We claim that momentum is conserved, yet most moving objects eventualq gzg* -ysbe2u;:j g :/0kkfgoly slow down and stou:;/-k2qjzkseggfy b:g*g0 op. Explain.

When a person jumps from a treet7xtk7 9 n xm51h* nzf*i og0zc11fqev to the ground, what happens to the momentum of the pe*x77c 1 ge 9imhkv*q f0t1fn ntxz1o5zrson upon striking the ground?

When you release an inflated but untied balloon, why does it fly across the rtcv5,-mzuy / hf;t/ vsfcms.3oommvc ,/s- vf. t/z5muhf3ct; sy?

It is said that in ancient times a rjc 0 9d gdq0on+; .abqr+,f1b bbr,srzich man with a bag of gold coins froze to death while stranded on a frozen ,gr.r s,azqc0;bbf +0boqr1n9 d+ jbdlake. 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 h2;o totzs) euudfq+y nn7 4)++kisz4 and is essentially in d+ne)+ o o +kqzui;4nstt2h) 4sz y7fua vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, t5wy: p )cbm7 se12li-vbtax(whe 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 and reduce the possibility of -wt5a:)ebps7yvwbc i xl2 1(mfracture or death.

Cars used to be built as rigid as possible to withstand collisions. Tod4 etx3kgu ov8a ,fak96ay, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage o,ak9 utv4o8afk 3eg x6f this new design?

Why can a batter hit a pitched baseball further than a ball to:d5bsk*,2v ovyqt -vl pyq i)7ssed in the air by the batter?l:5p)kq27,stivy oy-v b*qvd

Is it possible for an object to receive a larger impulse from a small forcd1kdss cdoak8u3 a/ 6.e than from a la k681 caddusk.d3o/sarge force? Explain.

A light object and a heavy object have the same kinetic energy. Which has the gr z,cy: p5 1grs;:*uh macay2zreater m*;, g hya2 ::s z1az5cycrumpromentum? Explain.

Describe a collision in which alpm b )hhwbuewve/o :a u(p(:*7l kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against turbir7u ia+6534o1hk (- tynt xzlh1oadszne blades on an axle 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 z ha1 3n-z54tho1 o+6(7s adkl itxyrurebounds?

A squash ball hits a wall at a 45 6oko ld+g8r9.bse / yz$^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel))ahw se 4cmbgwd1 f7; 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 that falls and stbcw h7 sedm;4w1a) f)gicks to the steel plate.

Why do you tend to lean backzd)s vss7uz0exo;6y x s2;w h1ward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point6q-ymvtpbtf, im m5b b1q-7*e, whereas this is not true-5m 6 eimyp-q*mbb f1bt7tq ,v for your arm or leg?

Show on a diagram how your CM s6yc )8 ltkg5+i2aouv90rnse :nio w:uhifts when you change from a lying position to a sitting posen w):v 85iirl:g yu s2cou9+o ktn60aition.

If only an external force can change the momentufn6kiruip6 p 12)w8merx 0; jhm of the center of mass of an object, how can the internal force of an engine accem2 w6 jue1php8k ir;6fi)nr0xlerate a car?

A rocket following a parabolic path through + .*++ n dippknffait 5uybn98the air suddenly explodes into many pieces. What can you say about the motion of this system ofa*pbi85y kd+uf+t9nif n.+ pn pieces?

  What is the magnitude of the momentum of a 28-g sparrowom6u+b ob1 h7a flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N ac hqcuct5r5e + v09hok +3j+tfits on a 65-kg skier for 20 s. What is the skier’s changehr cqe5t 0 u9icj35+ ftvok+h+ in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal l+ unll:p qgyx5jd.f++ine drive straight back toward the pitcher at 52m/yqxg5d p+.n +jlu f+l:s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a spee43 -bkkg3h4;on anypod 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 2n b3y-k o4nkgp3ho;4 a6.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases are en1oisr4z88 z9o+ s(z9 xz 8y.hoybhc txpelled at a ratezhz o1 yt89x 8yos+cn(i 9 .ob8zr4shz 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 movin2t a,,m::ae ox;ywax zwq+ja 0g at $4.1 \; m/s$ 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 cae0, m1rjqf-,r qvb2hu r travels alone on alevel frictionless track with a constant mh-jrrvq0b1 ,u,2f qespeed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at wa/uz(kicub8 a73tg ;m k;y( x$15 \; m/s$ 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 horizontallrkw. x 8)zy1hsy 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 wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum forcewkzh.ryxs1 )8 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 0qh +fop,/ accfs06i m.0/.omo rwcwdspeed of 8.6m/s on a level track. Snow b h 06mor0.p0,/i m owswdq/f+c.ac ocfegins 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 pdb9j h90ua 3q420m/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 93q9uj aphdb0a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet travelingna; zk,argabg r-xxi89/ 0me7 230m/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless sur09 kbz 8a-rx;7grgan e,iamx/face when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speed o- i+ ais g0xs)i+z7nrvf $5.80\times10^3\mathrm{~m/s}$ 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 oq,exakp0 *1qj k;hu0 2ei)ibmuter space with a velocity of 115m/s To alter its course by 3ie*mj exi 1q )2qkhub ,a;kp005.0 $^{\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/sabk t2ul. fz2r;w 7dq+7-zq hy The golf club was in con-a+7q t;kzqbrwhzfl du2.27ytact 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 comes to (azghe7*or; erest in a time interval of 8.0 ms. (a) What is the impulse given to the nail? (r7e gh;zo* ae   kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass34 mpj0we:i;mi,m j qv m=0.06kg and speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthiness of 2xg0p w0 -vb el6ar:ilnew 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 the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the bx2pwi bav0l r6e:0lg-arrier. $\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 stoppedp*5g s7kx5k yu in 0.75 s by a head-on tackle by a tackler running due west. Calcul5 ky*u5sg7xpk ate
(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 0.06z3c/88ms/ fprsfjv/ z0 kg) points in the +x direction and is given by the /f88z sjm/ 3v szfrc/pgraph 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 heig o5nm cc*qh-;n9e8y6cwlxc q/ht can a 75-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 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit ar ch96c8nn em -y w;ql*o5ccxq/ea) 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) with a speed of collides he3lcb31 sb 44ft qld,yqj1*at jad-on with a 0.220-kg ball at rest. If the collision is perfectlja1ljl34*fbttcq 4d1 3q ,y bsy 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, movin32eacjp vc*hof o(l (y6w. 7mwg east with a speed 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 r6 o(apjmefh7 loc .cw *y(v2w3epresent 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 colliszin 1op+9/n: fk ea.bh,v; ervion. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, rnk.:evai+ b,e9f/1 nov; z phwhat 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-o5zfkt8we; d7k v efk:6n 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 represent thf ;dzee kk68f:5vw7k te 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moj(ms8uz3.x kaj ks+f fr0,.qyving with a speed of 8.5m/s collides head-on and elastically with another ball iffjk.mx,jq s r 8uzk0. ysa+3(nitially 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 colliu 5)o6f k2jd)gfsp -sdde 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 approaches at 4.5m/s and car B is moving -ossgffj)dp25 u)d6k 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 c 66)q-khrs +dr2tpwt)zh0 cvoollision with a second ball initially at rest. The second ball moves off with hvskzhh+ 2p6r wd-t 0q)6rc)toalf the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionu(k,enf:ht 1a less incline as shown in Fig. 7–35, and elastically strikes another cube at:n fe k1t(a,uh 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 caseicay5x*g. ec1 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 pendulum experiment, projectile 1 results in a maximumih hpu.q-p :z, (rvh0m height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twicz vr-0hpp,:hq(. mui he 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 pendulu 2, a a0ck/*hkrlcx7 la5*zmijm hanging on r*aa l7x lja, kkh*miz2/ 0cc5a 2.8-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 the6ef y15zvd*sr9ot y,j 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 rest, into two pieces9i: eho5ca0kww n:zzlz2xy p82 mg9b ;, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosiop: ik9x5ba y9n0h8 2m c:2lezw z;ogzwn, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car c013 h 2bapg14bjluyfnollides into the rear end of a 2300-kg SUV stopped at a red light. The bumpbl 13ngpua4hj0b yf 12ers 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?(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 on0oksg o83a4c p-k:m to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of i8s0gkop- 4o nckma:o3ts energy?   

A measure of inelasticity in a head-on collision of two y bo b*;6)fqdrobjects is the coefficient of rd);fq6b b*yro estitution, 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, onel;vjy a-6 gf,w with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in il-; 6,fgwav yjt 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 a 4sa mhb0cnec.uwu/ (6t 5.5m/s collides head-on with a 10.0-kg object mo 4nm/wbs6ahec u(c0u.ving in the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a s j9ui yv*nyu4)i5f*p cecond nucleus, an electron, and a neutripn u ujv* 9c*iyyif)54no. 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 mas+ceedbs. 0ayrr 8 o5z+pvoo-4s $m_\mathrm{A}=0.400$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 coscr cx6zx2 z ov4agxp ;,cc*4.llision between two objects of equal mass, each having initial speed the two,cs6gc*.a z;4czxr cpo2x 4vx 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 angles and meet at the origibt(viic92d/*vu+ 9rjwv da - mn of an xy coordinate system. Ball A is moving upward along the(9vj-+itcu9dr2wim / *d v abv 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 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 another8 vtqzh/m d/i:ywq b0, atom at rest. After the impact, the neon atom travels awaq yz d/ mwh0:v,it/qb8y 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 perfe y6qbri iwy1)/ ,ul8b.unu6q)ap3 y vwctly elastic collision with another atom at rest. After the imw6quyv wly ) p.ar6 uu3iq/,)yb81bn ipact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–5ofl(t(s qop238. Specify relative to the left-hand 1.00-kg 5(f( toolsqp 2mass.    m

  The distance between a carbon li 8flk828w- 2qf xmszatom ($m_{\mathrm{C}}=12\mathrm{u}$) 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 frono,z*q (ud)o,xfiy8a m t 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 md*oz( ma 8,yui)foq,x 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 fer j lc+*yla8wp e93x*vgryboat. If three cars, each of massec8x*a*l9p +wjvly g 3 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides saam4k/xw 3)p$l_0$,$2l_0$, 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 0ifc1s ahzpg.)wr.1r cases of tomato paste (see Fig. 7–40),fw zg a sr0).hcr.11pi 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 of radius R cut out 1656lm* bh 81lmx.uivjr umodof it. The center of the smaller circle is a distance 0.80R from the 5ouh mr16xumd milv.* jb l186center 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 sayepwuc*( /( h3 pmtsv v-+gp8ume as those in Table 7–1, and calculate tp- 8tvsm(cgphvyu/ue p+ w3*(he mass of one of your legs.    kg

  Determine the CM of an outstretchz4ckyjn+g5o;n4tyy e6c6he24f x t2ued 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 position of the CM of an arm bent at a right myx tok c8zua0(d347nr +0tke angle. Assume that the persaokzxk8+7t3nm(dey4 0u rc0ton is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and i)k w7+t wj 9mc9z2p8treu-qdlegs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’rw)tpk-9+we u 7qd tjc8zim92s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earteu7hxl0 u, zkzcyf ):-h 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 o1 ou; bdhtn:vg5muc..3u9u kman 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 cylindriz/ p0fl8tvk2i cal 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 toss fpt08zkil/2ved, 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 cylindricks bo( 0f,yx u02jx5bm/(xaftal head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle ox,o0x(ft 0a( / mu5 k2fbjsxybf 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 Example 7–14 (Fixf*6r)kpwrryd;x+l4wpi0vm8f 4j-ij 3 f3z og. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and 6j :e8t;ybmc istationary 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 w:b;i6y8 met cjhat speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched hori7p - o0hrkhzti8j)x 33)ghalizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 mh0- 87oz3pxjhh 3rigk) )tilas, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travqva+8,xmkxzlnuo/6fb9l 9 3qeling 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 shown in Fig.g*(v m1 h:mmmx 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scr 1hm:vm*xmmg(atch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed ounj yjz7;xh ,h-1w (mtw/s ,ycf 2.5m/s by pushing off with his legs from an 1800-kg space cw7 ,u,zsynxm cy( -h t/hwjj1;apsule.
(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 z )4gjptede8. gujm+4mdgtx 8 z5 /,cykg and the other 80 kg, are initially at rest in outer space. They then push each other apar,ejepz 44cgd58x z.m)t t/ gmy+g dju8t. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second 4*wa axuc 8(xiball (at rest) and rebounds in the opposite direction with a speed equal to one-fourax4(*ac8uwi xth 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 eyl-b-2v6 y bvf5.rqwwxpert witness in a court case involving an automobile accident. The accident involved car fbwv.--6y y r2wb5vql 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 fl0v :oe 5shb3 a6uurob8ight of 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 h50o:bueovs8r a3 6bulower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest diremb5507k8yxrn ,zwk5 c4oox jxctly above it. If the bullet has a massn,xzw8 57koybj 5 r5km4xoxc0 of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.3p3x,l5qdbfclycad zm2z3zh9j*ga*hi 093 -i 5-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9l3b9gjlymqzc*a29 z hf idh, z- *0 a3c5x3ipd.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 massw.j8t c4pg;2an f2pj;b q ql*b 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? jpcbjaql b;t g*qw2n;f8p.2 4 The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was aboutfoj8o :7 :nrhh $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments by an exps.a t-a/ i*c.e uu;wkdlosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of t et.s *d ;uckw./u-aaiheir masses?   

  The force on a bullet iv/:ku8m-j 0,g y98jv3fnl:.g t jjxl(ie upve s given 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 cembqj 1s60 5n$m_A$ = 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 iypnrho4 )5uf iln,o:d(uqm3.c:59kw wthk .p nto an alpha particle and a smaller nucleus. Wha:wkh.3tp.wkl(fdo 5)u4 5u:qc9, yohm ninrpt will be the speed of this 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 targa4 rrms/0 -izkv q 8awp1/,d xqdtp6 rd1x6*ipet) 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=2.2kmxkwj3xd4n9 )2igyg+z,(1qat ;y lf vg slides down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mass m if it is to rem* ed yxmj2 kith0d/3wkg;-m9bound from M, slide up the incline, stop, slide down the incline, anm2k*309 mkhm;x yd wiet gjd/-d collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Sc l+rogm26i0 hg*0izpaturn moving in the negati6g 2ir p lzi*00gomh+cve x direction at its orbital 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