We claim that momentum is conserved, yrld3 tc:o1d+w et most moving objects eventually slow down and stop. Explaitr+3 lwo :cdd1n.

When a person jumps from a tred96 n azp7 dsl6e2z)88ln dgwc;3aitme to the ground, what happens to the momentum of the person upon strikin9wm)ezc6la7zl8g 3;dd pi6a8 nnt2sdg the ground?

When you release an inflated but untied balloon, why does it flof 8v-6-vqiil0tn l 4ty across the roomv8l v4q6on0l- tf-ti i?

It is said that in ancient times a rich man with a bag of gold( i.zx)tc px4go4(z mb coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push 4.c 4mpx(z(bi)ztoxg himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is fa qvx vva0i.++cr out in space and is essentially in+x0vca +iv .vq a vacuum?

According to Eq. 7–5, the longer the impact time of an impulsei5j1oyu8dtr:a po(- w, the smaller the force can be for the same momentum change, and hence the smaller tjwidtuypoa-81( : r5ohe deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstan eouu;k1uehuoep1 ( :0tz0 o j4i:dh2bd collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this new 0teeu12;0hjdb1ooku (zupuh: :eoi 4design?

Why can a batter hit a pitched baseball further than yk yzf1d4:8oq0 c,bx da ball tossed in the air by the b8 d :yq y1,40ozcdkbxfatter?

Is it possible for an object to receive a larger impulse from a small force tha1rxn (7q+voj- 7opq:ootot7 an from a o j:-r1poqtqov +7(xn7 t7 aoolarge force? Explain.

A light object and a heavy object have the same kinet+/fib/jxlg7/pn8 i dmli3h h, ic energy. Which has the greater momentum//+hlixdjbi i ,lh73p/nf8g m? Explain.

Describe a collision in whic5)+*cb*e uh 6tgxk zbwh all kinetic energy is lost.

At a hydroelectric power plant, water5mbd;s3c+f pq is directed at high speed against turbine blades on an ax q+msfdp; c3b5le that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at iygil p+ky182.oir3z gwdb63a 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 heigb;6 ib eks 60h6buvcf/o p6l.wht h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of 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 th f6 6o b6.s;0lc6/wvubki ehpbat falls and sticks to the steel plate.

Why do you tend to lean backward when carrying ani,r6bzr0/6 1m ejz hs(0xd qa heavy load in your arms?

Why is the CM of a 1-m length of pipe at its;7a;lxgbc v/h mid-point, whereas this is not true for your c/; ;v7lxahbgarm or leg?

Show on a diagram how your CM shifts whenqup4l,)n sp.m you change from a lying position to a q lp4)pu.sm, nsitting position.

If only an external force can change the momentum of the center of mass of ap 3v(pi,k7rx en object, how can 7ripx(,v kp 3ethe internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes into many xjls00; c-zbi;t s:yivmi,+ kpieces. What can you say abo c iiym tbsi0s,;kx:v; zj0l+-ut the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-gm,pw;na o;mm35h y4f)-ak:j )yefx0s cxm(v z sparrow flying with 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. Whax.oax j 2ld*:.jr+f vgl/. kept is the skier’s change .vx.lapd o.rje/fkl +:*2jg x in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive straight67u kx04m7f aj,trq,h1h iv qh back toward the pitcher at 52m/s If the chaht,h u0mk4fqv1 x,77irq6j ontact 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 packj+* l1 raxh4cjage out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. +4 jjl*crh1x a The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases ; t(,c 1wdeuyaare expelled at a rate of; u1 d,ctwya(e $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving atsjcy. /ut 3)vf $4.1 \; m/s$ 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//qdsq*y kom-w71 fplql,s l3 alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially yw7o/k l,sqpf-ql* /md3ls 1qat rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling arl)789sz68pmichx4 um 8 b tfrt $15 \; m/s$ 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 horizon au0io-u+9h jbtally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the 0- ajubu+ih9o wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed ofjh0ihs3yf/3m c .d) xu 8.6m/s on a levelyx. )/ chdfiu3sm3j0h 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 the car after 90.0 min?$\approx$    m/s

  An atomic nucleus ini8wia)kkun03 qtially moving at 420m/s emits an alpha particle in the direction of its q ku3a)ki0nw8 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 the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230xnm xg(h6 pa:duk,q/cw-p: gz:32pu v.*lz cdm/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a f 6k cvl*gp:z(z ,ua/p:uqd wh.g23xmcpd nx: -rictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a9b+ lkpu:fz*i abzgo8hs pao*t0(1d + speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a 2bt ralo61ofxt2,.,n ilz c 2rvelocity of 115m/s To alt 2.oz2bl2 tl,ir,fnac t61oxrer 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 speed of 45m/s The golf hvg6-.yx2tzxk9: j tgclub was in coxh:62.tj vzk9 xtyg g-ntact 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/p7)esn xm5nrl6 h*l9cs and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the na7e mhrsl6)p9nnl5* c xil?    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 w+s+ee9 b2e4jkc y48mqeiwx0ball 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 1mclbo+1sf1)z ys+cm charge of the crashworthiness of new automobile 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 )sc1+lf 1ozcbmsy1+mthe time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in 0.75 s by a 2lo qvjhc;p ,rv3j ueuaaa07 w9q743ghead-on tackle by a tackler running due west. Caluuawqal 9jv7v2,p3ja 0e;rc4q 7g ho3 culate
(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 ten7d4jvi zqyo5( k1a;pj nis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods ozvj7p1jd akq 5 (yi;4to 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 75t+s c*ay j4(yxj wu*r4-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of ut cax*+ yrs4(w4*yjj0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (igc 76mry +6auj9l4w z+x direction) 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 of each ball aftem7j6cy4u rwga6 z9i+l r 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 spe2cx.u4stw - cued of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 4c.s2u ut-wcx0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equuj-rm mvd0c1kq , p7j)yp4nu0al mass undergo a perfectly elastic head-on collision. If one bak00mupmpq74y,1ujj-v c)d nr ll’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 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 w sjzula 3n2i0d/a(7 kxu 7mfib y+a(-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 perfectlyli sf( u3 iua0n+/ x-zb7d w(2mkja7ay elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is movikx,zcfx.xje/cgu3qx7 1 a,4 fng with a speed of 8.5m/s collides head-on and elasticx7f f u xgxe13xa/c.z,cj4q,kally 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 approache*8oj ttorj zh f/k1lm5e-3p7 zs the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and carkolrtf/oz-5j3 z7p e m*ht j81 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 se( qe n/dvq0r.njg thvvmz385+;vmm5v 2qle y3cond ball initially at rest. The second ball moves off with half the qg0 h5vrj.n52v yvz;v+ v3e 8(lm3 nqtemd m/qoriginal 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 vkm3p77m8motg 3p.q2zva 7eo incline as shown in Fig. 7–35, and elastically strikes another cube at the botpmt3mv. 723o ao7gkzmq87e vp tom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case/vquu 0*t1hkb ) k :nes)9jjox of 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 penduy4aiqw(utc 2i/hlp6 db: 8: pjlum experiment, projectile 1 results in a maximum height h of the pendulum equal to tip6b(p:c i lh4d yq/8auj:2w 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg pe61 x2 zkazb3 lr*3uwsp m)vr+dndulum hanging on a 2.813u dz)s6r+2warzb l k* 3xvmp-m-long string, which 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 f0f59synjiw h 2rkj)o7raction 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, into two pieces, one sf ssi 9jq-ljw*3d2r4of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic ene* 23sijr4fslqd9 swj -rgy 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 stoppedoi(ryqo 57np . at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic frir pno i(o5qy.7ction 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 m and rebounds to a heightw+ 7dy 1ji nuu(hpq .801ufzgr of 1.20 m. App0 j z.rpu87gwud( +u1hyfqi1n roximately how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity inw f b7:s5dz: tmpysm -h-o (8ng0xrq7k a head-on collision of two objects is the coefficient of restitution, e, defpzb:8dys 5m mh-sxgft(-r k:7n0 qw o7ined 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+c bc 9,*tkxi5yqy -1h2bkjatk*jm u*bb/5xq, one with three times the mass of the other. A depression is made in both facbctq ,+kyi kc9b*q52ya5xj k/1bum- b*jt*hxes of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5. gjp: uv3osqd-*agvl4i 94e sm/s collides head-on with a 10.0-kg obje3o i-elqujvs. 4g9da4:g ps* vct 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 intrw;bs1-i*; erizle0fix)k1 fo a second nucleus, an electron, and a neuti0ewf1f1* ri-zs r xl )e;bi;krino. The 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 bc: (ud*l5tmmft84-l nkn1ju30 ciae $m_\mathrm{A}=0.400$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 ;glb7dx jki* 4two objects of equal mass, each having initial j*g 7bxd k;il4speed the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right an h),w-jrn fp as30f1aot sbc65gles and meet at the origin of an xy coordinate system. Ball A is moving upward along the ywahf)6jpnrc-bf3a, 0st 5 so1 axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (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) makeso :3h bjx-/ts.wixz3:t njn(lh(7hmm a perfectly elastic collision with another atom at rest. After the impact, the neon atom whb(n hi-tjm oxt37. xjs:mn:3( /lhztravels 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 i*m0,qhcjrry3hm0,dh3r l7dpln- r* elastic collision with another atom at rest. After the impacr*h,i3y p, 0mcdjh7n r d0lq3hr-l*mrt, 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 th5hg;u(igu 41 +nkgnmue three-mass system shown in Fig. 7–38. Specify relative to u+khn;5(ng1 gmu4 u igthe left-hand 1.00-kg mass.    m

  The distance between a carbon atom8ug cw (l+6dhaym*o a6j2w3ss ($m_{\mathrm{C}}=12\mathrm{u}$) 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 behiwmx1ts/xqzd6 ) kp ihv)f6d 7,nd 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 seat7)md),ifth zqkx1 6xdp/v6 w s 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is usew,ad uh5u w(+yap954ziw1y zed as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, detezaewaywu+ p1 y 54,9ui(zwdh5rmine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides mz*8jgm6va pnkdl 1;,$l_0$,$2l_0$, 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 pibv0fc1 )+g 4cddp.; z (vaiwdaste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load w i c)d1wdzpvg4i0;avf. +(dcbithout tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of; s)+qc- bmmvk/zyx,oc+ds,u/q o4q b radius 2R has a circular hole of radius R cut out of it. The center of the smaller c /mx zvy,; +b,-/oqso)mq dcc4u +bqskircle is a distance 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 Tabr9hak6je5i 1iri1 eb8le 7–1, and calculate the massk11beahi8jei ri56r9 of one of your legs.    kg

  Determine the CM of an outstretc/qlf6e:a pxw9hed arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the pospfv )zah4r(:b ition of the CM of an arm bent at a right angle. Assume that the person is pfh4 rv(z:a)b 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hang+kg7 x p 9h,ucsti/oj5ing vertically, and his trunk and head are /5o pg9+tu ,xi7kcs jhhorizontal, 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 Earthb e 6b7k0gaem7 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 qbgs; 1:3 apwrqon*+ gm apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diametere4idk p4as*b 7oo0+ob 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and 07o4doko+b4sb* iap elength 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 a uniform ,d:h fv8+g *splihiwx i/65zowlc,;g cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottomwdifo* i z:lx,,5pi/w6g+c ;h g8 lvsh of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14*i2z5 p+ckpwqq1utw, (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 gondolymh,lbn+ d:b08( j jsda, of mass M, are in the air and stationary with respect to the groyd db0 + nhsjjbm(,l8:und. 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 if the passenger stops?

  An 0.145-kg baseball pitched horizontal/ z nr f.(f.zkg1p)u+vjao:o rly at 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 average force on the baln(j.:fz1fv kog )poa r/ru+.z l during the contact.    $^{\circ} $

  A rocket of mass m travelf *mr1z 0y1c yte.,-(pqlio/ p xx:qiqing 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 is faced with the coq4;*ec, eos c .enrmu:,t*m pdrner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also rm,sp*e cun .dt,c;q:4 o*emefall into a pocket? Give details.

  A 140-kg astronaut (includ/)ky wvwp.wd0:w4xifa s7x u;ing space suit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-kg spwiy:;7a4s)wwpwdufx kx/v. 0 ace 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 k 6a/lq/ b5fj:kbyrbo; g and the other 80 kg, are initially at rest in outer space. They then push ebj6 o/ay;:/5 qk lbfbrach 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 c w. +lhy9(rvt+8gwysby/pma 3 ollision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original sp. 3pr8t(+9+yw shygbly/avwmeed. 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 ing/ sik:usxnfp w)0.ldjud;))lx i.( h a court case involving an automobile accident. The acclusk.up)/whxg.d dlf)j (0i:i )xn;sident 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 stea dn,z,9+nuxp b6d z)2zh,+rvtf7nr vyu c;g;ps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the b,z nxdyvp t;f 2n+d,v;9 ur+h,nu6rbzc gza )7ounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest directly abov/7kgck pir8*ymr.r8 c zq8 4eze it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes emberkg*pr 8yk/m .8zccr7i4zq8 e dded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood placed on3i , cmfyf l.e-cldb6ct-k ;f( a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.2 -f tcl k(.fycc;mi df6elb,-35, and the impact drives the block a distance 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 and the o we3q 8b6j/cfgther 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 jqw b/8fe3cg6the 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 a6o.r/nx je+pxip- x *wbout $ 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 fragmkcsn 86gm) q)pi9fj3 cents by an explosion. One fragment acquires twice the kinetic energy of thejpmsg6 n9c) 3cq8kf i) other. What is the ratio of their masses?   

  The force on a bullet is givqzr k)dx6, yvv2y01cfen by the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses ,rfqzvv*hvhsw. 3/ 1 f$m_A$ = 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 a w0iutc kn2.6yn alpha particle and a smaller nucleus. What will be the speed of thwk2c6 u .ityn0is recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay targe gn:ky gjntf88 57zox.t) is fired 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=2.2kg slides down a 30.0ui5 . 1rvgku(: ia-qkv $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mass m if it is to rebn1l) 4vd 2i wy ,.pi8cisjcj,lound from M, slide up the incline, stop, slide down the incline, and colcijv1 pljwl28,in di. sy),c4lide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figx tjb0qj:pz9* ure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the*bjtp90jx z q: 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