We claim that momentum is conserved, yet most moving obje:bkt zru (-hh.cts eventually slow down and stop. Expla -rhkzub.h(t:in.

When a person jumps from a tree to the ground, what happens to the momentj669 znmhfbn1u .z*oa um of the person upon striking thebf.6ujanz 6m1zn9 *oh ground?

When you release an inflated but untied balloohfn .64o54yo7tv )i k)mok gdyn, why does it fly across the room? vhy54o) 4kio ng.kftmo7 dy6)

It is said that in ancient times a rich man with a bag of gold coinsate; qpuh:; 6no vcg)kzc);b5 froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. v;: cuga)p ckzbn;h ;6tq5 )oeWhat could he have done to save himself had he not been so miserly?

How can a rocket chant4t7uxyi 3o) ki4zk)dge direction when it is far out in space and is essentially in a vacuum?4x4k t 3o7)kitu i)dyz

According to Eq. 7–5, the longer the impact time of an impuyf)8y:1lqi v c4 ygl9h0pfaf ,lse, 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 collision and reduce the possibility ofpac:fy90yf 8,ylg vh1f)ilq4 fracture or death.

Cars used to be built as rigid as possible to withsubly(z4 41 mpttand collisions. Today, though, cars are designed to h b1umpz4yl(t 4ave “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a bal/c.r 6i d +cs15vjep/:nehsbyl tossed in the air by the batce cs6re i/s+dv:y5.n p1j/hbter?

Is it possible for an object to receive a larger impu+lip0*53 rov/as hjx xlse from a small force than from a l ox+xvl35iha0spj r */arge force? Explain.

A light object and a heavy object have the same kine xqm7okw2 ;3p:jtt:cntic energy. Which has the greate; t: 2ctpmxnkq7:oj3wr momentum? Explain.

Describe a collision in which all k unv x/1/o)(2rb hdm rw*fs(iainetic energy is lost.

At a hydroelectric power plant, water is di6yi1:y.l *2p bjhdy..i em dpvrected at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine bladiljbvi1myy 6d. y d p:2.*ehp.es be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wa8(m3 e:b-aivp dsjk9ill at a 45 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto i p3kvm7c- :rza hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of th cm-vr3ipz7: kis 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 backwar y5cv-a/dtqa5 d when carrying a heavy load in your arms?

Why is the CM of a 1-m length of k7 gyi gn)ef4b)yf0j1pipe at its mid-point, whereas this is not true for your arm gfn)fy1i0 bg7e 4y )jkor leg?

Show on a diagram how your CM shifts when you change from a lyi.k+xo9 v f xky ky(4)or*(hh;gk;avyyng position to a sitkyh4 vkg a*. kk;o)xyf h9( ;(yxyrov+ting position.

If only an external force can change the momentum of th(xdtjg31 r fy+e center of mass of an object, how can the internal force of an engine accel+ 1gjyrxd t3(ferate a car?

A rocket following a parabolic path thrqbf-en.whi,,i65 s cb ough the air suddenly explodes into many piecei.- eh wq,cb5nb,f6si s. What can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speejqhs ,a /xx4dlgwz(. 4d of 8.4 m//gxjz4lqsw.h xd,a( 4s    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-k3 f.ixnw1vl zhfd0a,. g skier for 20 s. What is the skier’s chan1wf3zvhaldi.. xfn 0 ,ge in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horiv,qiw lchj9 c*d)h m:4zontal line drive straight back toward the phd wjh:c 4im*qc,)l9vitcher 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 spesvf*;ul wl 76sz/ gce5ed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. Thes;5vw7f6 *z/lelsug c mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propbfk0an g97 u, drek81helling gases are expelled at a rate of 15000 dk8bfnrgak , e1h97ukg/s with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an apparentio .sda jgh),. breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cog,ih. as dj.)ornerback running at 5.5m/s in the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car trav)p9zth p;fikvwi. 3f(els alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at (.i; fp9vzp3t fwh)ik rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling 2 u4w8lrslqy 2at 15m/s strikes a second boxcar at rest. The two stick together and move4qsullry w28 2 off with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip hor i3ifq6k)y94/fde4us zp)dlmizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meterld df)i39u4fep)/y 4si6mqk z and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of 8.6m/s on a lyd:3b7 f2;b12g gq bnaa,wumjevel track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car aftebdg2f 2a:qj7yawmbgn;ub,3 1r 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m2e:pjmcy9 0f i/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particl2jy0:9ci p efme 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 emee5asfq m,xj7 (rges cleanly at 170m/s If the block is stationary on as ea7,mq5( xjf frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is tnsdnsc3 :xc ,c xf xnqr:6,.y, lrm5z;raveling 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 travdm 5l;zjqeyjg r6af, 5q39l :neling in outer space with a velocity of 115m/s To alter its course by g:la zl65,qrym 39 e;qjd5fjn35.0 $^{\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 3,iurp.i5ub qc-ilb 0 hit off the tee at a speed of 45m/s The golf club was in contact with the ball fo, ii p-c.05ib b3qurulr $3.5\times10^{-3}$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 7s+z) dq-5(sber zpaq8.5m/s and comes to rest in a time interval of 8qbd5sr)+e z(zs7 -q pa.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=0.0zjju s )jp9e4(ho;eq3irf n6 qda z0v3ny *(y:6kg and speed 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 engineb7 da;fk25ht1jbc dw-er in charge of the crashworthiness of new automobile models. Cars are tested by smasc7-jk1a52twfd ;bbd hhing 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 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 4mu:x28( h0qb3odkk wyp /s to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due west8 0qkpd x bw3khou2:(y. 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 z gjzu: ix7s8 :pmx2opu:b/,b0.060 kg) points in the +x direction and is given by thoz:iu,b:2x 8m:zx pb/ 7ujpsge graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg persotdt p+k4)7vchn 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 seated position (that is, in breaking the falldk)7 hv4t ctp+). 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 direction) with a speed of coyl3cgcax :gs5oa,cic43 m 0 q5llides 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 represent the 0.440-kg g553x:mgsaq3l i 4ccccyo,0aball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-on collision wga7 1kz:b tw7luego; nt,z i97ith a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed an7 nb utgli 7,;etz:k zow71a9gd 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 perfectldpv jl: cl+(lbx *te3-y elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.0x(-:+3t elcd bv jllp*0 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 s zujpa y03a84/ zm/rdn v1xjhcbs:56jpeed 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 tesj jr 4x y 8hv:z60ap1ad/n5c3muzj/bnnis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s colomcvrankb1;u ui-yvu82 ()-b lides head-on and elastically with another ball initially at rest. Afterward the incoming softball bouncua-;1cb(-ruvb8yukom)i2 nv es backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as one approac i7n: t9/ 3s3vgtplrjfhes the other directly from the rear (Fig. 7–34). Car p/7s lvtif:3gnjr39t 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 sec9ds, mxx 3ix*nvt+ fr-ond ball initially at rest. The second ball movesf s+3 -9vxmd,itxr*x n off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as 51,,b qw k6lj1vfpsl gshown in Fig. 7–35, and elast16 ,j5lfbvgk,1wls pq ically 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? [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*;s: gdyqsph 346w gtg m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in gnh9gch1qb*)aa b6jr.1 afo- a maximum height h of the pendulum equal to 2hbo1 -aqga r1)cj ngb6 .a9hf*.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 in a 3.6-kg pendulum hanging7c-6evlwaito : 81eg c on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pca-8 6e: 7 lige1ovtwcendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for z +-.dy v+bbsdthe fraction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially zaxm:)n/c 8 owhgikjj2qm4/4at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (o4jxi / zc2mw:)hnma qk48/g jLet A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides intod6udu yr/x1z6 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, knou166yr zuxdd/ wing 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 qbjxzzc7 n7r0,srl/7 lek ic74sjk67 1.20 m. Approximately how many rebounds will the ball make before lo 6zc7qc4nx lj k /blr,k0z777er7jsissing 90% of its energy?   

A measure of inelasticity in a head-on col n+kyw1xm)7u2;v 8yo tohwcxm,2hsg9 lision of two objects is the coefficient of restitution+) wghu 192yxhm ykv,sox7to;w 2n8cm, 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 t4x 7;jissct wuu res-u,2/h4oimes 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 separate and slide apart. What is the ratio of distancestjcu-4,4e o;wusisrxs h 7 u2/ 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 collides 93otu,xk p4grhead-on with a 10.0-kg object moving in the -x direction at 4x g3k9puo 4,trm/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decapy :fk :5mf3/s 3aj c)cupj7bgys into a second nucleus, an electron, and a neu7 scm:c j3kypj3a:fg5 bpf)/u trino. The electron and neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of masss-hmc2xsgto v; g,b)8 $m_\mathrm{A}=0.400$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 ob/bza 826lzweg jects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial direz 82al gebz6w/ctions?    $^{\circ} $

  Two billiard balls of equal mass move at r8;kmloi b ow/i j5gi51ight angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What 1m55gjioiil8b ;o k/wis 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 collvh4o: *+ p0/ p audvw5ke(+ylwadb(vhision with another atom at rest. After the impact,ou4:0 addve (hv(5p*h/y+ v+w lbakpw 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 elasticahwu e7) ti,l. bbqgr7ks5; /u collision with another atom at rest. u u. trb7,gea siw/bh5q)7;kl After the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the thrlukn( y*(/ 4y,vxtgn yru1( vqee-mass system shown in Fig. 7–38. Specify relative to the leftkxy(,u1(yyn 4g rqnuv lt/(* v-hand 1.00-kg mass.    m

  The distance between a carbon ay hrtg3v4;+ daovwebd /3f.n/tom ($m_{\mathrm{C}}=12\mathrm{u}$) 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.:+ 0gjc6hfex t50 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front secgfh x ej0+:t6at 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 of 70.0 kg.    m

  A square uniform raft, 18+ yb38li9 ts mrv ,/uqvadk(4c m by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SWvtykla9vcisr83 bu+ /4q ( dm, corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side6t87ms sjzm)y 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 identicadx jp(nht h.4z/ +tnu(l cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity iu.tpnhj nx4d+h( /z t(n 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 egd(sw viw0i*9: *4h r-kb gyohole 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. 7–41. What is the position of the center of mass of the plate? [Hint:*b4-i9*hvw:y i gg(or0we skd Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and ce 8c-)zm5;mrv-b dvo o.meay 3alculate the mass of one of your le5;r- od-v.ayb8) m em3vez ocmgs.    kg

  Determine the CM of an outstretchedjp9ng v39y8 8pj5wzmc arm 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 CM of an arm bent at7g)xe(gwk 5sx a right angle. Assume that the pew(7esg)g5xx k rson is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and lec 61nsa :f/sb5hpf)da gs are hanging vertically, and his trunk and head are horizontal, calculate hob a1 /hf:6c5s s)pfdanw 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 ptq4)o9 xoae)d4who3 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. v,2ub 8m(t4hbaum.s6r(ckdt0 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 cylindrica wspgg0l4mtq)s d76rwfj 3 -,tl head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mas3fw ) 6s, lpstjmg7td- r4wgq0s 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mam r4s/j 6+cwqgss 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kgwgcrs4 q+ 6/jm 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 ;x63wp9ernco tdh4 yy*itp +)(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,8so0 c3oas5d( f) snoe9y1bnt are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measu3fao1 50)y9 s8nced ns(bso tored 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 horizontally at strikes a bat an7v -uvndg. +b)78.hsoqwbpzxd is popped 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 contact.w.zg -)b+.xu hb 78 vsvpqond7    $^{\circ} $

  A rocket of mass m trzu7i6)kwaq-e7fit8 qnes c :-aveling with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot showg:;:q(dkqrl j+-) gvsr3v fr ln 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 falldj+:rrqgv3l :(k;gls qv)r f- into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of.zjou5b zm0p8 2.5m/s by pushing off with his legs from an 1800-kg space cap 8z5jumpo b0z.sule.
(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 ezj- e(lq,ps,the other 80 kg, are initially at rest in outer s,z(es,eqlp- j pace. 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 elastic colrs k gi4q:2dih( 7yb*vlision with a second ball (at rest) and rebounds in the opposite direction with a spiry4 kv7b*h (is2gdq:eed equal to 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 a cour l kx5adi4nqp 69m)o2ht 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.x) dhmo9lk54 npa6i2 q 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 cow.ar(vi0pr * kncrete 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 krr*w vp(a0 i.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 reijpjd.ffo(9ju1 *l 5 pst directly above it. If the bullet h (l5jdf9* uf.ip p1jjoas 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 b8;ytsllmjr,-k 0zrhf 4nm f 07n;py6f.6cmeon 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 befoj8.4bfr e6csy70, my pn-0 kzm lnrfhmt6lf;;re it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 j9rm3m 8ec 9d.x;frsikg, sit in a rowboat of mass 80 kg. With the boat initially at rest, tm s;rxr 9iemj.d38 9cfhe 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 was asj 424 r5t.6vsersovcukb; b6 bout $ 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 sl3jjum9n re731yk kgv(dium 1hk:b8(uddenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their masseslv kiuh k(1 8gjmmjbn3:9y(d7u 13ekr?   

  The force on a bullet is given by the formula F = 580-(ae0k 5z7z ch*sj8 a;mw $1.8 \times10^{ 5}$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 massesgc9ee 8m9kieq ,:;ljr;w: txx $m_A$ = 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 de 9hf8y21;g1ylbhyytczv 2kz 2cays radioactively into an alpha particle and a smaller nucleus. What will be the speed of 8 zyky2 ; tf21gblyc2hvz 1h9ythis 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 g4n60 bng ,-fno,og.b r3ve vefired 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 slidego)oab(al 8 bkzc)2:bs 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 2a9f j,( m1g11caloehndj)nz1qz mb4 upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide with M4g11zjhelmn a cnb2 q1zj1o),m(f9 ad again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figukt8c1t cujn;4s vo *d1s0m3pd re 7–47 shows the planet Saturn moving in the negatic*pss j4 ;ktmod8ctv30n 1ud1 ve x direction at its orbital speed (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