We claim that momentum is crqzcpl92 ( 18lrht2n8 hjl* uoonserved, yet most moving objects eventually slow down 8zr1 q (2o lc*l8rnj2t hhl9puand stop. Explain.

When a person jumps from a t6oqtb:-t( daz ree to the ground, what happens to the momentum of the pqdo:( 6 -tzbaterson upon striking the ground?

When you release an inflat: r74 - 2ql0lipgwpjibed but untied balloon, why does it fly across the room0llbp -2gp q4j:i iw7r?

It is said that in ancient times a rich man with au w *1qy+x , z8nt/uugghzrb(8 bag of gold coins froze to death while stranded on au8 qngh 8ugxtwz1y+z*/ r( b,u frozen lake. Because the ice was 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 ou d8ilp8fro7a u, tj/cgx b.(t5t in space and is essentially in8f5t dxpgu/ot l.c7ij8,r(ab a vacuum?

According to Eq. 7–5,4uuwgr 3ad +c; the longer the impact 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 during an automobile collurcg3wd a;4u +ision and reduce the possibility of fracture or death.

Cars used to be built as f;8rqptd, 2gs rigid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage , r 8fdg2ps;qtof this new design?

Why can a batter hitqq1g 17fv*-aj h1b hc.uleg. a a pitched baseball further than a ball tossed in the air by th.jfu 1la -.gcgq ba h7e1qv*1he batter?

Is it possible for an object to receivl.cidxc1 a -l/e a larger impulse from a small force than f.ca i1/l c-xldrom a large force? Explain.

A light object and a heavy object have the same kinetic energy. Which hsira )0s9,7m fgpz4ll as the greater momentum? Expla lrg, a4)lpzfsi79m0s in.

Describe a collision in which all kinetic fbmvr8sg : qvb911n (/1dbgw j 6h6rxhenergy is lost.

At a hydroelectric power plant, water is directed at -a7jt9 w:uv4qwdy /sy high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine bladyw-:sq vta/jdu74y9 wes be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a 1r4bl8m , zkpqwc9kc 645 $^{\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 (fixed to -m; wy2xl( +rk*donwn jqjm04the Earth), from which it rebounds at very nearly itq jl;yr40*o+n k m-njxwm(dw2 s original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carryy msq21 ivj+e ))/msyuk3dul5 ing a heavy load in your arms?

Why is the CM of a 1-m length of pipe agm))w 71rqbewt its mid-point, whereas this is not true fo1 m e)7g)bwrqwr your arm or leg?

Show on a diagram how your CM shifts when you ch)k+j,gz r/ amhange from a lying position to a sitting zagm)r/+ hj ,kposition.

If only an external force can changedo/a,hu((k 3i7ldrc k /f1pmal5j /wj the momentum of the center of mass of an object, how can thd,kp/ 71jawmdh3rl 5(/ k(fc /uoilja e internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes into many e*di2ewec fxh- g,6; hpieces. What can you say about the motion of this system of piecd62ih;c*hweef xe -g,es?

  What is the magnitude of the momentum of a 28-gw8 3l)ee) e+xpo .uyie sparrow flying with a speed of 8.4 m/s pel) xeyiew) u8o.+ e3    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What is the ;batbwgm15t2kiz :. fskierba tztw 1.k 2;bim:f5g’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive g zc1w h)pa8i2straight back toward the pitcher at 52m/s If gc )pi2w h1a8zthe 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 out hr;oss 5*.1 rf1qeau:zm vuh5xorizontally with a speed of 10 m/s Fig. below Calculate the velocity 1*5urrvfq1oeu5 s.s: xm a;zhof 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 jg m:q jg0l uu,h5e1ho.t t4(ya rocket, given that the propelling gases are expelled at a rate of 1500kg/s with a speejyq4l uhh(tt:g1 mguoje 05 ,.d 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 n ;:q -0,p2eqabjf4 -cuxdkkeb-)usga touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, whaf -kxaqnjsge;-eubc: 4-qup, bd2k0)t was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictionless track with a con20 j/cue kl)3ifs7je kstant speed of 18m/s A 5350-kg load,initially at rest, is dropp cek72ukj f/e3i jl)0sed onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar at rest. The two sb u64x* mju1uotick together and6 xo4uubj*1mu 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 horizontally at spmwbu (pa ,9e.itx0x t)eeds of 100km/h If the air strikes a person at the rate of 40kg/s perw.xm i(ub9,tet) 0pa x 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 ckt ++of8 x8z gprvm6ah6(6ginoasts along with a constant 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 with the tracr (kx+mz+pa6gn6i fh8tvg8 6 oks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle izn wz ;3c6w4dxqkz c;(n the direction of 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 alphawwcd 3 n4zkzx;cq(z;6 particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2 fbj1mzg llv1f/0dgmmx 6 m0-7.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionle6 mm-07lvf mjzm0lf/b g xgd11ss surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is keaf 41j.u qh(traveling at a 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 travv pjq//-7u9bsp*)a. ex hjqodeling in outer space with a velocity of 115m/s To alter its course by 3u j7)hvao.9b/s dj/-eqp*p qx5.0 $^{\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 The golf crus,)d)jwd a)+d plp1)mea0slq.w6olub was in contact with the bd+,ds) ) a)o p01w)eqljmp.lu sdra6wall 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 rest in aor/c4 4sks s6 c)-pcio time interval of 8.0 ms. (a) What is the impulse given to4/ s c6scs)-r po4coik 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=+oyzd;;w kdbi5 k6,tu25m/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 crashworthinessi jrgc3/df3-lgn l /b* 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) Calculate the average force c fn3-/3lb jliggd/*r 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 toh,hl7w b13x mr the east and is stopped in 0.75 s by a head-on tackle by a tackler runx7m,3b 1hwrl hning 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 (mass8/4e 46zxdm/ lgpaocv 0.060 kg) points in the +x direction and is given by g/cvx doapmz84/l e6 4the 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 he;pqc64mcj e0p3l xq7kight can a 75-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seateqxl c;pcj0ke3m4q 76pd position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direc lzdz 7j.zzzh;8qc1/md c6,7bj fckq/tion) 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 afm1dj/qcqz f,bzdhlz/ j 7cz;cz7. 86kter 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 c k8., oplw48kkp;ow)crvd 5yfollision with a 0.900-kg puck initially at rest. Assuming a per,pdow)4ocv k.yl5w k8 k f8p;rfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastic head-on cofh)ke u )v)1i.n5tn-bry l88 csgnn(yllision. If one ball’s initial speed was 2m/s a(5 nhbyv.-f) 81nynle8kcrs)gn) iutnd the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, movinn ;kbr7cf7u)e g with a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tenne b7;cnu)7fkr is 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 ivk 2xws v3(uku,szj *p;)y f,with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming sofj;2vx*iu,3vyp )z fwks,u(ks tball 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 i igi7wc.eo*initj3/rl ):;icollide elastically as one approaches 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 moving at 3.7m/s calj : o ii)l/igiiiwe3;t.rc7 *nculate
(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 secondn5 e e7q)xk;euila;x2r: alj3 ball initikixee l) nl;3x uq25ae;r:aj7ally 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 aqsob2+/1/t/z /ffsesccq xa0 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 flf/ eo/0s/xts/fcb1q+ a2csz q oor, 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 ob6 r73m- reja.-y2(bq bvitdrrject of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum ;n)tn-t-inkufh f u-,experiment, projectile 1 results in a maximum height h of the pendulum eqh)ut,in;n-tu-k nf f- ual 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 itset. grbm83+ +rxm6fbjclf 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 vertical and horizontal components of thebrf8+t b r gc36mxj.m+ pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fr ln48p // /vfen/hwtmqg y;3jiaction 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 explosion breaks an object, initially at rest, into two pieces5vl a7ouvxv8h zs0(v+, 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 par hz +0xvv (lvu758vsaoticle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car corxui+s l vy)/:llides into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowingv +sr lu/xi):y 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 a height of d9d9cqmq2ymr xa7(q7 1.20 m. Approximately how many rebounds will the ball make before losing 90%2(dq97yqq mxar9 d mc7 of its energy?   

A measure of inelasticity in a head-on collision of two objects is th.k/9tq4e fxm l4c* ndfe coefficient of restituti/fqc9 4l 4mdnx.*ktf eon, 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 tm ; u3ahnt+f*kimes the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks set+fu3k*m; hnaparate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s cob8:3l6 vh lb /)debc.-sj(f dxyts,collides head-on with a 10.0-kg object moving in the -x direction cdlb)l6y3j-8dv e /s :(fxhboc.stb , 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 a2. qqkda o8 8d56x)tm -efdabvtyn43gt rest decays into a second nucleus, an electron, and a neutrino. The electron and neutdq tgk4aeo). y6b83 d8m52 -vdn qfatxrino 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 mass 0d*ln2t v;w r(wvpaf/ $m_\mathrm{A}=0.400$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 eq njqzjmm0s /qb7)phi9;.ly)yual mass, each having initial speed the two move off together with speed v/3 What was the angle jm7)n9 .imqq p/h;s )zyjlby0 between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the oivs8rb85s s ged f6 +82eq m:hoa)bm03uhxfi8rigin 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 of ball A and what are their two speedsu88)sxi0 m6 sm8:b5egqsr 2hv3aiof8+edfhb? 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 , hucq3aipcrh*) 3l7 nelastic collision with another atom at rest. After the impact, the neon atom travels away acr aqpi7)hl hu33*, cnt 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 b yeqwj,8: ;lv;;iviesk 1 ;iia perfectly elastic collision with another atom at rest. After the imiivjq bylw; :8,iiv1 sk;e e;;pact, 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. 7–38. Specify re-)um gpsg +;m6azc8melative to the left-hand 1.g;z-8mscgmaum6 +)p e00-kg mass.    m

  The distance between av y05 .s6jhsv:bdt6i x carbon 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. How ir0ilcv rd-xops2x93r ,m/ z 1far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass 19oix3s2 0rr-x,md z v ilcrp/of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of;2zao muj:d(u qa e0n, mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW cornao;zn:(q d muj 0uae,2ers, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidezkih s+id4hjwhed00 h 368r:l 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:cd zgekt;)htykx4 : + 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 t:tex :k ;4z+hy)gkdcthe 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 circu7.9n(ro xe beilar hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig.n.er(eoi 9x 7b 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–e;vv ka .2-7wvxqb+g j1, and calculate the mass okqw a+v-gv7j;e2x. vbf one of your legs.    kg

  Determine the CM of an outstretched arm usi2u;xeac;rs*og n idf4s7o98 kng Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM ofbs9 ,71 mb - gc,xpg8(b iv3olzlmc1zb an arm bent at a right angle. Assume that the zm,x (m3b c bibg8lol-,1cb1v7 zg9sp person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are ha;2ho/fo 3mrh dnging vertically, and his trunk and head are horizontal, calcu3o2of;h rdhm /late 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-jav .v oyjf8b6x *p-e 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 frictionllpo h8 -8csmeo-w (z*;f7evrx ess 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 arl x7e1kj//f bnd a diameter 0f lr/xeb1 jk/7.0800 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 of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylp 0/ d8byy2pajbg.qv ((zzb 5gindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and len(a0 bbz8zp (yg 2y.pvqj/b5gdgth 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 Exai+ 3knlk wax *3wqw/8wmple 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 ai *g2acx(i/m(ac, n af)8bodtcr 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 mo ac/c,xb(()2 tc onmadf8a*ig ve? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is n v;q8;oyi;-+hs zatb )kwz2gpopped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the abw;q)i-k;8 sz2 +z;govhnyt contact.    $^{\circ} $

  A rocket of mass m traveling withz9x)lir g h f7a9;be8b 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 corak. ;dg7h;pfjner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in whig;kfa j d;7.phch the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (-dhi+m6 g9 iivincluding space suit) acquires a speed of 2.5m/s by pushing off with hmi9ig vi6-d+his legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are initially at,wuyxe1d d9z:xsux.y2 k36 jn rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 ndy2xy1wkx6. zue, d3x9su :jm?    m

  A ball of mass m makes a head-on elastic collision with a second ball (atsm 4)d rvjtyx1shes:42p ;v+t rest) and rebounds in the opposite direction with a speed equal to+t ph t4v;vmd) 1syr:ess42xj one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a3+whr4+k6ktia fgav70 /jgdh 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 he3kiw+4vhj0/6g fh gd7ak +atr 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 o e --1ntw ut;)xn+ygbvf a flight of concrete steps of total vertical height 4.00 m. The ball hits fntg-uv)b+ ;wn yet 1x-our times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired ver-8kazyqlf2gj+:b,zm 7 r lm5mtically into a 1.40-kg block of wood at rest directly above it. If the bullkr2m+m :jl5 fzmay78g-b lq,zet 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 it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood placed on,c(i3xef hn7z a horizontal surface just in front of the gun. xchi3,7f( enzIf the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the oeq0 y:6aiqgrug6 inn mw/i+4 /ther of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initigiwe0i 4/ qq6gyni +mnu: 6r/aally 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 boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass w42 blm+ qcx4ztas 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 broken apart iyft wcm;i9 - 4ewbz+d/nto two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ra c/ m9f+i-wb;y4z detwtio of their masses?   

  The force on a bullet is given : 1 ogfvkdm r 3ped7p2ee*e3)rby 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 masses4d. rqyg1 eu/t $m_A$ = 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 radioa xar3eag2qwmwn+ 96 lkt604wkctively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the spgkrk+a etw32ww q4 a9660nlx meed 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 v2uz f+ky+ :,cedi3t)asjo,kz.a pj- 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 s pjohyo)qys*s6 46(hnlides 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 hadsx-ge i/ 0 7)z*ndwj( 0gfelimit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and coll)*0/d xjsfe( dgwze - g7in0haide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slinfq r)1h(y/e- fhr72w*ifm ve-c fv4hv gshot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (*v-c7 f4f-2wi h(/hfrrve)m1yqfhve with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s