( kiva2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ba(bk v(o:q: ivall, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 k/*)vd :,tkr suyjfkn g6b/ h.ag that is moving with a speed of 8.5m/s collides head-on and elastically with another ball inf/ n s.6kt,ukd)rb/:gvhjay*itially 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 arxu+ q8tv 5plstl)e9z6luy*/ musement park ride collide elastically as one approaches the tx5 lq6*+/v9zyl up st)8uerlother directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a secyzp))uo;m) w-j tiy j6ond ball initially at rest. The second ball moves off with half the )miouy )z ytpj;w)-6joriginal 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 cbxirad95gr rd7 sr 7:0yt- du2ube slides down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? rrtdyi r7d d:r7s5b2-ux90 ag[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 m1ehyh*q)gy5 ,yqr.dh $_A$ 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 expe6p*p4 p hzkv *k-8uaduriment, projectile 1 results in a maximum height h of u8u4hdakzpp*p * k-6 vthe pendulum 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 traveling 230m/s buries itself;+s+l- h6m:qky6b.,kcvyv7 ua6 nqg ws em.yf in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. 6,7wq sqg .ykh efs:yk vma6v+by .mln6u;+c-Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kin . 3jro61rhzqoetic 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 7 dn 4*l4oiqii8tcv1dbreaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. Ifto*l7v n4di 8i4iq1 cd 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 particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car col;h3h* f),rnpd)n;n p:bszc p jlides into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 nzh3ds) *j pbn):;,nf cpp h;rm before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What 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 yfmd)d f,f8 -g60k uuka height of 1.20 m. Approximately how many rebounds will the ball make bkf-kdf8 uf, m0y6dgu)efore losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the coe,/ uijg2 bl;zzi2 ww7qfficient zwgu ljiq7/b;2 i2 zw,of restitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with th-fk 1)8;ptjn oqmofgik46nm:p f 5 wg6ree times the mass of the other. A depression is made in bfnm:4g p6;o)k5 f m-kpnio1q68j fg wtoth 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 each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x directv8yqo 6w/j6gp ion at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass if:gyp6o/8jw vq6
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an elec9t f*jzd35jhl l osd2)tron, and a neutrino. The electron al9zjl 5) j ot*f23hddsnd 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 massy bbq 8*l7 p5ma 1ein1e10mnr:nu;zqu $m_\mathrm{A}=0.400$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 b+ew 4 kmx9-bycollision between two objects of equal mass, each having initial speed the two move o m +x9bkw-ye4bff 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 orymvxg150 evg zrx ;2hhwu u;0,igin 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 elastum; wh g2xg0yr;u5zxehv0, v1ic, 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 perf33f kkt -txnait(w +o5ectly elastic collision with another atom at rest. 3at(t3n tk foi5k+wx- 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 collisiony3fn;hxta zswy//3::y-c ig+4uip jf with another atom at rest. After the impact, t-/+ xi i :;3g4cz3yy:ufhsa jyn/pwfthe neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. Specify rt6h 5 ml3n2inrelative to the left-han6hmt2l5rn ni 3d 1.00-kg mass.    m

  The distance between a carbon8gu, xr ly9q4e 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. Howv m6pmpcveezm7s* 2+d+ 8l af- bk+k1-no bst/ far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front?ve-lb+sbdots* v8+17+6 m/kfpck-en am2pmz 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 fe(5m.b5v vh teurryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW ( vvum55h.btecorners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sideeb::q t+b6dft-a :gbx s $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of ident bnih07 :o.mn2aw uz*qical cases of tomato paste (see Fig. 7–40), each of which is a cuqu7wonb2manh* z0i .:be of length l. Find the center 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 circular hole of radius Rjzq 5n8jfn:6ep. ikw4 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 the5inz j.nqf86j w:p4e k plate? [Hint: Try subtraction.]   R

  Assume that your proportions ar q,g ,,lzi * ;k*27v 1difrgbj*7ikchidgrt f/e the same as those in Table 7–1, and calculate the massiiq /*7dfi,lkt dg *rk 2, ; i*,vjfrgcghb7z1 of one of your legs.    kg

  Determine the CM of an outstretched au; xr7fio 3po;rm 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 h/a5ota-)k rk CM of an arm bent at a right angle. Assume that the person k)at ra5hk-o/ is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such thahunl +szshg* - bna;52t his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Tabln5ls2z ;h+ *ga-nsu bhe 7–1.

The masses of the Earth and Moo 9q/km)vtxj kxjqro( **a( vz1n 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 2meo cysr ,qxf6+l3a av1v c6/10.0 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 cyli k;y8:9*pmhyi ppv1v qndrical 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,;1 *h p:ypm9piky8v vq 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 mass 2.00 kg and a diameyk p, o))4hnmkter 0.0800 m mounted on a uniform cylindricok) kn hy),p4mal 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?    d    d

  (a) Suppose that in E .r.k0z 6so(xeb qj(ywxample 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 and stationarl bqb94dc.: rey 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 (r4.9erd cql:bbelative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strigvglu- 1p/;og kes a bat and is popped straight up to a height of 55.6 m. Iv go/pg-gul 1;f the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m trav-m)rxgv- qe p36luwzz(p x5u0eling 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 cornev-rpl gv 9gpv5 l()3mzr pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall intg39mzvv(l-vg 5r pp) lo a pocket? Give details.

  A 140-kg astronaut (including space p(mo*l)erjx*c re. ,lsuit) acquires a speed of 2.5m/s by pushing off wit) *p,oclerr*e. xjm(lh 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 manm8:0af(kj0 2 o rds,c s;l)bgybmlb;ss 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 thks8j (0yrlc0om);bg,l:;bs2 nmbf ade lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (at rest) zyl7ejx jv:.jd 2m6,2s. u9tyqra+v d and rebounds in the opposite direction with a speed equal to one-fourth its original .a 2tdduqx6smjy 9rlez j,:.jvv+ y72speed. 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 i+:v j7c vdtr+jn a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 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 :+d7rjvc jv+tbe 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 of dni(*.yoiz33 p:ennnf the top of 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 height on the fourth bounce when the ball reaches the bottom of the stai(izn 3d. p*nio3nen:yrs?

  A bullet is fired vertically into a j-9okbp8h 3*ae tw z7fa/8pas1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 -3 ajhkze7s89 ta*abp/8w fop 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 striker6:e +fyfm e kq7: 8z)v.xstjws and becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, whatyqzt 6kv e e:f+8)mfj:7x rw.s was the muzzle speed of the bullet?    m/s

  Two people, one of massx1qao4 euqm2, 75 kg 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 a4m,a 12ueqoqxt opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was +g;8( zi *7x gahguninabout $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments be 08khnh;c aw+y an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their mahanwh; e +08cksses?   

  The force on a bullet is given by the formula F = qgc(u3jo,-/rlpu 3fv 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 massesf(q2m*ne bsavjh6c*,, t 9ybq $m_A$ = 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 re.f nm +9fxcw4s(vbf/zl0bo6pst decays radioactively into an alpha particle and a smallebbfz 0wsmc+( x.64 l9/on fvpfr nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angle 6wx c*ir1e gowe n/4+eof 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 30.0vg/g355k-du ma9rqk mpea*mt :hbb*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 7v chwjfm rgf4 +ady9v/ l1v,9kou9*mm if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide with M99va + o*fukdry/gw1v clj,vf4m7mh9 again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturndu* :f/y(s)ke xkt8c b moving in the negative x direction at its orbital speed (wit* )deuk(s8f:x /y tcbkh respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s