We claim that momentu o,ilmn;bi. 1hm is conserved, yet most moving objects eventually slow down and stop. Explail,1bmi;ni .hon.

When a person jumps from a tree to the ground, whsc oej+n 68ls5 +esc*g7 ;2- riyfocxkat happens to the momentum of the person upon striking the groundcg;fc k-ijrl682+sx*nco 7se5 +yoe s?

When you release an inflated but untied balloo xxmtz 6f0n;nmk8d 6c8n, why does it fly across the room 86c;8n tm0zmn xx6kfd?

It is said that in ancient times a rich man with a bag of gold coins froui qwk6jc0-r 4-( uttuze to death while stranded on a frozen lake. Becaus0 uwut rt4iju (--c6qke 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 wq ykn77jyhhheej; /u)0mt +f7hen it is far out in space and is essentially yh)m jhfhq/7 ej7u7n kt+e0;yin a vacuum?

According to Eq. 7–5,)ob+82z k gyhx the longer the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller )8yo 2 bhkz+gxthe 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 of fracture or death.

Cars used to be built as rigid as possible to withstand col;yl,2 sip1nob7wl cb,cr)qe5 :y 3pr rlisions. Today, though, cars are designed oby,w7e,y c r:n2p;q35blriplr) 1scto have “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 ball tossed in the ai-ll oaem/ hf7m;c0w9j.se mf6r by mslm ch 6-wflf;o m70./eea9 jthe batter?

Is it possible for an t a3j;2q-cdy diil8 2sobject to receive a larger impulse from a small force than from a large force? l 2q d3-8cs2id ayt;ijExplain.

A light object and a heavy object have the same kinetic energy. 3x m(gti pl;u.*0xdqlWhich has the greatexlg0*3plqmt xid u.;(r momentum? Explain.

Describe a collision in sjlj,c cq8w),rg azg oo7qwt(oe((. 7which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed aw(t-xj u*kwl *gainst turbine blades on jl*tu (wk-x*w an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a )e)bgp/y l1kk 45 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixe*dlvh gvik8v 2(-6l9h c9nb tcd 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 proce*9 v2k8(v6 chbghin lct-l vd9ss 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 carrying rmzj.i+ jn9ai:( fmvpa.0 5eea heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, wh dpfa io5y:fhv5u k-zs;1 /jy;ereas this is not true for your arm or: u15fi5;pj hdfo-vzay ;/kys leg?

Show on a diagram how your CM shifts when you change from a lying position tos6h/y nax- +vr+v qc9ynv nd ln/417jc a sitting nc -nqhran+ 97 6+j sxvy// c4y1vdvnlposition.

If only an external force can change the momentum of the cente zq(bz-4v ,mkzwqzg- 4r of mass of an object, how can the internal force of an engine accemz4zq-(q gw4z-, kzbv lerate a car?

A rocket following a parabolic path through the air suddenly explode8z0)jiklji: e tddc8.s into many pieces. What can you say about the moe:jik)i l8z0d dtcj8 .tion of this system of pieces?

  What is the magnituderl wqfg-jll xn2/7o kk+++-g3xyp na2 of the momentum of a 28-g sparrow flying with a speed of 8.4 m/s2j+yk2g +k-fr- lq xa+nllonwg 3/xp7    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 sg fe9wtsrac 9sz25l, 7. What is the skier’s chst,gw e972l5 cfszra9ange in velocity?    m/s

  A 0.145-kg baseball pitched at 39 l 4fgt;hy (e-rm/s is hit on a horizontal line drive straight back toward the t(re -h4 fyl;gpitcher 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 spxe p;i0wf( 6gweed of 10 m/s Fig. below Calculate the velocityw( eg0x p;ifw6 of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a zvfs 7 ti3274on b;bvjrocket, given that the propelling gases are expelled at a rate of 1500kg/s with a speed of ofsv;zbn jv2ibt4773 $ 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 breakawa;) . 7r+gwbgqj1zx 1t5nkjquny for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what wb 1j1q)rt.7g gnuk;nzjqw+x5as their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictionlesghdotx 5) 1k ;7s9qmmas track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s ne om 95k;gdats) hqmx71w speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar at rest. lt2ax q7hada*n5ww+9 The two stick together and move off with a speed of 6m/s What is the mass of the lan*+t 9a2h a7dwx5qwsecond car?    m/s

  During a Chicago storm, f93.y5 eovmr rwinds can whip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assumer oye5v9 mf.r3 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 alon/.br zsp bv-h0g with a constant speed of 8.6m/s on a level track. Snow begins to fall vertih. 0pz/ v-rbbscally and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in t fa;),-4 73 8+sl hfuynt0kefnrkbvwjhe direction of its velocity, and the remaining nucleus slows to 350m/s I lh v7 4k8-na,0)t+fuynwk fsfj;3re bf 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 blwv h,i0jd sq5-ock of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move aft5dwj s0qhv-, ier the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveli 8n/3neqx 3bnlng 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 traveling in outer space w owp)l :hs tu);42vpddith a velocity of 115m/s To alter its co:vduop4wl ;tp)2hs)durse 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 o -kq mhuh;47)rq syxz+f*d+f xf 45m/s The golf club was in contact -m )q+hx;k 7uffh4sy zrxq d+*with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and csqcqhm9m d 0u)5 4q*egy ql0d ctor):9omes to rest in a time interval:q )qcs90t4q q*l)eomdg09r cd5uhmy 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 at a 45d+m;k: nit+63b d iooy $^{\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 theo 9j:sc+z;hvi:i prw4 crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph).+ ;zs4jcwr :vohii :9p 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 4m/s to the eastp/ jf 5pyh0q/c24ad po and is stopped in 0.75 s by a head-on tackle by a tacklerp42p h/c oq0adfj/5py 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 k) thjnx ,8,8 msj:fdqlg) points in the +x direction and is given by the graph x,qt)8m,ln:jfs dj8h 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 person jump without breaking the lower9sghjog0-mff i r5 )5e 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 o9 0 -g5mfgh 5fsjrie)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 direction) with a spetho0 b,h81 hkfed of collides head-on with a 0.220-kg ball at rest. If the collision bkh81oh f0t h,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 a12;ld7ky zeg:bx,( f- qjhxlv speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg p hge, x:(2 1lf;-zqlxd7v jykbuck. 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-ot-i,ubdx2qz /i/ z+lxs-u bb2n 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 movi2iz/ x-bt-,xus ibdl2 +uq /zbng 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-on tsyn9 (e- ( fihik0c(gwith a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a p(ki-(ihsf( e9ygt c n0erfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5p drtr9)mql 1y9i) axfr2p p6+m/s collides head-on and elastically with another ball initially at rest. Afterward the inc 9r+ p1lp)r dyatqrf2)m6pi9x oming 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 amusemen.1lllm +m,vjjuh0wq2 t park ride collide 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 differenc h0j jlq1 2l,lmvm+uw.es 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 second ball;cbtm v22hcmj r /-ii5 initialtmh /2mvc -b5 i;irj2cly 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 a frictionlessyw6u+p/9 h26ovsadmxr ) arn3 incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leav)oa63ru h96a+/ynmpdrv wxs 2e the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an 0mz/ kfx;gz0lw4xyk , object 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 experim6-:amqjnw7*ci, pd t)i-vnc hent, projectile 1 results in a maximum height h of the aqc d*tj- ,:6nv mihi7cn-)pwpendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3w7- jpa agw:v7zb6z. bobxb)6.6-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 the pendulum’s disp w.bz)ovbwaj7a:-p zx6bg76 b lacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction o5ffdrzx c zs+5),x7ipf 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 uvd5ig, 3 i3oltwo pieces, one of which has 1.5 times the mass o5,3 dgiuvli o3f 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 particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300- ,l (9s)1+coe3bhjkv akh :emqkg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0l qmjk1k(3 h,)aho+cs9 :ebv e.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 he )hxfjlm b-- pcvbc48tu u+/c -acx01wight of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing8amx0b-)w 4bj1+ ul/h--tc cvcx pfuc 90% of its energy?   

A measure of inelasticity in a head-on collision of two obj+la.r kwpv6o 3 vin2h)ects is the coefficient of restitution, e3ha.lkw)o6r vipn2v +, 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 the 7rsj50oybs-ix36iz35b)myr z pyl m9 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 dr3 xl- 6oybyzsy0p)irmm z79jsb535 iistances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in ht4navh,6u:(eu3 jur the +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of r4eh(uhuj :6av,tn u3 each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, a (2e0qhcggx5.oy: qopn electron, and a neutrino. The electron and neutrino are emitted at right angles and hg .h :g 52qqeypxoc(o0ave 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 mas kl5c k2wr,bh4s $m_\mathrm{A}=0.400$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 inelast68n ;za+nz w4+mhwu 9s;r s:uisra +rkic collision between two objects of equal mass, each having initial speeds :6u;uswna4n ksa h+r izrrz8;9+w+m the two move off 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 th- j laz5m- afrn+5 1w )ba,gfvcue40tye 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 (m ta4fv+)uz l1wy5-0baa5f-j ne ,gc rFig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision 2j(pd/s/hkgfv tkgl yn . /4-*uwc5m1ys 9h xawith another atom at rest. Afte4m gg-1lyx/vacj.9fskh dt */ w2/nyu hs5(kpr the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) make 16pqppnheh (,s a perfectly elastic collision with another atom at rest. After the impact, t1np,hephq6 p (he 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 F* hx q1ixyw74cig. 7–38. Specify relative to the left-hand1yixcx*q7 h 4w 1.00-kg mass.    m

  The distance between a cavcl 0oa12wlu6 cawz2- rbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of the car. How 08f88peq/lre 5zis1fj5 asj yfar 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 cal015ra zfiee y /jpsj58 8s8qfr, 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 m by t,akis :7b-s n18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loadenk,s 7- iastb:d ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side( s/mn,ungudf k33s3vs $l_0$,$2l_0$, 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 identicax./xc;y t z iyt+ dl5le6oan+8l 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 xx5le+anid8y.yzl c6/+ t o; tplane, 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 ha9 oda0 8x whd,9xqnif fbp74/es a circular 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. 7–41. What is the position of theafei ddq 9p4 /ox xh,9w0b78fn center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in n7f kj1wuc+ t6Table 7–1, and calculate the mass of one f tuc1w7 k6j+nof your legs.    kg

  Determine the CM of an outstretched arm uyadz8d yu z 3yf*8ct,+-hit z*sing 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 tt br 0(9dyz1iof an arm bent at a right angle. Assume that the perbiy0t( d1 t9zrson is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and le2 qa/p.xgiyb2 gs are hanging vertically, and his trunk and head are horizontapbgyai/2.q2x l, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth 0 jfhq rtjh2(g,oabj*ta+*v 8and 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 10.0rr 32:un0to2u mf0bt1me0nks 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 s5fwhut98qz:ecy.t 1 a uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. .5ufec: 9wz syt t1h8q7–42. 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 ma3tgyd.fc3d; c ss 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottdc 3cdft3y.g; om of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29qi5h 9 p rapqwfm4e/,5a9r 7akplad6 1asj) t*), $m_{II}$=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, oflgs(6h0zb(vbif5l i i2el 3.q mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (re3 e(fzlvb.ilgilhsq(b605i 2lative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball p 3/kry9tbzo.v itched horizontally at strikes a bat and is popped straigrzyt 3bk.o9 v/ht 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.    $^{\circ} $

  A rocket of mass m traveling with sc 2xtq1mqvo.- rkvc9dzh )-v+ peed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown in Fig. 7–43. Reqx./+kijc t7f( 0av w/ j4tj7qmyf q*rlative dimensions are also shown. Should the player be worried about this being a “scratch shot,” irf yxa kt( w q7.m*7q0vfj tj+cj/i4/qn which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed 2-afv/ 6qzyb tof 2.5m/s by pushing off with his legs2 vtbq z-a6/yf 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 an ; kem,k8hzo6zd the other 80 kg, are initially at rest in ou,e k;8koz6zmhter 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 elastic collision with a secon 0 ;fl0 d,o wu.sfsni6b mr3zvae6vh5-d ball (at rest) and rebounds in the opposite direction with a speed5n uvvo;d.6 fl azie,fss630b hrm-0w 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 eu+sal ad8d jz: 88cn4u :zrl;mxpert witness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B d u 48mc:+alz:8rs8 du a;jzlnslid 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 fligu xv 95-om6dgt2cf //pc i-ztmht of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce whe5 /iu/ o-cx6g9 dtmzpf2m -vtcn the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of ws 8um3a6j 0zlfyj-- + aha7ojfood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the bl-yajj+7fus- 3a 6z0ajo8mf hlock rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-k01kza2qn4f(d83wur ql b/ mxr g 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 m3 al (0qz14 ruf wrxbn8dq/k2of 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 other of mass 60 kg, sit in an(xdk -*euqm ; rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boa(xn- ; u*eqdkmt 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 abom ql5 k;u7gg) bb;ud*9 jeozyp; d(-ueut $ 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 twow 9ldbo+oj ;x- fragments by an explosion. One fragment acquires twice the kinetic lb;9o+wj d-x oenergy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 58ut. c c1q*2ipu0-( $1.8 \times10^{ 5}$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/xiu7jfx4 +v f m0ysq) $m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha particle + qu6irilnh(mwe sebt m.)(1) and a smaller nucleus. What will be the speed of this re(bihr) e l+.wnu m) (s6it1eqmcoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angle of(aqfb 5z i+ydrh8 xm+3 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.0 p0h xp( fk6a;3v2-wcpc fp pv2$^{\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 uk le 04lm;km58opn/q-8e ) 2ctizukgppper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide with Mim;g zpk)25np8m-eoe48tkk 0c lq /u l again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn moving irl9h8)/kd8 )tcyczy0- u*)pt ke wdpsn the negative x direction at its orbital speed (with/ pty t8)wkd ecu9-z*sc)ld)p8 hyk0r 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