We claim that momentum is consd v0zestok(rj e7(8ds.en36werved, yet most moving objects eventually slow down an8s6.os en3 w0 7ekt(zj(dd rved stop. Explain.

When a person jumps from a tree to the rn+z60 -tcqpwground, what happens to the momentum of the person upon striking the grounpwq+0 ztnr6c -d?

When you release an inflated but untied balloon, why does it fly across the roc xak(lm:oo7tv+m.ggpa7 x s :uss:8*om? o.: u*t:ss+vpoc778:lgxmxksgama (

It is said that in ancient times a rich man wi(gfq dvk )txwb+0/ k8)j7enec th a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he notfwkc k)+gv0 exd)jnb7 e/q 8t( been so miserly?

How can a rocket change direction when it is far out in spap-4)wd )0mkat ,kekonnwgg bt d, 8b2e au34(bce and is essentiallyd)ob (gdakg4 kmnb)wt 2weu8,p0n 4ebka t,3- in a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse,j.plfsqee41 vf+5 /qn 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 bags, which are intended to inflate during an automobile collision /jsf1+elf4.v q pq n5eand reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to wj, 3fi .x)yu:q+deivc ithstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of t qujy:f)d+i,3eci .x vhis new design?

Why can a batter hit a pitched baseball further than a ball tossed in thed5ivg aa c(ht*iv +(q)*f m6ik air by the )g(5d t6 +* va*iakv(hfm icqibatter?

Is it possible for an object to receive a larger impulse from a sma:myv vlxb1 f ,rpl/-e(6nfby; 0q,uf all force than from a large forc f/, alb1l ef,0-p yv v;qxy6mbnruf:(e? Explain.

A light object and a:5ml zxsfv *9hvop07d heavy object have the same kinetic energy. Which has the greater momentum? zsd 79:ovl5f *ph m0xvExplain.

Describe a collision in which all kinetic enqfp (.-r.i na2lqt9d; bbqw o1ergy is lost.

At a hydroelectric power plant, wa8nnr 5+w6mmav eqxj*: ter is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbinen arm* j685nmwxeq:+v blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wally-1gqhb1+gd ;ytbwmm 9l1. nc at 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 heigd97hiu h9sm 1bht 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 momentu99 bdhu71mih sm conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backwarynmq93 v-wi4yo +es +ld when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas thisd dv)yeda7:.p is not true forpe:a)dv 7dy d. your arm or leg?

Show on a diagram how your CM shifts when you change ccqdnmvfjq7 //s -+c0from a lying position to a sit/-jd 70vqccsf/q c+m nting position.

If only an external force can change the momentum of the center of mass of an 9 +3xfr1hpgufd0v2vvobject, how can the intedv9xhvf1gpr+ v3f 2 u0rnal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes into max,3hb xxu6 wtne5c(9-3nn g-a:vwrv any piecesgx(vxa:bwev w-x9nan,thn6-c 35u3r . What can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of ajj/r+(t ezh+np8t+ me 28-g 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. What is the sog6py3.c 0qwf g4 6r (qzmjh-gkier’s chaqozg(0p-rhj4 f q c.gg6 ym63wnge in velocity?    m/s

  A 0.145-kg baseball pitched at 39 yk(mc ro7dk e(*avx, ow5ngrwa 9+)7em/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact ti 5arm7w(re*9c)+,w7a kony(v dkego xme 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 outk1x6ilhu p d+ze:+s a2crq9f.m5 bn;m 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. Th;bamp56s:n k2 .r u+9izcdqelf 1hx+m e magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given qf )qkl4y8 ak 3pak ;y2hnta60that the propelling gases are expelled at a f tk0l k y3a2a4kqnahp6); y8qrate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving a120ww7u uvnav grc fg6 h7b2.yt $4.1 \; m/s$ 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 carzcvd/ p, z-ty) travels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the cp d,czyzt) -/var. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveligexf j pulzdj)5; m;h x45iw(le( r,/cng 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 horizom48kvshjxzg gf/ hw b,x).v;4ntally at speeds of 100km/h If the air strikhvjvg ksm; 4h)x8,.g xzwb4 f/es a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasf ixj5mrg//4lc9apl:z-fys )ts along with a constant speed of 8.6m/s on a lev4ixjlmz fl)f9y-g5 pr /cs/a :el 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 initially moving at 420m/ zi65z,f5pzcvrb fwdp /8e()es 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 ori e5, pcpr/b6(vid) 8 fwzfzze5ginal nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.06*(y kywc1 4hu0t*c q t9twgnk-kg block of wood and emerges cleanly at 170m/s If th( y01*kt ycn4uc6wkgtq wth *9e block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is travelinyj8 *-/:1 ha: k -vxyydplns+thq m)cwg 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 traveling3tb *w3 f7zymr in outer space with a velocity of 115m/s To alter its cb3 73tyrwz*mfourse 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 )vuwf/x; aj/e.045 kg is hit off the tee at a speed of 45m/s The golf club wa /waxeu)j/v f;s in 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 nail at a velocity of 8.5m/s and co+i d) jth72sh8u+swt : gk3x 7naon*7q+qskn bmes to rest in a time interval of 8.0 ms. (a) Whatkskqjs 2+i 7h73a)nh qxt 8on:tdn +g*w+sb u7 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 strikes a wall at a:z w4 c,tieq(1mbupr7 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthiness of new automobelt pjz ef+ mo6-56yt ahy0+4jile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of maot6 zj ly++j4 0f-t h6ym5apeess 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 runninf b p5vt,biwd 4c6h n-.da+t3vb5 )pzpg at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler runni bf ),6tzhdbv5d.inwt +a bpv-c43p p5ng 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 teqb8e+c yg,hy2:4)s-j y q m(:jyj a*effkilj 3nnis ball (mass 0.060 kg) points in the +x direction and is given by the graph gm+-i,)q 8yh:*fej(yj yeblsjy qj 4:2cfk3 a of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking the lfd n5) 4hrvc+ dz8dcr.n/j(cv ower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking t d+rn/jdz54c8ncrc() fdv v.hhe fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) witnw ,foo; vl; *pzb wi1;qe4f,gh a speed of collides head-on with a 0.220-kg ball at rest. If the collision is per,i q1l;zwg* ,fefw vn ;b;4opofectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-on collisionb n5o ctm5qz24 with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction5ncb4zqto52 m 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 a perfectly elasti9ce wda5i8 q4mc 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 represent the ball moving at 3.00 m/s in the opposite directio5 9we4iq8cda mn. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/sr5xeh x(am.6rah9 9p q 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 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 representar9 phh69qx5ax.m re( the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is movi y (*cyb;j85x,crjk lcng with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incry clcxjb(; j,c*y8k5 oming 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 oneihf vl 4 8,*5afnvjfhzm ,z un)qt9g/5 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 approaches at 4.5m/s and car B is moving at 3.7munz4 5 ml,q*h),5fvig8a/ tvfn hzfj 9/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 colz 5 2vt j rl30kjzc.bt/t,:jzclision with a second ball initially at rest. T0rzz/z,v2bjj5tttk c3jcl . :he second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube sl.f)bocw9l1 w iides down a frictionless incline as shown in Fig. 7–35, and elastically strikes anothef9w il cow)1b.r 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 horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an xft: jm kc9b52object 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 experimente5ms.psejzx3 lq:b4g t r**v) , projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. Apjvt *elb) e54sxzsgm:. rq3* 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/sei(l 4s pf;f7xskl -s qw;wav:wo/,:a buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string,ss:4eqa : kwvx li ,ff -sa/owl;7pw(; 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 oq /658u0ma52 -vt k/rgzfrhnoa)ob qj+ll .d fraction 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 4u-(of l rgm4 nolgyg ,nrie38,b*kt1rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how g,k(iyul 4t 3enmlf o8r-ngb *g ro14,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 at a ocx8 jg;ci rc+iv b4dpw) ( 9g7sn6*zzred 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 coeffignc6zcivr9; sp*o (j8b)4 dgiz+x w7ccient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a heigmv7i)qcod e**( u w0t5p+gmvoht of 1.50 m and rebounds to a height of 1.20 m. Approcgwve+t uvom* 0(i7d)mo p *5qximately how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity inxba iy07 hd8f6 a head-on collision of two objects is the coefficient of restitution,ab7xi8df 6h y0 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 three times the mass of the oth ab):qg;d6qnad: /ooqer. A depression is made in both faces of the cut, so that a firecracker can be placed in it wiad:a;6b q gq)q/ :oondth 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 cdm( f 1tvxap.ae 5) ile2gry;5ollides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass if: vax (dgay5te)21pir5.eml ;f
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an electron,r( x bq(rt7bkrdhgtgo *o1lq i: 8 )n3pf;n0w5 and a neutrino. The electron and neutrino are emitted at right angles ot: (ndx)tlh0b(rq3k7 og g*r 85 n1qf;r bwpiand 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 mvsrc3d1qx+ izb rv0dq./-+utass $m_\mathrm{A}=0.400$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 sz,3:dulo 7rhtwo objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle betweehrzsd l:o7,3u n their initial directions?    $^{\circ} $

  Two billiard balls of equ;9hf 8 t7zwwcf3nkvr6. fyw+ -1cbujaal mass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to.-fu9 8;3 bj7cf hw6vyw1k +catzrwn f 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 co jj-7qp0kx2 gs/q6axbllision with another atom at rest. After the impact, the neon atom travels away ata07jg6pjq x-2 sxqb/k 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) make1m ;g3wuz+ hdys a perfectly elastic collision with another atom at rest. After the impact, the neon agmdw13+y ;u zhtom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass syzg+oy gggo0:vb1js 89stem shown in Fig. 7–38. Specify relative to the left-hjgggzg8 :09+ovoysb 1and 1.00-kg mass.    m

  The distance between a czbg, 8 otko0by4 ge5/yg; wo0dmr1z+marbon 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 1d kh-2xks9nwdw440rz 050-kg car is 2.50 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.8- dh494xz2r0sw wkknd0 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a ferryb/m0e, s;hb zkhoat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corner/,h 0z ;hksbems, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides i-:8/nor..2mcwwj z zcdv v7h$l_0$,$2l_0$, 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 aa71hx 3a l;o;p fs u60kxbp-rrqld l;01hh o4j load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane,bk;;fq;u3h1doxh 0 r7lj1hlxp p4o ls06ara- 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 of radius R cut out: fp 1oil-jlw qr)8y:m of it. The center of the smaller circle is a dist::lf)1mow ij-yqp8lr ance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calcula*(p vd,evjwo7 te the mass ofv(,owv*d j 7ep one of your legs.    kg

  Determine the CM of an outstretched arm using Tab9rp+q zw on)l0le 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calcu2l.c0.u 0k+ozya druelate the position of the CM of an arm bent at a right angle. Assume that the p.zlue0d o0y2+auck. rerson 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 hdf0qoce ,2* lzqf waah:yy62 zt;3)fr anging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will *3q0t;rwz hezayf q)y2f ,adl:2 6focbe. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moo1)xuz0 gc: ezb w*isn/n 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 8b ql7deu,u /1g0-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 me-my85js v/ w:xodprmr v5o*2d/4xw a 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 tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a paradm:oy2o wm rp5xe *v-/jd8x5 m/s r4wvbolic trajectory?    cm

  A mallet consists of a unif4 0ma(wrde j)z;v ;x m.emlt-qorm 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 bottom of the handle is the point that will follow0-lxw ;rdvt4 ja me)(z.mqme; a parabolic trajectory?    d    d

  (a) Suppose that in Exa2*l2t(mwia m wg t6xu lvy(p.8mple 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 e4n t lgdo aee;h25v1u 50e8qfgondola, of mass 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 direction (relative to Earth)5vueh8d 24ngeq;f50le e1 ato does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched hoqc77j whzron 8-gxp1fby 4 ,enod/f4/rizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is nof/1o8-7rg f yd /ejph4,wzn4bcx7q1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m tra wh flff-of be41rb46+veling 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 corner pocket shot s0rf wywnk1r , o-9dhz5hown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scrrhdk fyz910nw5r-,w o atch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a spe5 p-cj;oekqi1r/fs 1ffb9rq; ed of 2.5m/s by pushing off with his legs from an 1800-krqrqfo-esp j;1f/ b kfi1 ;c95g 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 ab f 2f-oi-pq c krdzxqvx,;it36 5a8/nt rest in outef2ft zi86ox/; d q,ikbq5-pnr- c3vxar space. 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 s lkfu)9x fk5k t71i03v4njcp jht19o with a second ball (at rest) and rebounds in the opposite direction with a speed epiuctl j54ktf1kn9s79x3fj ) vkho01 qual to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving au9j 53o/xzhyl n 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 55539xyl /jou hz-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total ver zx4eb u*u(i acoql.+2z 4mic-tical 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 ismo. z2 ai 4-+qc l4ez(uxci*ub the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood nuv, h c*rdp+e+ml:+r n ps;(sat rest directly above it. If the bullet has a mass of 29.0 g and ,+p d;senslh:v*+p ur (m+rnca speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block cvucg(iefufz r z ;uf.31n49+ 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;.4zc9 (cifugzr31+v fe nuuf muzzle speed of the bullet?    m/s

  Two people, one of mass i *0lyw hjy:3 q:nhg2l75 kg and the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, whoy23yh* wiqh:lg lnj0 : 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 was about 9g/4v4jbsq u( dco1yx $ 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 yd2+hrk 4x:u8iy)uaa+ g ka4rby an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of theiruyiaraah +2uk4 4):+k 8rgxyd masses?   

  The force on a bullet is give:i4 hx tzpe+n9n 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 masseshuxaq qsu4pi2das3pv ka 3,;8sh57z ) $m_A$ = 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 intg wk* -/lv7nljo an alpha particle and a smaller nucleus. What will be the speed of this rec*/vl7 jklnw -goiling 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 angle of 30:j;baa/ctk+n x6 k0b k $^{\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 slidepi0apv )(;ynmlbg+ g9s 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), what is the upper limit on mass m if it is to reboun0 xgcbz 3f:6) lrdb:frd from M, slide up the incline, stop, slide down the inclic60fgxfz:3 rrl)bdb: ne, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7mo dsk :w1rt,kwh) aq: 3dn1nnu49*ed–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect tohd w:oukrw *ske9 3) 41ndnmnt,1q ad: 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