We claim that momentum is conserved6f*bf0tq wv+a;f tf 3l, yet most moving objects eventually slow down and stop. E3 0+aftwqb;v*ff l6ft xplain.

When a person jumps from a tree tn8 tdautd/,u 29vw 0cd m(ex*xo the ground, what happens to the momentum of the person upon striking the m(t, dxvd 2 weca *d80/nxut9uground?

When you release an inflated but untied balloon, whbb g zfb)+g *k,buw9wx2+lo0k2foz (zy does it fly across the room?kg bbfbuw wkxz o0,)92*of 2bl(+gzz+

It is said that in ancient times a8 b8bcu4b jbo4jv7alui9zp6 / rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have don bb8 7u p44z/l 8jb9bc6ojuvaie to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is . q,m;k)jywb-0 d 3 jn0trwxzxessentially in a vacuum? qxyjm3bk-)jx d.wt0rw,z ;0n

According to Eq. 7–5, the longer the impact time db1*2 a*d 6 cx1fa3by 2rskw06,pmdjk v rere,of an impulse, the smaller the force can be for the same momentum change, and hence d,wrsbybk6 0a*13de6, mkjadp rv21cx*e2rfthe 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 of fracture or death.

Cars used to be built as rigid as/mu+az ne.4ks possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collaenka+u / z4sm.pse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further v-w(:gmpcq7 u than a ball tossed in the air by the battev p(m uw:gq7c-r?

Is it possible for an objec(44qc bg ebyi48y1vnap /m:ipt to receive a larger impulse from a small force than from a large forcpiy4avngbc/q (b8e: 4pmiy1 4e? Explain.

A light object and a heavy object have tkv)h(1v-nb 2c*p 7dez0hi al the same kinetic energy. Which has the greater momentum? Eivd)el 0(- v7*1a bkpcn zthh2xplain.

Describe a collision in which all kinm4x u dunlphlmk27 (-:etic energy is lost.

At a hydroelectric power plant, water is directed at high speed againbw9x63xk/:8.bd exc i0ufa3vbe :u lost turbine blades on an axle that turns an electric b 3uvad9/c eio w:bxxl ukfe x.0:3b68generator. 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 1 zl2p8wx9y61xjotgb wall 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 a de.il.pc gw95rr)8fl 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 this process? (b) If wed5li ..g)lp 89wcr erf 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+frj ciy chxd0n qmt+6n) 9*.g when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is not tr b3+spc 6suv+.kc(maxue for your vp+x(a.3b6c+us c skm arm or leg?

Show on a diagram how your 5q-,nlwb g8ktCM shifts when you change from a lying position to a sittinglt- gbk5 nw8q, position.

If only an external force can change the momxb7pjayuj /63entum of the center of mass of an object,pjjb36ya/7ux how can the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes il)f6n3 6g.*gq7whnisr tzcuq;28 j l tnto many pieces. ih8r)2fgcq; .qgt6z*tl 7ns 6 3jluwnWhat can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparl wxyvb .4*ff9xj tl44row flying with a speed of 8.4 m/sf4y4 v9l4 lt .jfb*xwx    $kg\;m/s$

  A constant friction force of 25 N acyq5s4ob;0eyof7jj * s ts on a 65-kg skier for 20 s. What is the skier’s f7jysoqobesj50; y4* change in velocity?    m/s

  A 0.145-kg baseball pitched at 3z *r6jtgx,d g gl*zy1:9 m/s is hit on a horizontal line drive straight back toward tltg jg *zz*r1gx: ,6ydhe pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a spee6e qgg81zmg ew9-l0. ak,o llxd of 10 m/s Fig. below Calculate the velocity of te6-0 xkm9.azogg e1ql8g wll,he 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 rocket, given that th)doc3cw l8rm4euw6cg d -i8 i,e propelling gases are expelled at a rate of 1500k3cwm8,-g 6ocdie 8rdwc4uli )g/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 nr0pn* ctgz)2an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the sam*znn ct2r0g p)e direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel jz)zbmhjle .v4tk6 ;4rm-lq1 frictionless track with a constant speed of 18mj146bvz r4mhmtk-;q)j. l zle/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a secoue9 wx+jv.pt n*hwq7ik5x v5 0nd boxcar at rest. The two stick together and mo.x59+wh*qu j te 7v ikwxp5vn0ve off with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizot pig8bi2xi9hn1 5ip *ntally at speeds of 100km/h If the air strikes a persongii1pi x bt9 i*82hn5p 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 e0pzn, wm6p7mnd otxz 68za37c. fym4a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what i,37mam74oe 6.zt8nzw0 mdpzpxn fc 6y s 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 du2 nkc :+co9 9zl3*wag y3 vp7lc)qagthe direction of its velocity, and the remaining n v*w7z k3ug9ga)3 2+lnc 9ydoc pq:alcucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block ow58u ez*ozqzq0bh ek5v 3 yqgka4/3n,f wood and emerges cleanly at 1704 zqwq08 ykg*z, 5h3 eeq3ua5bn/vozkm/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket i68)h n)x;of ym8 xuslzs traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in oute0 h q6rstvb:1rwz h5c8r space with a velocity of 115m/s To alter its course by hrt r bhsc06qz w5:1v835.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed of 45m/s The golf 4 h8xrv 64y;;v5y1*ulxha 2 vcpx.g rhjf+ccbclub was in contact with the ball axj*84 vfh cv pcxbr 16c.r;4y;gh2lh x5+yvufor $3.5\times10^{-3}$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 3ulthppo: je9(pf ( (.)ceci 1 c+wgiaat a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given t gh(i1j(:o iccc+t3pufp pl9. (we )eao the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg an0ryy 5j 6okyj2d 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 engineer in charge of the crashworthiness of new a:j6no u, ao;hc np usa-flb2( 2)4kuuautomobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Ca uunbhu2ku;oo-c j,2 ls4) a f:pa6an(lculate 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 st zbah:4qs,*j )xtodt9jfta*) opped in 0.75 s by a head-on tackle by a tackler runninqjxt:* *bt j)fda ) oh9,tasz4g 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 baln s -z 4a 1x4mui wk,vbnvsmqj2;t);8zl (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as aj 4xutwm,i 4;a 82z1bnsv)q -m;ks vnz 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 loqhjf9dhry * 81/y8yh ower 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 ihh8o yyj rqdf/*91h y8s, 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 direct:4ac( u6- advysn16lyyq 8 rwdion) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction wy 68 csu-1l (nadq6yr4a:dvyof 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 speed8kyrsbas+v89v :ok0 e 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 collisi vs08k8sb:9yr e+avo kon?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 perfectl*yv wm/;48, s6rhnt s:xbo1 doqawm s;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 collisa 1x,yrm*;o:db/ s6 4w8qtwmshvno;s ion?(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, movingvf l( 6 saw-9n+rgy*4pup.smg with a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming u g4g-a+wrf( .pm6*sp vs9ylna 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 0.220w. nn q(a4h2.rn/ jteq kg that is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incow( 4 nen a/2hq.jtqr.nming 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 amuseme hv *fkp dxufe51z-lu* 0f.f)dnt 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, ow ue -* ffhlzfd05.u)dk1vxp*fing 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 mak+h* n n2k8vuy* vs*a .qxi9bkhes an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of the firshn829 yuaqxk n* k+*vb i.vhs*t 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 7ft u(q3k/ u k*hdqdm,in Fig. 7–35, and elastically strikes another cube at the bottom that is only onu*ku(dmhqfk t 3d 7,q/e-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 .1wy 5irrm0x6tu:c+kbw -u e sm$_A$ 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 a maximum heirlw: e,lz cyl9vb +(j,ght h of the pendulum equal to 2.6 cm. A second pro:rwljle(c, 9vzbl y +,jectile 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 travelinglopp6lqt1 :j/ 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine llq6o: p1pj/ tthe vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energ-cko ;4(1m(a(xnaaxo f ezo 8 c;6lswqy 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 uv nv6j44ehjo/ oh3d-f jn:h9c6u;py an object, initially 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, how much kinetic energy did each piece acquire? (Let A represent the he/4yu; vpjhj4nf6he u 36oh : d-9cnojvavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides intxnl llgl5*hq j 4my c cq+htoe,o)1-19o the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars tc*qh- +l1o4oclymlhj)15,x e 9nqgl skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 2dm-f(n g7szjh2i. bxyud /xfsf:/)jm and rebounds to a height of 1.20 m. Approxim2j2(7 xid)f/ s.f u x :jdsyg/hfbz-mnately how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the coefficieu8ih3 sjx: cb*n oml92nt of restitution, e, defined 3hcmuji :l82nxs b*o9 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 wi6g;-mxt7qz b+r/ sjfuth three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can uf6j mb-s;zq+ /7 xrgtbe 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 distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x di k(e:kb og3((-d kyyslrection at 5.5m/s collides head-on with a 10.0-kg object moving in the -x d ((3yd(:ok- ebyksgkl irection 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 rei .lkv7vfz+ ojve8b19 st decays into a second nucleus, an electron, and a neutrino. The electronv+v8.zj k7if9ol1ev b 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 mjnz.fcci*d .4+b j-zi ass $m_\mathrm{A}=0.400$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 c /a6) ddnxkfit+g1 ) lx,.umknollision between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the ),xik)+x 6 ntmaf 1/du .gdklnangle between their initial directions?    $^{\circ} $

  Two billiard balls of7o3ez 4j2icicn;osp 5.gh/vq7 e3 pgf equal mass move at right 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 qho; 3i .cp7j/c7gs2op zgf 43ivn5 eeto the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two 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 collisio l:n(kyeyy ;ailjnq aa)(.l 2+n with another atom at rest. After the impact, the neon atom t2e l+lynlq(.ia)aya : kn ;y(jravels 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 elastic collision witpeu5mo vkiajs 0l+/800. rm8 f rvyl3uh another atom at rest. After the imp/e+.mrmr0 u03 va8iyksljvo8p l5u0fact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. zs2 .ce4knp:k uqj 0/tSpecify relative to the left-hand 1.00-kg mask2 secq.:40 pjk/ zutns.    m

  The distance between a carbon )x(onn pnqlvtdl1e qc)/a 0.0 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*m0 7 u1almudb car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person dl0 mu*17ubam has a mass of 70.0 kg.    m

  A square uniform raft, 18 m2i fkux :qy.u, by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy ,qyu2:ux f i.kits NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sideqy d.5d3p,te ys $l_0$,$2l_0$, 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 hsmd, 2xzi/:yfz9uq l18d f1ffas a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, sofx2zds8ul19/ff md yi:, f1z q that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular pla zrj4dx g mvl-q1/b2 n7r4fxfpvh s892te of radius 2R has 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, r8mlzb4xh q7-4x2gr vdnf91/vj2p f sFig. 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 thouah7xh8gadq (93l: z j7y4 mlmse in Table 7–1, and calculate tl7 a8mlamjd7hgx3uzhq(y 94: he mass of one of your legs.    kg

  Determine the CM of an outstretched ah6m4h0fhju u*rm 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 an9um( n i3 wcgjz+a92rm arm bent at a right angle. Assume that m(uwc +ani2m j3z99rgthe person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms afz( oi:(:v jgcnd legs are hanging vertically, and his trunk afjg(vo i :c(:znd head are horizontal, 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 jdm1yt-m7)d b and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on fprx iz v7:w 97q69g5bp4xk -2coczjt yrictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diamg56ny y6nmci2nkg 4 m9eter 0.0800 m mountednc6i2 9g 6ny5gm4mky n on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of f i33;llvvv(y 6g8e dqg., pi7e.awlca uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m movaf yp l8.3 gl;(6we,v 3ig.eivldc7qunted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Examplklx-l -xv73 zue 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are inu,ij ti:8f :os 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 (relative to Earth) does the balloon then move? What happens u8toij :s:fi, if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes 94awolt-y89 7gilgi e a bat and is popped straight up to a height of 55.6 m. If t9ol9ielgw it-g ya4 78he contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travelini ocrh1z:2wm 4lgbt6 4g 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 i7y)kp5 l:mw3b1oi xl hs faced with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worri5m plwi7 o 1xl3)k:hybed about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by +pn76byn2(ubdzb kw( pushing off with his legs from an 1800w u d(nbp +bn26kb7yz(-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are initially at rest in ss f9ae17m gu se)n;x8outer space. They then push each os)8sgx1;fee u79sa nmther apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elasti.igeo6i:qn+ c c collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its origi cgq:e6+nio. inal 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 wit 3h c- ltr7 ,zsa2;r:quwueh(gness in a court case involving an automobile accident. h lsa tqr (u7w;crug32,-h z:eThe 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 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 td**9w og6 k:xye,ukw2 btl4leotal vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontaleukg ,4 y:w6wbtd*ekxo2l*l9 part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg bloskqj.p1h*dp mp7dv1le + e-0 tck of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how h-1 th0lkqp7 dv msp+epd 1je.*igh will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35ren(t8sa8r m.v 9b3-jfpofe8 -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 i.fvps -rftbn3 m (ao88 8e9rjet 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 -9p3jgj fx.a4dleaa m1r: wcl(e :j- ma 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 w 4m.la--j:em3 a e:rfj9ldap1x( gcjexchange 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 abx0rp +/ mt.lj8qwngb4out $ 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 w;2dw yiyh r0h8aa fp; d6wn(9an explosion. One fragment acquires twice thf6i9w dpw02 ah;wr8dya; y nh(e kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F =+5qj4 vbuy uze 4fg)pxcrhc2,8nm5 g: 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 massesm/b(5h cwy8 k5ut)n5izdn7 nx $m_A$ = 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 acwam/:txr lc5l*ssiw j,m wza w:9 p28wn.5l2lpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particlewrsja l:.w t5l:w2z *is 8m/n,w 52cpcmalx9 w 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 ang4gmei+ll74u-u c2j0 w late2a le 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 slides downrmi:k1 s72 wol 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 l1 0 (ixq:1szqg hs)ey:.ptxzqimit on mass m if it is to rebound from M, slide up the incline, st (yqqqi110ges)h.zx: :pzsxt op, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure- lz,qo ,v8*wc)1w -sumrhh ce 7–47 shows the planet Saturn moving in the negative x direction at its cwh em8u qr z,clsw,o-v*)-h 1orbital 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