We claim that momentum is conserved, yet most moving objects eventua5*u2hi6c hbx5c g-eodlly slow downdi*ec5bho5 2 xhgc6u- and stop. Explain.

When a person jumps from a tree to the ground, what happens to the momenajmrh-k7) ksgg-ea 164:o 2jcr no1ry tum of the person upon striking the 7nyg 1):ejhks-crj1 roma 2r -ak4o6 gground?

When you release an inflated but untied ba8jc 8 y,zpv,zxps6qf ,lloon, why does it fly across the room,v,8jf s ,y8z6 pqxcpz?

It is said that in ancient times a rich man with a bag of gold coins froze t; kcrlttn82 .x7 c/pqfo death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. W/2pl7cn;qxkc 8f .r tthat could he have done to save himself had he not been so miserly?

How can a rocket cha (y myppl88mi: e.dhvj b(/he,nge direction when it is far out in space and is essentially in a vacuubmdm:h8yphe iv (,ljp.(8/e ym?

According to Eq. 7–5, the longer the rd3d gg lr;d z)p(3k1quyr*s4 dj+ z+oimpact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the objectd pzy )dg( 3dz r+4d;krqlg1rju*o+3 s 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 collisions. Today, thoug;kgsiodl49 qag ,nr )3h, cars are designed to have “crumple zones” that collapse upon impact. What is ;ir, gq3slgd9k4 )ano the advantage of this new design?

Why can a batter hit a pitched /w6 s7qmu6dyow2 hm d;baseball further than a ball tossed in the air by the/so;2wh66 d ydm7mu wq batter?

Is it possible for an object to receive a larger impulse from a small force th934/epocphw b2zpsc,anp5 y r3m o-2z an from a large en,azs4hp o p2/3o y2pc-pz95 bc3rwm force? Explain.

A light object and a heavy object have the same kinetic energy. Which h0hf5 x7cns6 m50e)ak(szpltp as the greater momentum? s05 xn )a5k(cemzh7ls6f0tpp Explain.

Describe a collision in which all kinetic energy is lostpo 2qm+ysa; bae.5,jr.

At a hydroelectric power plant, water is directed at high speed against4is8i7c(l mwwu 6 elx. turbine blades on an axle that turns an electric generator. For maxieux4.m8liw 6l(csi w 7mum 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 wal8oeye q kg8 ykrgp,.f6o :+wy1l 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 hard steel plate (fixed to tpa,srlle6u (: d9,ndcmmn0 i:he Earth), from which it rebounds at ver(,nr,0pn9 las:du:em m l idc6y nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in y t2/cuud /rlbe,a o,.tour arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is not tr3 jusb:r h(ff*ue for your arm or l rj:h* f3f(ubseg?

Show on a diagram how your CM shifts when you change from a lying position to a 5ry i:uxc056 sob3cbositting p6xicb3 5 0oro s:bcy5uosition.

If only an external force can change the momenty1 j.cr rm b.+b+of)nlum of the center of mass of an object, how can the internal force of an eob+rl1bj.+r cnf. ym )ngine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes into 6 v uk5/-)si.cero l4dxy0u nemany pieces. What cad06vksx ee4/u.l5 co)ru-i ynn you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow . fx/q2r;qzki flying with a speed of 8.4 m/s r;. /2iqkfzxq   $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. Whau5i4fnoj a+1r k;fp7ut is the skier’s change in ao ur7p1uf4 k+5fin;j velocity?    m/s

  A 0.145-kg baseball pitched at 39 t*r :-uh6nwh nn2qkjkr;i x(8 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time between bat and *rrqwnn k(tu:nh8i 2x 6hk;-j 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 of 8kerz9k d,ct) 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it wakckdt )9r8e, zs 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 propelling gases are exp 5oi2o-uv :lxg:jo8- ate+j:dxgu k*p:t1fft ellejdg x:8uiovfolg:j 1 o: 5a:e *+2 t-ftk-xuptd at a 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 a,i*8qi3hhmm lpparent 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 immediat*l3h mi,hiqm 8ely after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictionless track with .,osej :/ylvzz :0eq2o0yzpza constant speed of 18m/s A 5350-kg load,initially at rest, is dropped ont 0 /zlq2esz.yeyo: p0vzjo:,zo 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 rest.-53a j hzphqqbfo5u 9xsh3d93 The two stick together and move off with a speedz h-q5hdo9q3x9s3ah5pubf3 j of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speeds of/o4l3eqq zt 5r 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 perl/ qqo3r4t z5eson. 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 alopcb.w w5 5yqk+ng with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car b 5pq5y+.wkw cat 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 particl12isxj 3jr3fe e in the direction of its velocit 2ej3xfijs3 1ry, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and emerges rpajb3(d r:;dcleanly at 170m/p3ba j;rr( d:ds If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speeq)avjnc7f 6 6zi-kjufqr 7 84sd 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 p9, 5gp 4klqwatraveling in outer space with a velocity of 115m/s To4l5a ,qpk 9wpg alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a spern0 4,8bel ogmed of 45m/s The golf club was in contact with the ball 4 merlbg,o08n 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 comes0v7:o7 )q .y bqgqxtbl to rest in a time interval of 8.0 ms. (a) What is the impxqly.7gbbot :)70q qvulse 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 -0; tgh v01kieuu+mpyll 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 jztv m*0 2s;e8qxm :awof new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 150vmz xesmqt2:a;* 8j0w 0 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/ ln+ / f 3z);z+di9di)(hmaq)bs tzkwrs to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Cm+rl w kz zn9d; s+)( i)/i)aqhbdfz3talculate
(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) porgn;a zo5 *g4sints in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Us rzggsan4;5*oe 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 brea8danivvz m/v1u g,(rq9fki: .d 8bv)aue*)m nking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m d*,fi qv:1a.u z 8r(/knaviemg mnv bu)d8)v9from 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 di2ka2 gr0w r4zerection) 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 a4g rwe2kz 2r0and 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 heaj(pdv.jmx+6) /ruwc e vndn(2d-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 covjjx/d nvwmre6.( +cpdu 2(n)llision?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 efl ry;f)k qyxo68 :m+tlastic head-on collision. If one ball’s initial speed was 2m/s and )8qkym 6;l+trf fx:yothe other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 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 with a27;;gq o8 afwj hsjl3l 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed algl7q o s3 2;jwfj;h8and 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 iv h7ctwp:cc w:h969a-u 4maw8.5m/s collides head-on and elasti :i huhc67 vt9cw94waw-:acpmcally with another ball initially at rest. 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 apx :/le: wee*q+7vru3: qlcsuhproaches the other directly from the relqu qw/ *xruh7v:e es3l :c:e+ar (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 ball iy0npjj oc:re5m n6cg45zo c4sj2vp01 nitially at rest. nm 1 z40cc0r5 pcj: oj6oysvp4g5ej 2nThe 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 frictionnvjt ;gldpr7 .y. s59mless 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 9jsm5nlv7.dg.p ty ; ris 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 ofk c9.v:fhexr+xxc/k/x, 4um x an 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 experiment, projectile 1 resulhk 9ph/ i(gl:uts in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swin l: gkuih9h/(pg 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 itsljj5df w8urb0 8z t,8velf in a 3.6-kg pendulum hanging on a 2.8-m-long string, whbu5jw z8j8lfv,t 8r 0dich makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic xl(t;8t+vxcrhne7 :r 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 obj1f.ynd3kt9ozp07 cqlect, 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 apoy 0q7f39z.cklt1n d cquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car coll ;a-2cqodol *qides into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police offi-o q*;qo2a lcdcer, 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 frw+ (fga+;ktj fr e+i4fom a height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many re+gtk+4i ;rfjwef+ a (fbounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the j4/m: bel vd4jyl(h x2coefficient of restitution, e, definj hydx:el2v 4(/lbmj4ed 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 wi pp orcryw k4s785j2m(th 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 reassem7( 5c4yjo8wrpmsrp2 k bled 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 ir *4kogtsev5- n the +x direction at 5.5m/s collides head-on with a 10.0-kg objectesk g*4-v 5ort 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,;abn nbbic+.z- sd *end a neutrino. The electr bn.-za*; beis d+bnc,on 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 m8u6 pmwt+:ew;,f poibeu6 ga 1ass $m_\mathrm{A}=0.400$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, eac h2yfb,w* n4pwk;rn/w ; t.5tt3fh8zy0 qf mywh having initial speed the two move onwt4/f2w n y03bf.,mq h hpy w*;5 z;rftykw8tff together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move liaab6 df3;sf no e,/2at 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 to the right along the x axis wisif / la6aeb n,f;32odth 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) makeyhd vmv2lqg0loba2i()r d4:i )2t 7kjs a perfectly elastic collision with another atom at rest. After the impact, the neon atom t:dji2q 7lb)2o) g 0rdl4 (aykhiv2m vtravels 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 with another atom at .i2j(zkb lzarspio / wc12*fv r o08i)rest.po f * izswl c21koi0v28ar z(ijb/).r After the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mop-6 0m9pm57hmqg nizass system shown in Fig. 7–38. Specify relative to tho -90zmqhpg5 mnmpi 67e left-hand 1.00-kg mass.    m

  The distance between a carbon rou;a*s 5l5me9l08q1 z qmdep0bmln6atom ($m_{\mathrm{C}}=12\mathrm{u}$) 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 105 iv3h)gmj pko+55m8kh -lhq: a0-kg car is 2.50 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0)8jh q+ :5kmg-al o3kh5mv iph kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is usedpig)n,1;g;hl p :qvid as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corne1p ,vplnq i;;i h)dg:grs, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides;jmlc 6m wyc8. $l_0$,$2l_0$, 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 identiauugm - s)y95 h0.lofqcal 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, so that theg0lms.h5uf )q oy 9-au crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole7 x ;q1p-mjqfd/ ft4 mtua(c0b of radius R cut out of it. The center of the smaller circle is a distancx70tbmj -f1;dap t(/fcu4m qqe 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calcue r 7tlekg9h afb/2lsddsa 5,ge20y) 8late the mass of one of your l edke9tse0 g/ g,bfsha7l2l)8dyar 25 egs.    kg

  Determine the CM of an outstretched arm using Table 7–1bn46e ey5r 7ew.   % 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 a. v hz8:9px6u33 gmxfbow0apat a right angle.6p3axbp :.9f 8 0uogzwmxavh 3 Assume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are han.bwolpxz7 jm1 3p0m:n ging 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 bodmpjl.o 3zn10 7:pw mxby? Use Table 7–1.

The masses of the Earthtnncpq2ro jdgr. ;/drd 09. .z 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 frictionlecxq ;vlml;bz )-)1kf zss 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 mg- kp4 ;3jn9vp3sd+d os guou,ass 2.00 kg and a diameter 0.u3k9p ;n-4 s,+sp3jguvgod do0800 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 bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of y) 5o1md 1m 6i/fesnfza uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounn)osy /1fmfd e5m61zi ted 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 Esyal6ub6k )ke 6l7l9wxample 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 in the air and:1au.xwjh/ 3iiwo i)p 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 speeoihxw. jpui/1 3)i aw:d and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally yf r:4wx.zao 7at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the ave.4: w7y ozrxafrage force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling wicp* om; unbjgu+5k+-qth 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 5r/92sm.kk h u hy2kdais faced with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cu udm92 2yhk/kshka .r5e ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/sw s*ow//;4okjjmue* f by pushing off with mf*ws/jj/o k e4wo ;u*his legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg ) ivodm/* /sfpand the other 80 kg, are initially at rest in outer space. Theym)* f/s/ivop d 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 ch:6oroh,re2 tsx c)6eh,cjh6ollision with a second ball (at rest) and rebounds in thes6rhe h):t6orh chxc,,e6oj 2 opposite direction with a speed 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. -fais98 tpdp 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 slid 30 m. The coefficis9i 8p.df-tpa ent 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 9)gbs*z8 a/ufr8psinvertical 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 heightfns 8igaruz/*b )s98p on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired verticallyk5 2xcngjl w4 mbp qd6+:u5ml8 ek+wj) into a 1.40-kg block of wood at rest directly above it. If the bullet has a mass o mx le kk5qw+ud4+mpn8b)wlj2j 5:cg6f 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg blo; rs do9(df,crck 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 (rfd9od scr,; of 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 ao g *,;qfzwg4and the other of mass 60 kg, 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 direction will the fgw;*oa4 g, qzboat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was about -q/k: )hlz vbclto(*mq:b+ye $ 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 sudden :j tmrcvcf(ld*5r :i8ly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratictm 5fj:(v:rl rdc 8i*o of their masses?   

  The force on a bullet is given by the formula F = 580-yjk4z.ol1 znge h,gjx;cs 7-+( $1.8 \times10^{ 5}$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 dj4hr6/,f jgn $m_A$ = 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*jg poc;f409tnovnz 0 and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed o*f0ogzc4tnpn0 o9 ;vjf 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 30-4t2rpvs0jnuy0uo9 l $^{\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 dx o9:*0xqzgpforyv0o 3cx2. nown 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+vp 7u-zte4w t is the upper limit on mass m if it is to rebound from M, slide up the incline, stov+ze utp7t4- wp, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshbici9+ 9).n d2vb9qexl6om u iot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s ii q9 ubc l99imdx.2ben+6)voThe 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