We claim that momentum is conserved, yet most moving h3oa,2x:xc0b 9 cxw sak+w ht 8om;ve1objects eventually slow down and stop. Explatwoc9v:xoxms3h2;kacx8e0+b 1w, a hin.

When a person jumps from a tree to the groundisi kvpl /v2cg2 c-d:/, what happens to the momentum of the person upon striking the grouci2gc kd/ilvv/: 2-psnd?

When you release an inflated but untied balloon,3l9ocqk9;rpi /)v6k lc.i5ps::xpjg,sq yjj why does it fly across the room.i jr:gyvjjc63:opk ipxklslc,/qq) ;9s 9p5?

It is said that in anc0hasnqpqmr:2 *b (36ew0 s.-jxsbcoa*m y i2zient times a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not 6q(as*sw 3o0b2 m*cipsa 20 qh. zbrxmneyj:-push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket changx6w3. wqky)yy e direction when it is far out in space and is essentially in a v3yx) qyw6 .kwyacuum?

According to Eq. 7–5, the longer the impmyt/t x 3zsb:u7ipgh1de:1p )zr wt3.act 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 bags, which are intended to inflate d3 tmtdsx1:erwg ):putzz/i 1p.h b3y7uring an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Today, thougi k:0rcvup u0:h, cars are designvkuc0:i u:p r0ed to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in ogs)cw7/tq8u the air by the batte)8gwsuq ot/c 7r?

Is it possible for an object to receive a larger impulse from a small force th)jw82-yu2 o qzvd.ug77i ; r.txzipokan fromkix. q)wz ut7 dug. privy7oz-8j2o2 ; a large force? Explain.

A light object and a hejyy- k(x8ozjkp :9af 5avy object have the same kinetic energy. Which has the greater momentum? Exy-8 ax9pjy 5f jk:kz(oplain.

Describe a collision in which all kinetic ened hvfn)- g*e/dh 3lv*(kf9si jrgy is lost.

At a hydroelectric power plqcj w*(lx)fhst )0fo6 l-y;i hant, water is directed at high speed against turbine blades on an ax0hwlcj h))ffxy io-;t l sq*(6le that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall ajq 9 zrv 8cii1o8-uve8ozp00yt a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixe6)ff7y/ ea bs qihb;6hd 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 sticks to the 66b7);hsyhfea if q/bsteel plate.

Why do you tend to leanrt7qsrc27s 9n backward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pijhr0)6/t /v0prf nry ope at its mid-point, whereas this is not true for your arm or le n r)yjrh0 /6fo0pvtr/g?

Show on a diagram how youru5ov2cyg4w38j7v rw p ima 92c CM shifts when you change from a lying position to a sitting po 94v7j32v2amucigyc orwp5 w8 sition.

If only an external force can change the moment5w,exztg-0su1aa:cuqql w 3pkw(di( x /o 1) tum of the center of mass of an object, how5l-w ou0)/ x(q:ts d1(iqzwkx 31a,pg eautcw can the internal force of an engine accelerate a car?

A rocket following a parabolic pat bswil.t*s ucb+h.1e0z jb. 8eh through the air suddenly explodes into many pieces. What can you say about the motio0ec .lw i+.jzhbtsube. *8bs1n of this system of pieces?

  What is the magnitude of the momentum of a 28-gbq:7 xv3rv i6e sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 22 tv ace;92fip5 N acts on a 65-kg skier for 20 s. What is the skier’s change in veloc9;tvip 2face2 ity?    m/s

  A 0.145-kg baseball pitched at 39bh+) 6hysyjqx/ fc8q. m/s is hit on a horizontal line drive straight back toward.qh/hsc xy) 6y+jf8qb 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 a 6.40-kg package out horizontally with a speeds)hs8 fkbyf98ssg0fy63fzb 6 of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially ahsz 9s 63fgff8yy6 bkb fs)s08t rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gab elmgj4)k7zc- i3vy3 ses are expelled at a rateke33zl4- bv 7i yj)cmg 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 moviq pw:mw :u3:hxng 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 capfy8k vj6xskt ) 62fn2r travels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is drfkfn pj8txs) 62kv2y6opped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelikjfc 7 o6pac bpkrfp/.h0 763ing 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 stohmuf chcdey 85s,: dty6 +v 059ero7hjrm, winds can whip horizontally at speeds of 100km/h If the air strj,h9 tc:7ms50o cfrde+ 6euh y h8d5yvikes 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 coasts along with a constant speed1*erd gu;fptu2h a 7 :(lfp,qp of 8.6m/s on a levqtppp7a fr;ldh2 ug,1u:e( * fel 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/s erslh; 9q q*o, ef5g1tjmits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of9, qgs5ol1f qj*t;ehr 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s2too*ney yaj w if6*)2pj -,au,rvoh8 penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it movw8 njo yy-oa vhi *,rje2p6* 2tof)a,ue after the bullet emerges?    m/s

  A 975-kg two-stage rocket is travepxcq0l74-a-*e ii utx4mi q d:ling 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 thg:50m/ sxpmo62r5ywikwtj 0raveling in outer space with a velocity of 115m/s To alter its coursr ygphwkjw m0 i 60x:o55/m2tse by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit oft5ee x-7uuq-c;a8)9s l)q yx z12s hrkwk)dv xf the tee at a speed of 45m/s The golf club was in contact wh) xrte e 1yz8xq-2)kl5 d 9;avwks7q)xusc-uith 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 8.5ma+d:tg 5fg1jc /s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse givfcag1t5+ g:j den 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 speue)0b )+s2bphabrb zaw(:1zeed 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 ,cw wy6 yamjtjgh:m9+6b:u 0y s1v6bv in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A y0:gutj 6myjvhw a1 ys cvb,bm96:+6wnew 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 stopped in l7a :iiub k3;h0.75 s by a head-on tackle by a tackl:3u ; hlbkiia7er 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 tenzlov; ,w1umdxge /bb.c(2)o nnis ball (mass 0.060 kg) points in the +x direction and is given by the graph of1gnbolxw2m .d,boev ;/uc() z 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 cnb27o e x,ss3fkp e1k+an a 75-kg person jump without breaking the lower leg bone ep, eos 1b f3x2+k7snkof either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of 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 direcrlu nv/ 2l95xfu*u- uxtion) with a speed of collides head-on with a 0.220-kg ball at rest. If thl u9rx2n xu-/lv 5*ufue collision is perfectly 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 hatl+nfsugdy5 +p+( : zxs 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 0.4++dn( :fxsly5gu +tp z50-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 undzrn ss 0;o a8u5*w0ltjergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3. j uz8 trsa0*lo0w5n;s00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed4f 5 hx-,g* jstf9tciw of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a,*sxjgfi5ftc h4w-t9 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 the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is mg s/esv 6nw0g+c(z3ug*b-w a loving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate gvlwg6*g 0e -nazu /3w bscs+(
(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 2wd/tcwq: hj0 j/mr1v6gd6 uq ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A har j/:c6vduh/ 2mqwj6w1g qd0ts 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 3.7m/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 -f 5 gom9/ r 6wacw2ym-efzv.ymakes an elastic head-on collision with a second ball initially at rest. The second ball moves off with z9-- 6frygmy. owvac52/m wfehalf 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 frictionless incline as shown in Fig. 7z.6tjz q.f(hs b;rmf:–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? [H6tf r.m:zqh (f;. bzsjint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object hduokf q b1y1*p(so-. 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 exxd;ux3w2;uzm periment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendu2zxx 3um;;wudlum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6uf0v9ivd gpmm7r7u+jq2 8.ox -kg pendulum hanging on a 2.8-m-long string, which makes the penjm9d 7 u 7f8o0gvi+vxq2rup.mdulum 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 fr*n6 .zn9i/8 .ixk lg;h qtelejaction 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 -ag6zfg -uxq.object, initially at rest, into two pieces, 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 eaq uggf-z a6.-xch 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 endn6xlo5 n uocqo,:2;cr of a 2300-kg SUV stopped at a red light coc6our:o2ql n,x5 ;n. 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?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a hehcv(mj 7 2dd0ni4mqd 2ight of 1.50 m and rebounds to a height of 1.20 m. Approximately m (22ddj40dhvmnqic7 how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on colloo(u qw7(1lt lision of two objects is the coefficient of restitution, e,wo tll(q( u7o1 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 thmll b dn(j2 :luhp6l-u k(+lx6ree times the mass of the other. A depression is made in both faces of theb(m:n6 l lup(6l - l+hudkjx2l cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in gi(.ha,o9p-v es s9cg(c+n ): s appntthe +x direction at 5.5m/s collides head-on with a 10.0-kg object moving ina )(s v+ai-9otpp pch,n:.g 9(gecssn 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)f*nahg4tvh0d*h1 (r kj8nsq a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and havg qt1 dh4s*h 0v j8n)(arfnhk*e 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 mass2apujdeuu9* :s8y-* ujf1x/ rhdcqe 6 $m_\mathrm{A}=0.400$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 objects t+,u9lvxko5z(fg2br2s ,qll of equal mass, each having initial speed the two mvll+f9qg x ,l5s,zbkr2(uto2 ove off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right ;1yaj7kns59v xtc fk+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 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 (cn 7a+jy v9k5stfk;1xFig. 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 el9m h h7d+hin9oastic collision with another atom at rest. After the impact, the neon atom travels awand9m79 iohh+ hy at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision with a8qb/n,ms9g vcnother atom at rest. After the impactsb mn/8 9cgqv,, 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 Fi(g*- x*fgu myeg. 7–38. Specify relative to the leffg(u-gmex y* *t-hand 1.00-kg mass.    m

  The distance between a carbota -1f 5 +t;zswypf/f8zpv, ctn 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 il v(01g,qxzys p /b7kbehind the front of the car. How far from the front of the car will the CM be when two people sitgv,psi7z/0k1 (xyl bq 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 mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a ferryb-cr)(ist e7 mroat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryb(r tmecs)7ri- oat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidewtaq bo.72tuq0qyj2 zps2 k 7z9 zi6x1s $l_0$,$2l_0$, 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 h w;no89xk+nmyd 2*zd mas a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of 2*on+; mn8m z dxwdky9length 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 rx0yjc a8)ajmpltid63 7)j 4wfadius 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 cdwja6i0p8y m 7)a)j ftl3jx4the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are th,scz9,d qr0o2 wurca6tn r+ p8e same as those in Table 7–1, and calculate the mass of one of yo86pr+, ,2rco0qudtcn aw9zsrur legs.    kg

  Determine the CM of an -l./0b(vfj k5e xmw rqoutstretched 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 7l ipd/v; xnq/ c2+tohof the CM of an arm bent at a right angle. Assume that the person is 155 c oqdvnli 7/ch/2;tpx+ m tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such tehzs5 ,fat,14vn( 0a2ai (vjzw1w2pwp dpg o;hat his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate howaw2(1ap vv 1d2wstophpj(zg05, n4 ifeaz,;w far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon ** h:bwdh/ :/gzbb1q 7kjtr7 mhe+ t*q:zj feuare $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand3fazwe e 6lye-ot q.pd.dw y46g-z:3u 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 cyli d+86fmlm7 qpendrical 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 bo6mm7el8f qpd +ttom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists ofmjj5kml6o7;0od qo k6 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 t7qdj6km6 ooo0 ml5k ;jhis 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 (Fig. b48: a d jdcpj(-7ooq .-tfon edhq9t67–29), $m_{II}$=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 kq4 dcw(ne8. amass 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 tock .wed q8(4na Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontallymcf:) w5c:a yh at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 myah: wfm5c):c s, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveli- ,,) zm0pqq yw5tquidng 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 she ;nn3rpg3+(hn uf p k.(i1bbcot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratcinnu rep; fhnc (p3k3bgb(+.1h shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speee* 3wl-v7bkuit0,e: +weezj:zige 5 e(ofax8d of 2.5m/s by pushing off wit*vl7: u fw owe+0:tx3ea ,i8 5kjez(g-eizbeeh 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 masz,z 9rh 1 nk(39y77wa rmvubif sin3 r6rdo+f+s 60 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighte war+ hmzr3n99s6uvb+3k7fr(yiz,if nd 1ro7r astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (at rests0-bw rleyu,qff-/:26xj qwc hj6v/a) and rebounds in the opposi 6cwubxfa-q2 r/-:wj j 0e 6s,f/lvqhyte 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 5x8ft pwm 4di+an 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+it p5dxwfm 48 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of c.z rqw+ny25ugy-, +g+x nps+ -tem-ueue g.reoncrete 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. If all collisions are perfectly elastic, what is the bounce height on the fzu g.w n.xye--g + 5 ueyen+ge2trmrq+pus-,+ourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at reew61j* voj u9tst directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s howv*1t eju w9jo6 high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strike i2mlhp fsv;-:s and becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in frontvpsm;h- :fi l2 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 muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the )w.r8xv dlr3yother of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends )wxy.r rv83dlof 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 3:;oj3l uhbeey l;* sb$ 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 cc7lg m 0sxr;9n,7uakinto two fragments by an explosion. Onkas 7xmg ;9c0rcu l7,ne fragment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula z -9y7i-qla nd,d-r 4p)acxgaF = 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 massesp;1v*t odv0 a/spaf,q $m_A$ = 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 r.2n icr9v(z g)+blm2ckd:po an alpha particle and a smaller nucleus. What will be the speed of this recoiling nuclerzvnpc ( 92.og:k)md +rc2l ibus 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 tar),vju2f z tld;get) is fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.0nhb8.1lhyaenw7 ) as; zhm45jw y ,bj3 $^{\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), t* 2j 8y-ypp5geaa8pvwhat is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide with M y v8pajea-t8p*gy 52pagain?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn mo5v*a9s y rm x+*+k pj2f-mqixkving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s T a+sy+*i9pm* qkxxj2 5fmrv-khe 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