We claim that momentum is conserved, y+ma0 xj 9ehaq5*hk2ztet most moving objects eventually slow down and stop. Exp9x+ j5 e tmha0kah2q*zlain.

When a person jumps from a tree to the ground, what happens to the moi0( 2qlv(mh 6auhmsh;mentum of the person upon striking the groh0mh2 lmia6u (;q vs(hund?

When you release an inflated but untied ba3cpw ,rhwdg 28lloon, why does it fly across the roomww2dcg83 h ,pr?

It is said that in ancient times a rich man with a bag of gold coinf:mu35 e+zoz;n p3 5pye-dw ols froze to death while stranded on a frozen la ueme; p5o n-+f:z3zdlp5oy3 wke. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is 7-vsgjt1ty*z essentially iz *tjsv17- ygtn a vacuum?

According to Eq. 7–5, 2tc uut3 o*bv8the longer the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bag*u8t otv23bcus, 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, thh0fislnx9.9wn tkbq ,fi38w -ough, cars are desigh3isq9nf9,ixb nw0ktw-f.8l ned to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball ,dg x, (bi1cyffurther than a ball tossed in the air by fyc d(i bgx1,,the batter?

Is it possible for an object to receive a larger impulse from a small force t q 8se+-/fnc1q fv/g*n1wri ybhan from a large force? Exp -fqe8n 1r+snb/vcfgy*wiq/1 lain.

A light object and a heavy objectw0x x3blrcj x b-x;*5a have the same kinetic energy. Which has the greater momentum? Explaicr j0a*-xwb bx3;l5 xxn.

Describe a collision in which all kined zm5 csklc+9c2cx3ik im17 4dtic energy is lost.

At a hydroelectric power 3o.dq6-ryb yor;ivqw lj7n: ,12 xetiplant, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turl yqvoboi3:q2ji - ;.1rn drtx 6,ew7ybine 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 a 45l(*lkpqq;a n ku6gw025t; tbl $^{\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 or/ja aj- f d2ea*6/dwjnto 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 any2d aa*af/d6j - wjrej/ 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 u.kwaa gu9pthw592 o/ a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, n.r8tl+ohm 8sldcn4 7;vms o9 whereas this is not true for your ro sm4 n8d t7molh9;8nlc.vs+arm or leg?

Show on a diagram how your CM shifts when you change from a lying positi e77 s)24ftwexh*ncsb on to a sitti4w)ent2 cx7f*s hs7beng position.

If only an external force can change the momf7sok 94-vekfo2;6w geehb y 0entum of the center of mass of an object, how can the internal foe bgo k;-74k9v2 0shfee ow6yfrce of an engine accelerate a car?

A rocket following a parabolic path wg3jo-g(c::aulpp t g.e,v s/through the air suddenly explodes into many pieces. What can you say about the motion of 3lj.,ta(gpgv : -:ogups cew/ this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed of gis xwlecl;29b6( cg)8.4 m/s es ;lc9g(2 bil6xg) wc    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-j2gj5+p:c-6xjrgqf9sg q 4i ukg skier for 20 s. What is the skier’s cg:rgq5j9su- 6qfp4jxi+cj g2hange in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit oxisu )n+b et6;3 j8r.m b2whlgn a horizontal line drive straight back towar)3u+s i2bw. mh8e x;tlg6 jrnbd the 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 5hn lcu 0j:a)ja 6.40-kg package out horizontally with a speed of 10 m/s Fig. below C5n:0acjlh)u jalculate 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. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases are eleg.5+xw5 werkj32g f xpe +3gkf2ej.wr5 gl5ewx lled 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 j. mz:clnf.8l,. jlwkou9a5l on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual speed immediate u.k.znl ol85l :f9cjl,w.ajm ly after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictionless trac keb nma.qql)8p;q.j+k with a constant speed of 18m/s A 5350-kg load,initially at .p k eqm)nb+a8lq;q.jrest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar at reo41m4go-a:mby-yxvo.mc :q vtyt v*0 st. The two stick together and move off with a speed of 6m/s What is the:t o omo:b *v4y-m1q0mayvy tcg-.4x v mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at sbra 5e2-/:f ci7ctqd, e6aat usz: k)vpeeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to5 -du:tf:eqs) 2 atz k7br6e,ic/ca av rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant sp*c+56v*naxqi lr5m vweed 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 the car after 90*r ci5q5xwa+mvl v* n6.0 min?$\approx$    m/s

  An atomic nucleus initially movinefg./+eg/awu g at 420m/s emits an alpha particle 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 spef ewgu+ ea//g.ed 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 9dq,+bzm5v(s nsv vqvv7v+q1o; a5rnwood and emerges cleanly at 170m/s If the block is stationary on a frictmdrv 515 (9+ ov,nq+ a vvqq7z;bvsvsnionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling hftl; k97du1awnsv4ab,0pu5 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 outer spo8rid ltkq*tgvt . c(j31lg4/ace with a velocity of 115m/s To alter its course by 35.0 v* ok4tgq/lt r.i3 1(c8tdl jg$^{\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 Theye - 8nh zac-w3w3jzgucc*5s8cs51z t golf club was in-aenjcgh*s3 zt8c5u 3c-sz 5wy 1wzc8 contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a(rq+fn 6btp* j nail at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (q* j (p+ftb6nra) What is 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 strik-aj6 gg; rhseqdp 8,u,(v. gjc;g, ,lv.wig kxes 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 chb xy al xrd:7)6jwj z zi)ovmkf6h)136arge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50koz :) jl6fkazbvdr )1m6 jy ix6)3hx7wm/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 at 4m/s to the east and is stopped6 wk/7myxas* 4z ersqgz )yf)fwi-j)9 in 0.75 s by a head-on taz)zj *imxf krqwy7- /yf)4se9)sg aw6ckle 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) points ib.y, cso8i9u-iedo+1jap.w i n the +x direction and is given by the graph of Fig. 7–33 as a fuoi.dia+ y8 jue-,p.s 19cw obinction of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking hina 3 lp. bu-:u06zqhthe lower leg bone of either leg? Ignore air resistance and assume the CM of the person move06b n-uz pu:iq. lhha3s a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg movnb-xa9-sri, z ing east (+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--9xbanir zs, 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 auyfd-./ 8 5xz.lutz uiepnb(oep(1v+ 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 eachiz vuf(1 8yo-5(t/ +u px.d eluz.pneb object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastic head-on colli*6r wncxdj 1y7sion. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite directio76y1w*drj xcn n, 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 wivj:)vk* gj wtv-h2tv *th a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfec*t* v)kjvv wjhgt-v2: tly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s colz8r/b s:p. (eqs9wzl7jswmb 0lides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounl pmbz0 s:wqbesr9.(8j/7s zwces 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 co7bc0p3gg jxb3 llide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A appr 0jxg3bcp7bg 3oaches 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 balutr0d),( ksi v2s9vfpl initially at rest. The second ball moves off with half the original speed of the firstp2i9 dv(tskf)s0vu r, 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 shoz urs8-eq qf((wn in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontal(r qs(z8uq- efly.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an objectsgvb: w2a0k8l dq9)d v 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 maximum lez2 xsh3.q ;7b+hbn eheight h of the pendulum equal to 2.6 cm. A second pre; s2zeh qbbx.7h +n3lojectile 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 inii b8t53c a)yc a 3.6-kg pendulum hanging on a 2.8-y8i 35tc)icabm-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 fraction ofb8w*jk z:/g6lwtio8 r 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,u1 z9xx1kyr 5p2ihn-o 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 pioixxk 5 1-hnuz9ry21pece 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 sto 3p3os-brh1 g*k5jydqa(mtzx* pox2f- zm)j) pped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Le *o pmr*jz5z 3bm-1hqgp3o x- a)2f (tydxj)skt 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 jl.-yf ugq9 (3wna o3n3 qc,qaa height of 1.20 m. Approximately how many rebounds will the ball make before ly3.qo, q3n j 3gcaa(9n l-uqwfosing 90% of its energy?   

A measure of inelasticity in a head-on collisioq dfab(e l51qwg6;a4x n of two objects is the coefficient of restitu1 (dgxbq6laaeqw ;4f5tion, 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, one with thfw2) arbyv(xn, n h,)hree 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 wix2v (whrba,nfyh), )n th 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 56f2tw0k lo; eh1n0 yjs.5m/s collides head-on with a 10.0-kg object moving in the -x direction atyokw t0;f0hs6e l21n j 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 electrb3ig7 wrjgfn*2/c3 gvon, and a neutrino. The electron and*/b2 f3jggwc n7ir3vg 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- ru,c85t,w o* ghvbol $m_\mathrm{A}=0.400$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 objectnq1kqwmfg,8y7g u ;r3 s of equal mass, each having initial speed the two move oqq,1u kwryg; m7 ngf83ff together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and melw7- nhtus5i csq+k(6et 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 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 5q+s(iws-t6 l kcnh7u 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 with another atom ai1/t ( mlfnv 1f7)eubwuad)*at rest. After the impact, the neon atom travels away at a 5a wfidfab1v1t/l*e)m(nu) u 75.6 $^{\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 re8f1gzt;g* nvj. 4 epbust. After the impact, the neon atom travels away at a 5f.1 t ;*ngp4ubej8zvg5.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass seebepk (u lc8h/510k*,: ql nol rjdg;ystem shown in Fig. 7–38. Specify relative to0;nekc*o ( bh/kl8pj r degq:,elu15l the left-hand 1.00-kg mass.    m

  The distance between a carbonz9u-nlw,2m-*g;zv gja/qnco: ps b6f atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of the ca-85ptn-nlz,x jp tv 61y dh(har. 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 m,zh-x1n a h5d (jtn8vty-6pplass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 ktultiall1; 58 r26za kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SWu6 za5;tt 82lalr1ikl corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides xr*j 9 0c* vqx14httq5cob*ibr2 b*ag $l_0$,$2l_0$, 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) pallvn5qg.7 uq h6xet has a load of identical cases of tomato paste (see Fig. 7h76qv5ngu . qx–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 circular hole ofvpfl.g5ai 4 n+6,pzka radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate,zi+v 5gp6lfna4 . pak? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those7e wua r 6h 82/h)nfz5zcctrf8+uz1sz in Table 7–1, and calculate the mass of on)8 r/hehw f+sf67z8cza215zrnut u cze of your legs.    kg

  Determine the CM of an outstretched arm using Table 7–1. s7wlqux*sqyl7 u(azr( d, 5t.  % 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 ang8jl2 wm0+a+q* oy5ll;b qlshe le. Assume that the person is 155 a2 lws*hl5 qe yjqb+m 8l0;+locm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms.m4 6jow)(c-q dhpg/bou n,vq and legs are hanging vertically, and his trunk and head are horizontal, calculate how fargn wm -dq,qv/boo6 4(p.c )juh below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon c yl*rb ;ijf hv862o*xbqq8o;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 anz tdou(n1 6hxrr,4 dg) 80-kg man stand 10.0 m 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 dmni +cf e/i-/ziameter 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 ti n/c ez-f/im+ossed, 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 cylindrical head of mass 2.00 kg and um-ym*gsy(k 0a diameter 0.0800 m mounted on a (0y ysmm-ugk *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 Exam 0rz rog+pek01ple 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 rnfue:rddw9 fj .,7a7 M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and directi7 der9n ,fuwa:.j r7fdon (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at 8eh5nwev8k gqkk *livy)6/2jstrikes 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 6 gnqveh)yie8 kwlkj8v/k52* on the ball during the contact.    $^{\circ} $

  A rocket of mass m t-bks2u*5nx) s sauls5 raveling 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 cor 32hkqq2cnp t3ner 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 balp q2c3tq2k nh3l will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/70jqamu+9 z yjs by pushing oj+u ma0yj9q7z ff with 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 and n j0wu6+bhxc+fbur8 i5+,5hjjpft+v the other 80 kg, are initially at rest in outer space. They then push each other apart. buf x 6t+j ru+wbnijv5jhp8+ c0 5+h,fHow far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision h/5m1sg5zrxcisx q,gy):( yz with a second ball (at rest) and rebounds in the opposit(z5ry/5g:gc1,mhsysx xz iq )e 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 3o78fu a-vmlt expert 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 applying the avo-u3 l f87tmbrakes.    mi/h

A golf ball rolls off the top of a flight ofn1btge8 :gk h07m+s9t mqgwn5 concrete steps 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. n0:s te9 +5wmhtqg1 k8ggmn 7bIf all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40(z 7y4g efisp82 f3fgm-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 5figpf3smy (7ze gf8 4210m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes em225/:egquu/v eccj jlbedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficiec v/l/j2uj:cuq5 e2e gnt of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowboat (/myu 2 d8):h drocqiyof mass 80 kg. With the boat initially at rest, the two peduymc h/qdio2)y (:8rople, 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 boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass waskd-f2+9x os g; ;uhegs about $ 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 i5 w3 fne)8oj22rynzovm;ls 8gnto two fragments by an explosion. One fragment acquires twice the v slg2fwz); r52o83ynn ejmo8kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 581 -venuz/ g6vz0-( $1.8 \times10^{ 5}$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 vog 5qmy2by9 -$m_A$ = 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 particb) :j ;xq,6dhfr jdl;y xbgk8h3/ih* ele and a smaller nucleus. What will be the speed of thiyd ;h;bd x*)ij6l:8r,3 /g fhkbj hexqs recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an i,x;2 z4+ffyqju o5(wx1vxwr 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 3nsxz/4a/p )u gr ltrq4i 9mh2 dc.5)bg0.0 $^{\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)ww/ tbs.. z)bapsc*c/65volqdtw94 d, what is the upper limit on mass m if it is to rebound from M, slide ubpss).9tw4wl abd65q t w*.ccovd/z/p the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Fig5g)8zdn7j k(j weo vr/ure 7–47 shows the planet Saturn moving in the negative x direction at its orbita7r( e/w5jnvjk)zdg 8ol speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s