We claim that momentum is cy;ut;/ myi7gq0k gz9yonserved, yet most moving objects eventually slow down and stop.7z9 ygg u;im/t yqy;0k Explain.

When a person jumps from a tree to the grfp k +*tz0i9.4:4 orrt op, c3lddk.edqw6vpwound, what happens to the momentum of the person upon strq 4v fdpp:*4p3kcr9otlwd .it .eodk0+wzr6, iking the ground?

When you release an inflated but untied balloon, why does it fly across thetw2qa1 h*a s; zh mm8d*ha0(pr roomh2mh*r 1mzshtp*qa8waa d;(0?

It is said that in ancient times a rich man with a bag of gold coins froze; (mwtkg ;r*hh to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself (;rtk; *ghwmhto shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when itgjmznm / z54m,.0yyrev 8+di h is far out in space and is essentially in a vaiyzhg/v m8 5ed4,z .n0mmj+ yrcuum?

According to Eq. 7–5, the longer the impact time of an imp-l ,2 ne8japqoulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the qjlpnoe-,8 a 2force 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 ,u: pt/fi+4fxz ikjre))jo1mwithstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this new dej r/im)f1 )px+4fzijokue ,:tsign?

Why can a batter hit a pitched baseball furthe+f *meqfsaw s ra4w60df0b4 1cr than a ball tossed in the air by the batt+was4e qr0 ffsc 6am0d4 *f1bwer?

Is it possible for an object to receive nch7ocj:kr/r : v/(sua larger impulse from a small force than from a large forcekvsj/nr(/ c ch7uo:r: ? Explain.

A light object and a heavy object have the same kinetic energy. Which fqn5kmsyveb -hxy ,8(f)nn 25 has the gr)y-y ,n5 b8x2hve(mkn sq5ffneater momentum? Explain.

Describe a collision lvc;v6+rjn o7cdd.v w.45 uimin which all kinetic energy is lost.

At a hydroelectric power plant, water ijzp*tpwc7( k2z m ;k0ns directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power jp;wnm0k2z*ctp z k7( generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at y j9:43tr/lyp (y3r:vpu schx a 45 $^{\circ} $ angle as shown in Fig. below. 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 phi2 q9 yk0x9nt3b 8qrflate (fixed to the Earth), from which it rebounds at very nearly its original speed9yi hqbqx tr082fk9n3. (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 carrtid:v*edg x5+h,fy,pmh gv )5 ying a heavy load in your arms?

Why is the CM of a 1-m length of pipe atk:q5cfke 7+ ht its mid-point, whereas this is not true for yoh ef 5kct:7qk+ur arm or leg?

Show on a diagram how your CM shifts when you change from a lyiz tj jz*i07uvx3k zm9,ng position to a sxvz 3t7*zu,mi9 0jzjkitting position.

If only an external force can change the momentumj9v)vyq6/duv*td d+. sfpl a 3 of the center of mass of an object, how can the internal force of an engine accelerate a car?ldvd+ytj.up 3)/a f*6v qs9dv

A rocket following a parabolic path through the air suddenly explodes into c j.sm f.o-nfhe /.go+l/z6g bmany pieces. What can you sjch .neg +fl-fm/ ./.soobzg6 ay about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with :l.na9cu1gmeh/u h6 0thgm xjn1 m3p)a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. Whak* + 1k*,zh6 ywi on)x0lgfr zq+vp.gqt is the skier’s change*rnk1y6x*) pl gq+f,v0ok qzwih z.+ g in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal et wiftr1 s-zvp*5x*+ line drive straight back toward t+tsrf iz*1xt ev-pw5*he 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 o6.0ahi*-ir h saj/bg n14xoskut horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest*io sbi 01ah-hj/4.rsk 6 ngxa. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rock5cq03kndf *mmzd z4-cet, given that the propelling gases are expelled at a rate ofdmz dq3 m-0nz 45fcck* $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving aqs 8,3chzz+ ,xkkyk*tj 5s+idt $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless tk*b wjopk54cctm0v61rack with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the carcjv 10o*kck4t 6pmw 5b. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelifw/ sksf /sr -08wmsg:ng at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of 100km/h If )j5k vbk)17ecmlbtj1the air strikes a person atkv1bbc m1ktlj5j)) 7e 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 cons- 0wu3nj cfo8ltant 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 is the speed of thn0 8ou3cl-f wje car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha pa py+agwnyg)zc7j 5i .;rticle in the direction of its velocity, 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 c.wjg57 n+i;ga)yyp zthe alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood yooro: mvao 6(.(zy r,9k1qfl and emerges cleanly at 170m/s If the bl o:fz (k(1yq9lv aooy.o6, mrrock 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 tra8z 8f xnj ;2z8po1trslm4o4usveling 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 outeow(ml2oa( d-l 7jxfo9(yviu:r space with a velocity of 115m/s To alter its a2f( -7yxdlmiol:( juow( ov9course 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 ateh81fd,.tz.i -.vqeu8h ypwg a speed of 45m/s The golf club was in contactthyp fq8ed-eug,1.h.v i. zw 8 with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and yc v6nce3lp v2 ;zs6 :+ck-ekxcomes to rest in a time interval of 8.0 ms. (a) What iscl6-:x6ecenks c 2y+;vk3 vpz the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes 0 (pmo eci6*2brio8wn 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 6mgesqt.pq l*jooi7-63 ks gv-esn 52of new automobile models. Cars are tested by 6s-etlk * 3m5p-sqggno7e vsq. i6o2j 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) 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 atff8 0f(09kh zcoaka:db 0i 0yr82mb xf 4m/s to the east and is stopped in 0.75 s by a head-on tacklf8yk0z(foi acrbx8afdhb9m 0k20: 0fe by a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) poxkz/gbbo: ( (svb-t8o0 grv+xints in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical mgo+otbv( 0 :sb/x( zxvkb-8rgethods 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 winmmhwqb ak y68w+a+7h2kel5)v ai+.a thout breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of boa8lq7av w2hi +)eaam.+kk5bmy w6n h+ne 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 collides so)yn w0g*.qo 1d4hagv3paa3 head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each bal3q aogw.h 1pdyagv0as n34)o*l 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-on cb.9lojc0n:* zi mmp 1*8y qtleollision with a 0.900-kg puck initially a*.198q :mlncozmpy l*bit0ejt rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo en)a arow4o sal; mb7urs4)(y5 g.q*pa perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent4wab .yur4gae;onao q pm(*)s)r5sl 7 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, movi1r,z5hqzd v6 qng 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 a perfectly elastic 1dr5zh6, qzvq 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 withcqn):k bbe; 7q a speed of 8.5m/s collides head-on and elastically with another bab kb nqqe7c;:)ll 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 kud3 p;:ao/qdpark ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a md3quk p:d/ ao;ass 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 (g 6p,tsgmh.c elastic head-on collision with a second ball initially at rest. The second ball moves off with half the oritmg6h.(p c,gsginal 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 s h5 3r1g i9i2lz5gprwin Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 ci2g1r39rhzi lp wg5s 5m 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 objecj8q*o)l+2 m .i m iim lf fg8j/27kve8a+mmjuht 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 results in a maximv4:*ler4:s sw ly0lcxq 8ef4w um height h of the pendulum equal to 2.6 cm. A second projectile causes the thexw4fv ls0 s8relq:4yw 4 *elc: 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 t 5v 9myl-hrn8*nr2 uenraveling 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 the vertical and horiznh- 5m8*rvruy nl9e2nontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fractioj vi .dz 1uxajes 1:oafw.2-)e*o2zrd n of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, in 8vjw70sad wd3to two pieces, one of which has 1.5 times the mass of the other. I87 w3dasvd0j wf 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped af g2sjnvv: :*gt 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, cal* svg::2 jvnfgculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds t 4hyl0* 6+jqri wk1p7klp jf(no a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% l*jwqy n4phkr k f+7pj1li0(6of its energy?   

A measure of inelasticity in a head-on collision of two obelvna0 xl2ep vq 2z/u 73(x.vojects is the coefficient 2vp.x3u/qnvaeloz2l 0v e x(7of 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 pieces,0 0 ufkj53qejp1r9eg(tlw(g z one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can bew030fk t( gg5zprjle 9j1(uqe 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 direction at 5.5m/s collides h.dsfiiz 8( /ozead-on with a 10.0-kso(d8fz .z/ii g 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 decs u 9 1tt:4-lqzu/zt+-umgks z2ju5 vqays into a second nucleus, an electron, and a neutrino. Thu kt/z154ug: u-uq+ sz- 2mqz9lt stvje electron and neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of mass (;lt7k se )awzb/.b/ gcwrg)n $m_\mathrm{A}=0.400$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+ 0bf0 vuaghp; objects of equal mass, each having initial speed the two move off together with speed v/3 What 0+b;v hpfgu0a was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles 5 3id3 e9unj4me:wvc sand meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis atd34:ene9 5vcj msui 3w 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What 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 p :go*kz w5+qco: 7yxdwith another atom at rest. After the impact, the neon atom travels away at a+: oo5cwzgqkdp: *7yx 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 atos7 moorq6nm78 m at rest. After the impact, the n8r7om s 67oqnmeon 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-massv8iejdt 80zyk 419ves system shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg mazsj81e 4idek09 8vytv ss.    m

  The distance between a carbon atomvkzc b:guvs -.k: /)p3vsv4m r ($m_{\mathrm{C}}=12\mathrm{u}$) 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 beheo0mcw;gegd +rbs2 2ta9 .v1 mind 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 amwt ;ad 2servg e2.g0+b m9o1c mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used asplw 0ycjwg7 4) a ferryboat. If three cars, each of mass 1200 kg, occupy i4)cyg7 lwjp0w ts NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides255 be ptiy-z.zmki 8w $l_0$,$2l_0$, 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 of tomato paste (see / 9 bpx2/ljzjbFig. 79/ blj x/2bjpz–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 load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a cir va.(:.+ ysg8u 4lfpy7mfbudzcular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from ( a.buzfm +sg7yfu.l:8d4vyp 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 thpj qa*kq -/w+zose in Table 7–1, and calculate t z/*pa+- qkwjqhe mass of one of your legs.    kg

  Determine the CM of an outstretched arm using Table 7–uk mr gn;t18q11.   % 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 right v*n8ic)26qbg n4 zoseangle. Aceb2iv nsz84nq g)6 o*ssume 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 h;wervxoe-i /*anging vertically, and his trunk and head are horizontal, calculate how far below the torso’s med-evxowi; r*/ eian line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Eagqh1t-go , cuseh8-i alo -42grth 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 a7gofx/ u2zpz5 part on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform 17ljz6yt y5mt6xn b h qevpq4 a28j28xc7s9dpcylindrical 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, sj8j8xpv7hem6b z6 nyx7s42da9 t51p q2ylt qcpinning, 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 - 5wj. r aofl2*aci5eta uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossc.lea55 j-fo2tarw *i ed, 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 Examplea,- -d59 zkpm0zh0zxf(jy p fj e n8c5lw9ec.f 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 :pz yasee6*w0in 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) doesp: e*y0azes 6w the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is poppe) 2vrkf5 tz 8hqyhye87d straight up to a height of 55.6 m. If the contact time is 1.4 ms, calcuzh8r8tk vq f)h 275yyelate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with g 4 :fo/miiiu3njcahk1 g,e 02speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot s *qv6gedca)(f;by*u vhown 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 willa( 6 vgdeb* ;cyqvf)*u also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) an2y8*ly/t.sp .k,bx wyhz)lb cquires a speed of 2.5m/s by pushing off with his legs from an 18 yk 2p,b.y).ywl*ztnb/l shx800-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 adv) ;vxeg )7i9hvnubi -vy:fi,f.a;f t rest in outer spa.iahy )ff7 g:9f;vib,id;-xve vn)vu ce. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second b dl/+s4ct*ix whz6m:o all (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mas/x6thom+ cdsil w:4z *s of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an experbvh*.d9z m70jkiol92uq i zwl01d*)l3 ze nnpt witness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B 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 applyin0dz9v3 u27* lzi*omlhbidj 0 .1)wzl9enkpqng the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total verti sp grg r025t/a1rgh5qcal height 4.00 m. The ball gt5r0g s 1qrr5ah2/pg hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a asse( rda/8)8hyh-(m ye w894gt q grv1.40-kg block of wood at rest directly above it. If the (( )ye d-ey48ha8sqrmw htagrg9v8 s/bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a k( k ,bi 5,k-u1lwumlb1.35-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 ibbuu1l,,k5 km-(l kwmuzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and th s/nt-u3svl a6e 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 sittingvt3ns/-6as lu at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abouocv 45v8lv;x/v /g zzxt $ 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 an explosion.6c-fr x::oi wv One fragment acquires twice the kinetic energy of the other. What is 6f:vc w:i- oxrthe ratio of their masses?   

  The force on a bullet is given by th j*2-g) w,klczdq2j jqe 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 masses - 11bq5rjp wee$m_A$ = 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 deca*fh5f3 plsvvtda; :/yys radioactively into an alpha particle and a smaller nucleus. What will be the speed of this reh s3/5v: ytp;valf*fdcoiling 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 firehatm 5g,+m f*a.()izba0 hnbid at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kleozym7+ll 8pj g i-j029c0zrg slides 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), t6)f(hrvi sa8y *ixb f89fz0xw ox 8m4ek :(yrwhat is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the inclif8izvof*48x ey)( 8r69 sf:xx wkhay (tm0ibrne, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 sh c3dc ; xyxvbhs);uw*i m.4x4x.-fq wrows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn i ru)b4cxf;s hy -ci4*.w q.dv3x;mx wxs $5.69 \times10^{ 26}$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