We claim that momentum is conserved, yet most0pwap.d8 i;+c,oho68h9 9n ru mkjuj u moving objects eventually slow down and stop. Explain. 8 m kh.u0o+wjr 6ijcnpu;,uo9hda89p

When a person jumps from a tree to the ground, what happens to the momentum o7tp2vdtn dkv971ea-s f the person upon striking t -7 dntp1tv7eas2 vk9dhe ground?

When you release an inflated but untied balloon, why doqxy iz ,:/m.ik6gyev1 es it fly across the room? 6vi:yk ieg, x./ymz1q

It is said that in ancient times a rich man with a bag of gold coins g gje2*h amxf6dkfz18r.r .*nq;e)ptfroze to death while stranded on a 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 mz.*jxq1 h6k rf;e.rna dfp*emg82gt)iserly?

How can a rocket change directie61a ,/dadfcc on when it is far out in space and is essentially in adc1a afe 6/d,c vacuum?

According to Eq. 7–5, the longer the im(dvotk f ,i6m.pact 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 the6vt (do,i.fmk 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 ah j,h4-2p3vbrt++ ykqve2kv dw) twn-s rigid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapswj k, 3 -t +)wbp2v2t-h+dqrv4kvh eyne upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ba5, 4n;kbc jxt6hv- v2ecz+kgtll tossed in the air by tcjv2 g 6nbvk x5tk+z;c,4-h tehe batter?

Is it possible for an object to receive a larger impulse from a small forcp7tch8nhy2w1r(3ok 8s(a, n0lb qcg se than from a larqb,g chkcrlyn 7on8w8sa3 h20p t(1s(ge force? Explain.

A light object and a heavy objx 4dn) x.tkji2ect have the same kinetic energy. Which has the greater momentum? Explaixxk2 i4).j tndn.

Describe a collision in which all kinetic enmf4*chr (hb2 j c:mgah8er*j4ergy is lost.

At a hydroelectric power plant, water is directed at high speed agains.fowu61k sm( qt turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is qk(fm. uo6w1s brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a ybbn 0w/m/)u ft.81 u:rvmhn(dix0m m45 $^{\circ} $ angle as shown in Fig. below. 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 (fixe t c2jalz-o f*+rh.3v-cg6yxdd to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls ana-2r-l djc6.g 3fyvoxczh*+ td sticks to the steel plate.

Why do you tend to lean backward when carrying a hr 2mztd3q*hem.8 zq*e eavy load in your arms?

Why is the CM of a 1-m length of pipe lgua2s,t)2 geat its mid-point, whereas this is not true for yglag2 u) ,s2etour arm or leg?

Show on a diagram how your CM shifts when you change from a lying co 9h j+t6ojv2position to a sitting pos hc+oj9o2vt6 jition.

If only an external force can chaqui3kv4 p3y3 z:un3e7 j jgzgin-q39knge the momentum of the center of mass of an obje: 3 u3ju p4kzgig3k3ez-nyqn 73 9qvjict, how can the internal force of an engine accelerate a car?

A rocket following a parabolic path throughrvze 0c;hy qkp*xmpmx+: d);- the air suddenly explodes into many pieces. What can you say crpxmm0 k+-q;:xvh *e);d zypabout the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g spa ni .blwu;i2/g0j)qx9hxtao* rrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What is to9+p x f o0y.yqro63nnhe skier’s chanqyr+ pnnof3yoox 60.9ge in velocity?    m/s

  A 0.145-kg baseball pitche6h+ctldc- j . 4kpprwffup,;0d at 39 m/s is hit on a horizontal line drive straight back th rcp+u lpd -cfwjt0.4fpk ;,6oward the pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a speed oftn4xf+mad d )yv+s 2h) 10 m/s Fig. below Calculate the velocity of dd+ h)+ as4tmvn2f yx)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 magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given tha)ds1l uzmq o20qie;i4 sxi)y2 t the propelling gases are expsii412ez imq) 2 oudl;)xsy q0elled at a rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving0 b0k cyrp(+uw at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ 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 wt2o:me ow9-k sith a constao-ow t9s:me 2knt speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar trav4w 9bz (qspyv/x35yr2o1zwp o 3*gbfveling at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of 100km/h If the t/44 eiqnvc m8air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force oftn e4mcv48/ iq 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 speehx3h*gn w b 25ru-kg+vm 3;cb zqxv+8pd of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a ratqm n;pgg- b3xv8bvh*+c52z 3kxu+rh we 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 moez+)* i upvzqc:2t 5esm90ioc ving at 420m/s emits an alpha particle in the direction of its velocity, and the rem :cm2) q9o*iezcv5pziue0t+saining 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 emerc zzpfzg g:3lopj75 f*44goo 3ges cleanly ogpz45zof c7pjfzgl*g43o3 :at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speed 6i x;1 (rhzvc)zj itr4of $5.80\times10^3\mathrm{~m/s}$ 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 witxa0x ( v6qi o mwkmck4.f28322jsu obqh a velocity of 115m/s To alt .uwo60sx24mm (2 kj3fkbcxv o 28aiqqer 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 a speed of 45m/s Tho jrei2 (67d3tn l4kkme golf club 2km lejt3d7 64nkr (iowas 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 8.5 d,s/b)-brh*x)n4 j 0dhiakqnm/s and comes to rest in a time inter0hxj *sb h))k-n, dqad4ibr/nval 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 strikes a wall au6p f+ mxk8pj:t 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 crashworthiny:d a/do- cy(sess 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 y dsca(d:-/oy it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is sanl5oeb ejq5+ fy8bc5 u z8geqp546si .q7)lntopped in 0.75 s by a head-on tackle by a tackler e)a.qn75gifb +eqp 6ejnzs8l bo4q5u8y55l c running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) xpk x*z3jw 9/ppoints in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to/93 wpkpxz*j x 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 heigh6).n jcsi20rdpy r jg0t 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 mg r6ny0pjr)02 sd ij.c from the standing to the seated 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 t/*cn3yxmx m4kg moving east (+x direction) with a speed of collides head-on with a 0.220-kyc3x4 mm/ x*ntg ball at rest. If the 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 hej(6w b5f7vi4rc. hkvkad-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, wifc65k vkv4h7 rw(jb. hat 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 collision. af (r.orkc5pk+d9q01iid y)p If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite dq0a5i+( kdy1pcor)f i kr .p9direction, 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 2.5m/s collides head-o;*9b8vqwkohq n 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 h* 9woq vbq;8kthe 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 th(k3w13dbekp rqhn 0z+7 2f.v( fxckwb at is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at re wx b(dk vrp3 +f.w7h(zf02ncek qb31kst. 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:rk yn8l1fkc47iv c/s collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 17y :4kv/ ccn8kl firskg 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 uku8o x2md,mkd-+swm p.:n mim 3w(- jcollision with a second ball initially at rest. The second ball moves off wi2 ,upsd-o-nw jm ukm m x:w(d38m+.kmith 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 slbbeg2qz)v8 w *ides down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is)bb 8v2we zq*g only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of ma:y5s1ffr bxx bey8 h.0ss 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 experip bsjl t43/g kuept+fm94)iaq+t f+-oment, projectile 1 results in a maximum height h of the +-oguek + /3p+t p9t)4atfmsbif ljq 4pendulum 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 bunnt8jg:e. h,sjmm9 u*tec6 2nries itself in a 3.6-kg pendulum hanging 96 n28:je* mu mj ,tgsn.ehncton a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the frac3hqx vfl2uq:;tion 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 re6ha1 g6 m6tu(vprrg9ast, into two pieces, one of which has 1.5 times the mass of thea6mu6 v6rgg1ht r9p( a 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 particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear endg+w-or 3vtl7 d of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are lo3- 7+l vgtwodrcked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at 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.kq1k,s ,y bzi sz20m6kj;3 mgl20 m. Approximately how many rebounds will the ball make , s0;z sik,g2b3lyq6mjm1 kzk before losing 90% of its energy?   

A measure of inelasticity in a head-on collisio);qr .9*i b;uwae xjxcn of two objects is the coefficienq)j.xa i wc; xu9e*;brt 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 three times the mass of-hk, k1db6 fxopy/x(f 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 py/(-6x x kk,bo1dffh distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction a3m 1akgyh-v:gt 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Finv3m:1 h-aykgg d the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays ir33a 04nxpfxcij.,yw g m2kp, nto a second nucleus, an electron, and a neutrino. The electron ,xig 3cmpwxr4,0 n.ak3y2jp fand 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 mass iq flq,7r amxprdy;1fs*,. x)$m_\mathrm{A}=0.400$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;typm+h 1gi6 eual mass, each having initial speed the two move p;yh 6e1tim+goff 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 origi*dm/,vze9bgm n 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. 7–3 b, /vzgde*m9m7). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision win0ac;0r fb2usj* a1eqs(zz ;dth another atom at rest. After the impact, the neon atom travels away at a 5dfbs ;zae zr1*j00a; n2s(quc 5.6 $^{\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 r 3.l,jxksmy 8perfectly elastic collision with another atom at rest. After the impact, the neon atom travels away atsyl.8xmk ,j3r 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 masu5ce2ouzcx .o-dcxg k: (-dw -s of the three-mass system shown in Fig. 7–38. Specify relative to th-xz wkgcce.d-5c-x o(d2o u:ue left-hand 1.00-kg mass.    m

  The distance between a carbon atom :)heak+2sv3bli gj1 5xjs7 ed($m_{\mathrm{C}}=12\mathrm{u}$) 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 bejfg2- lmea 0)ni1gks5hind 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 from the front? Assume that each person has a mass o1 g-5)l j fegask0m2inf 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is uswf/6estc f qgg*+ x0/hed as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determin /htc+/ *6wqgxfgef0se the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides*0fkzhne( sf6nv)1b rd6xn)s.x4vbq $l_0$,$2l_0$, 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 wr7exzxp-/ j-of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of lengxx7p-wrj e/-z th 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 R cut outvr7 d+tx6yt+, 6blzxu of it. The center of the smaller circle is a distance 0.80R from the center C of the laybxv+7rz+6x tlu6d t ,rger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportionx6m9frfwp xw,;sg) :q s are the same as those in Table 7–1, and calculate the xw,f:p6q gfmw; 9 rsx)mass of one of your legs.    kg

  Determine the CM of an outstretched arm using Table 7–1.) 7k , : 6zdn9kvm1shklcjz.fy   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate th-i6vb 9ddl0 gtu vg6n .ol2t0 p4s:wxse position of the CM of an arm bent at a right angle. Assume that th 6u v.bs-0g lts46xo2: ddintwp0v gl9e person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that hisfge-zrfy++/- xnnac irv4n3ia 3u7l 2 arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below thngi-ulevaryar 47c+2nn/fi x3 z f- +3e torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earx i 0vl5:z3f*3-zlsjy)scqznth and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m2,w5k7bwq+ydhpoepgk7*x 9 k 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 diameter 1m7tc gj6uar07 qegme; ew.t90.0800 m mounted on a uniform cylindrical handle of mass 0.5aw.mjtq61t ec9 e0; u7 rge7mg00 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 heam6 d kp(k+,qwbd of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cyl bd,k6+ pw(mkqindrical 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 Example 7–14 (ntd2n g7byb(82gm+ s00sio2 xjwcbj5Fig. 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 stationary wzkz29u2u(op fith respect to the ground. A passenger, of mass m, then climbs out and slides 2 k9fzuz(ou2p down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizonta*gls8f9nhm/ n lly at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 8lfg/ns9nhm* ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speed v(7. 9+8v+bjhj,+ek wa py nwmakeiz :$v_0$ 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 x(8z+hzy3ne nis faced with the corner 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 into a pocket? Give detaen+zn8(3 hzxyils.

  A 140-kg astronaut (including space suit) acquires a speed ofleu99uh u 2*il 2.5m/s by pushing off ulluui92 e*h 9with 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 restgbkqx u4v/20euxs(i6q .9jhtgq 2 s-p in o b 06 ksuq9ji utpvsq2.(g-xqg42x/heuter space. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on eliw;3hpa+8h sp eh.(t*og5 q ylastic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the secwh ly+*o(se38 p;i qhtag5 .hpond ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involviyn.e b3mcqh a7y:t /y6ng 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 h 7t h:abqec6/yn3myy.is 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 of a flight of concrete steps of total vertical heg6rjsir::w t 9ight 4.00 m. The ball hits four times on the way down, e9wi jrts: 6:rgach time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest directly abovi43ox*s+ 7 whdbd+yom e it. If the bulld+3 4mbd o+syohi 7wx*et 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 eja/qvqw) h5q5t+o2oand 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, whojteo5w5qa+ )/qhq 2 vat was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mar-dx,jk j0.4mzfe fm) ss 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sittingdk. -zr4jx f e)jm0mf, 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 was abo o e63jlbkb/p0)0ch 1up2ptpvut $ 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 cnep,1be(q44dhu,tu by an explosion. One fragment b,utu4h 1cedpn,e ( 4qacquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bulle1g9sbh11qe*3 ab ugnc/kii0 bsi3mcv 5s9ti - t is given by the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses zatrt9bf )b e8s us,:+$m_A$ = 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 radioactiws7.;cx1pgbhv x72pd vely into an alpha particle and a smaller nucleus. What will be the speed of thi 7d1xbsp2;xwpvg.7h cs 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 tarpmmj (*;g ) ajz-fdlj.get) is fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg sliuxe je.q0 5 p/1eof5wr, -gjtzdes 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), waufa z n1p93l vp69ru )si9m3ahat is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, sln9 zv3afsui p1lr9 )a9um63apide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure kdzc.r028szw 5 xp8mz 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (witk8 xzrmwzc2p 80dz5. sh 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