We claim that momentum is conserved, yet most moving objects eventuallli:r rasxjc4 dx0yxrm 4 vz,n )8)g7x*y slow down and stop. Explainn vzra)xxjlrx is,g4*r cx048y7:d m) .

When a person jumps from a tree to the ground, what happens to c 05:v (tg (tzzsjjn5cthe momentum of the person upon sjtj5v :0zc n zc(s5t(gtriking the ground?

When you release an inflated but untied balloon, why does it fly ztm8:e sr94n.z mnwz-across the room?nmmz49r -seztz n.: 8w

It is said that in ancient times a rich man with a bag of gold coins froze to-dm5nxmlc(- brxy s -0 death whi-y5nxdsm bm-r0 cx-l(le 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 miserly?

How can a rocket change directi.sc hf0 9hw(uton when it is far out in space and is essentially in a vw.t9uh c fhs0(acuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smalleyvfa+vv1xvxgw, wifk o( : f4 ,c96*f(g0t tjur 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 k(fyf9g v4j,gv(:woux wc1tva f+*,v x0i ft6during an automobile collision and reduce the possibility of fracture or death.

Cars used to be buila9tmtm* mftit* x4sg*g81 ;m at as rigid as possible to withstand collisions. Today, though, cars are desig*tg;ga *s984*mf1m aittt m mxned to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball n nz7fl1jnhd)ze5k g5ex3.i i a)2 1ctfurther than a ball tossed in the air by thk)nczz)d1jantx 531ie.i f27 hlg 5 nee batter?

Is it possible for anmaxgoe.i t4/s(74ong-i * ycj object to receive a larger impulse from a small force than from a la ii74* og(a x ygjem.-csont/4rge force? Explain.

A light object and a heavy objectn w8(/xfibpn)ot*d q / have the same kinetic energy. Which has the greater momentum? doi/ 8x q*p )/bntn(fwExplain.

Describe a collisionwr5e dgpzto//4 oexzeyr 7.je- lw 4.)o(ocf; in which all kinetic energy is lost.

At a hydroelectric power plant, water is dijy6wi (m g3e)f5xbm/8ere i1c rected at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, shou5myx m)c 8r1iwe3jg(eeif / 6bld 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 w ui2fq n29g.vkall 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 f xvg lw(pgz,f1c) ec+3rom a height h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of t,3px z lcw+fg)g e(1vchis process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carryinn(.-on*zib 0:a da*xxx v ,rwtg a heavy load in your arms?

Why is the CM of a 1-m lengz)wb +al0aw fry,m4t t:h40uqth of pipe at its mid-point, whereas this is not true for your arm or leg :t4rmy4q ,wh0zbf+uwat0 al )?

Show on a diagram how your CM shifts wh56v q1 fugcvb+1,pan vik; f6hen you change from a lying position to a sitting pos1npfav 1 q 6hg u6,ci+vvf5b;kition.

If only an external force can change the mo- .ziv3s0vy+r+cnvo6ys u o,qmentum of the center of mass of an object, how cs+onu y ,-v z3isvvqr0o.c+ y6an the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes into many /d( y:ktrh2ow 39fymwpieces. What can you say aw3dytwr /m2kh 9(fy:obout the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow f.sj4w16f 7f;cva b,ktow;slz lying with a speed of 8.47j;6z 1cbswl ao k.vffws t4;, m/s    $kg\;m/s$

  A constant friction force of 25 N actswthm8z s/t z2lo,+2i( qx5f xm on a 65-kg skier for 20 s. What is the skier’s change in velocowx q8zi tmxt(m 5 ,2fs/l2h+zity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horio( :; iyuq+ c6y72 q7dhq np1mbul1glrzontal line drive straight back toward the pitcher at 52m/s If the contact time between bat andliqy1b 7qhoc 1rm l2+:;pyg(uu7 dn6q 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 of5*ppyy :u gln/ 10 m/s Fig. below Calculate the velocity of the boat immedi *gyn p/5py:luately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propbrukhfq) uo u5wj/ :(3elling gases are expelled at jrubk:fu5)h/(uoq w3a rate of 1500kg/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 apparena9upyr (o- ;yjt breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual speed immediatoy u(y-p ;arj9ely after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictionless track with a c0is z/r ,w4b( s1xn rkueq6ht+onstant speed of 18m/s A 5350-kg load,initially at rest, is droppi /sq+ezh1skrn0t4x b wu,6(red onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar at r y6qk uxm yge/k;tag2)s8a1t hd32l 7mest. The two stick together and move off with a speed of 6m/s What is thedqa;71)m86ygak/ lthg2ytsk uemx 2 3 mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speeds of 100zdsvjo zb*j-i1x*.bl dk4 y .,*6mwsmkm/h If the a ,s xv .z.j-dbls woyjm*1bkd m4**iz6ir 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 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 oasq1a /j- .ojjdh u0;ff 8.6m/s on a level track. Snow begins to fall vertically and fills the car aa;. qsj01hfdaj -o/ujt 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 alphvu3y: 40bqn rhw+fr 8ua particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4. wv3+n 4u u08rbfryqh: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 w8v lskn4 ing4 ko)0+dmood and emerges cleanly at 170m/s If the block is s40vi8nkk+mo)dl g sn 4tationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is t2;)krnm c- wc jt):vgcraveling 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 tra(ldszz .dg*;bveling in outer space with a velocity of 115m/s To s. bd*zld (;gzalter 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 i 8cp4nfjbngfm4x+gwm+q/; f/u;,k s hit off the tee at a speed of 45m/s The golf club was 4 x4c f/u;fnf i/p;kgw8n+mm +,sbgqj in contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s ansgj0(h)vs.wbyvqcf,s7d y;b1 ivm4 /d comes to rest in a time interval of 8.0 ms. (a) What is the impulse(sgbsfh v7v.mb)/yy0j vq cdsi,w1 ;4 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 wa* dii bs n.3rk+g2azv0ll at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthiness of newih7 4 80jrokxa5 hhxxcs8z2lf56v,kj automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg take684hxozxx5f5ha j0kkc l2 jr,is h v87s 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 east and is stopped in 0.75 s by a he7nks2j8bbw/a ad-on tackle by a tackler running due westw/27na8sbj bk . 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) points in the + m 1l2h759. hldiaurjvyne,u;x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methodma1. u7rih ;nue9,2lh jy5 vlds 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 breab8 p1buudtjdzhc y 58-ipd2-0 v*s)r kking the lower leg bone of either leg? Ignore air r81i-z) ch5rk b s*jdvu80-2ytpbd d upesistance 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 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 speed of collide q,; 95w(zxx pocbt8*am1mgvx s head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will*1m5bwzc ,txvmxgq8; op x (a9 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 head- 6z1cvl/,skeu on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direv c/ze,lksu 61ction 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 4 sf*+rj. jqc;4xfu ijelastic head-on collision. If one ball’s initial speed was 2m/s and the oth jj4*rqf+fxcuj; 4.iser’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2brzs,4 yo/ajn6c6b* om jx d3+.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of yo6d+jcsxzj *,ob4m6rn/a b3 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis 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 collides heab(/(bxng y ,usd-on and elastically with another ball initially at resg(/s nux b(yb,t. 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 collide elastically as one app7(w)zdo)alic2 c 1lp/kuda4yroaches the other directl4cdi7cup)(dl l )y ao2/wzk1 ay from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a second ba n1ke/5 a,vxsyr7r(vbgu )8 roll initially at rest. The second ball moves off with half thsr,r8 vxg/v1()ye ob5ranu7 ke 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 shown in Fc v c/i5i 1mgr,np 1llarv3mxhbx 329mm3w0t/ig. 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 leave the inclinem,h3 bwl3lvrpmmcr1 nx0/g i3t/a1 x5vmc92i moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of mass :4 )qqye8fn3lza5bu om$_A$ 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 resultsg+elq mmj2( *oe.y j 5(nehgn8 in a maximum height h of t+je(g*2nm(hgoq.5 nem8 lyje he pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-p-:fc;si8 vo0m hmk7pkg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and hpo- f8:7 smim v;0kpchorizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kbzf2j* iu :7 xmgwsn:n9(bs 0yinetic 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, initialo6a:bxiqakugg0 c +)x8wg ;s ;ly at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, ho;gg+ co ;xa) 86sba:0kxgui wqw 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-kg0yd,i w*xly+ 1 uom 4tv6ffp,er )vc,b 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 0.80, calculates the speed of the spo,)l yf1xu6ibtvc,wmo ef0 ,+dvr *p4yrts 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 1.5jds efwr6+q/bjto 4wf(9t;v: 0 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of it(j:t; bwrje o/ q6+tsvfwf49ds energy?   

A measure of inelasticity in a head-on collision ofgjg b0rk3y1+yyvlpzz6o. y38 two objects is the coefficient.oj 1v8ky3 yzgpyb6gr30 lz +y 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 pa1ti65. xdg :ot 6ez d3hfxc3dieces, one with three times 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 distagf3ic36 h 1ad txdx:ot.z65 ednces 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 collp q o6o2a 2qs+hfj91dcides head-on with a 10.0-kg p 6d 19fhcoqsaqo2j+2 object moving in the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an electron, a a:lwd*wu4fft )0 n.icnd a neutrino. The electron and neutrino are emitted at right angles and fa0i:u*dn w .4wtlcf) 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 m6ti uza-(jd .bass $m_\mathrm{A}=0.400$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 equal mass, each hgcmy ecm p7 2lo,+2vv e(,f:ngky ,l7gaving initial speed the two movelveg7elcyv 2,,m7cgy om+ :p ,n g2k(f 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 the origin o-/r w6bg *9r)dxiun cvf 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 alo/-rdu9c bxr)i* gvwn6ng the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with77oual1b2s0sub ti hi3 u.llm.y j d2) another atom at rest. After the impact, the neon atom travels ajdst 37)2b2ulo1a7si.l yh0 blui.mu way 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) mame6g.lz qi :9jkes a perfectly elastic collision with another atom at rest. After.9lz:qejgmi6 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 three-mass s/reym . x6w;2pqll.vnzd k,r 5/g rnt+ystem shown in Fig. 7–38. Specify relative to t.n rz /l+k / eny2qw5d,m;pxv. rlgt6rhe left-hand 1.00-kg mass.    m

  The distance between a carbon aqchvb5 k -ntjt,jh76-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 2.50 m behind the front of z) -dqi6a m(oux5 4ilnthe 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.iaq(d x4u )liozn-56 m90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of massqudcc i) 0 u3uk49,yjs 6800 kg, is used as a ferryboat. If three yuc4c )i9d0 ,uqu3jsk cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesgt0-teg r8e 6u lsyubkh/+7- :* bwmcw $l_0$,$2l_0$, 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 identical cases 71bt mmhgg 8ls0 -cty2of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the loactm mb281 ytg0lhg s-7d without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cut out ofza zoht;6 3(iyb-d 0bl it. The center of the smaller circle is a distance 0.80R from the center C of the larg b(h dol 0iazt6b3;yz-er circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and 55l mk xdj*.ybcalculate the mass of one of your legs. d*b 5lk.jm5 yx   kg

  Determine the CM of an outstretcht-6pkn (:c bgzy2fd 4xed 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 at a r x6rh,k7 7 pex0nxc8ojight angle. Assume that the person is7jpn8e6 7,koxhx0 cx r 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in ag02 i)m; wemjs position such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Tamgme ; ws)ji20ble 7–1.

The masses of the Earth and Moon aregzmw dost2 -y,-fl6 8d $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on zc;it7s5r * qkd(h z)ufrictionless 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 uzitf5z0w 0ff, h0u/gt* ifx8lx+j7mu niform 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. 7–42. If this mallet is tossed, spinning, into the air, how far above the bo780lu+x*tg/ jimt5uzfihz0 w,xf0f fttom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of s r:mk036*yot:6iubd ggphvia650 ypa uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a unifopp m:o:a y*5rb k g tih60usv36d0giy6rm cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fi0s ++9v/r,c;stykj a8yk pcxig. 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 gog/ 3vvyx60 g3 *qde7gu;rvx snndola, of 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 withevng/3u;qd*3g v xrv7sg0xy6 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 ste ;otw+fcw0 8vrikes a bat and is popped straight up to a height o0ow 8tf+ v;cewf 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 y d*n-cb ;* f/zhift2z*+ijglspeed $v_0$ 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 l3 op +2 -stqt7;kuylwi:vyy/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 poko u:ipll tq7+; -3wyst2v/yycket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2. i43f/ iqgjledmr1p)+5m/s by pushing off with his legs from an 1800-kg space capsuler14em+ dl3 if)qgpj /i.
(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 and4:-bib) uzua4m br5ck the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart ar5rmkcau-b b4z:i b u4)e they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a ks;xk 3imf19hzbly-qz 3;d;i second ball (at rest) and rebounds in the opposite direction with a spi-i1;z kdxl m9ykb3;fq; z3s heed 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 court case involving an automobilvu00xdf k a9/de accident. The a0ux /va0kdf9 dccident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to 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 vertican pwdeo3:3sj+8+snx dl 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 fourde3:3x+j+wn ssnpdo8th bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.1jy4fv3k* grqme0 .u b40-kg block of wood at rest directly above it. If the bullet has a kygr3.* b0f qej14 uvmmass 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 embedd3yo knkm+46 4hcz,j wded 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, what was the muzzle spmhwk,zn+464oj 3cykd eed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg 8. w95u+2viblh2ink /hgjteu*oev,m , sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what dirje. btkigv9uh,lu/v8ei nhm+w 5 *22oection 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 aborwp5ap d. l7jy7(xg8lqdm4 +gut $ 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 by ao wn aw a,d:*sx38+scvn explosion. One fragment acquires twice the kinetic energy of the other. What is the ratnwa3sa *s8c:ov+xw d,io of their masses?   

  The force on a bullet is gavd*7(ge27iknyp6m t iven 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 massesjk 02i2h e8tn4allq *l $m_A$ = 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 and4q-0drw4pxg q a smaller nucleus. What q xp-0 44qrdwgwill be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an au1 wwp 4 qc3f7n/e4oagngle 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 sh6*7f;hh i se.i + *jj2dcybitlides down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on ma vwcea k.a*na*glv)- 5ss m if it is to rebound from M, slide up the incline, stop, slide )e5* navla.g- kva*cwdown the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figun7 (s hk-p2 kzqf:2zqkre 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.s k2q:- f7 h2z(qkzknp6km/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