We claim that momentum is conserved, yet most moving objects eventually z8efxnk1, txcqa) r hx98hwmp azli8fk7-:34slow down and stop. Exxa987-,ehw8 a 3nx:f 1 kx8p 4zlzfmhqt)cikrplain.

When a person jumps from a tree to .7inu2qmd6 - pzzrk(uthe ground, what happens to the momentum of the pe2zu-rkm.z ui ( q6p7ndrson upon striking the ground?

When you release an inflated but untied balloon, wh95l4 +;wm5owqvu/sxx 2 xg yujy does it fly across the room?jyvxx+ uusqg525;4 x /wm9olw

It is said that in ancient times a rich man with a bag of gold on(hj i7*f ch*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 nio*(hc *f h7jhad he not been so miserly?

How can a rocket change direction whlwqw1 pwba*cjgf1:r.e . x j1p1cud (8en it is far out in space and is essentially in a vacuum?1l*px(cf.1w: 1g juad.wbce1qrj pw8

According to Eq. 7–5, the longer the impact time of an impulse, the smaller tmt )n2 /ktnke .3sff5ihe 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, 2kn3nf ) s/t kfmti.5ewhich are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions-psxbp+n u0kw*.x7zre/g1eq w1 zg ;j. Today, though, cars are designed to have “crumple zones” that collapse upon impact. exg qg.ejp;kzx1b0 +- zs/n7wpu*wr 1 What is the advantage of this new design?

Why can a batter hit a pit p vkj731(x:td ughybtd-1l-3ou sp)wched baseball further than a ball tossed in the air by)t1 pt3hp-3:1xdsuko uvygblwj7d(- the batter?

Is it possible for an object to receive a larger impuij 6gh-x ymxgx*2.i, jlse from a small force than from a larg-gjm2i,x x.j y 6ihx*ge force? Explain.

A light object and a heavy object have the same kinetic energy.+kfaq b:( 9sqhl/v((l0e7ml5 rx 9bfg yu6jdm Which has the greater fhs5fgmv7 (d rmq( 9l j :ull(xqeb+y/k 0a9b6momentum? Explain.

Describe a collision wl9ke2-x a8: khgw ;qlin which all kinetic energy is lost.

At a hydroelectric power 0m bja mker zzsl)pkzw +*6ja62 4wy:;plant, water is directed at high speed against turbine blades on an axle that turns an eleczkjaks6 )ry l +0m* :w42;be zazjw6pmtric 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 atm 3e anq449a ;oag85rpiq0amv 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 (fixed to the Ecm 3amf4. )s918armugxudh. garth), from which it rebounds at verm 4mra 9hgaf..sg18d uxm3)cu y 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 steel plate.

Why do you tend to lean backward when carrying a heavywqd w. h2ldqpjv1g8 y v/l187.ri8mgr load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this (eimpna/-zu ;is not true for your arm or lempi ;nua(z/ -eg?

Show on a diagram how your CM shifts when you change from a lying positiom4mx 0 dirdbf(,n6n /yn to a sittdyxbmr4md/nf0 (6n, iing position.

If only an external force can4uy*aju( omg :,q jj-x change the momentum of the center of mass of an object, how can the internal force of an engine accel 4*uajyju jgmo(xq,- :erate a car?

A rocket following a parabowt1ad9oqp 1.(o;va h q p7roz3e;bzf (lic path through the air suddenly explodes into many piece (f1.pzbevto pa; r9oh713aq d zq(;ows. What can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed a6i 6n *rtb0mmk6q.qz.s- t hiof $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier fore4bp1butja (p .vk0)w. u c4dh 20 s. What is the skier’s change in velocity?u) wv h41p.u.( kjb4bate0 cpd    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive straightlpz1ztx./. hhbn n 18s*b q1ei back toward the pitcher at 52m/s If the contact time between bate h/.t izbqnz1.pb81x*1lhns 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 witc b0phfbr/ k:8h a speed of 10 m/s Fig. below Calculate the velocity of the boat hbkrb8p: f /c0immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force b k2r06(fhb ebpkvb(2exerted on a rocket, given that the propelling gases are expelled a2bbkhv b (rb06(ke2fpt a rate 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 at h+q3ouq7yq 0e$4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless tracdqbb) wozd(j)l10 f:bpa 3d :fk with a constant speed of 18m/s A 5ddlf :w(oqjb p))fbb:azd 30 1350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar trave+.mk*-e ow.r7qhx)txyj5 -k ebbd* rrling 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, w+52 qnu6tebb grs0t.ninds can whip horizontally 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 fq2bnr+ .b5u n6ttegs0orce 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 coas(q yg.vecdb8 r+5z w+ ea3ss*vts along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the ybq s c8 *eg+ev+(s.d5zawrv3car 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 42a+d bl o;ximu: / 7peqgr7l5w80m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when ib /xur o5l piem gw:+;l87aq7dt is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg bljkdg/ 5kd+. tiock of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface dtkd.ik 5jg/+ when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is trave.y z9 3cbxrwqh)/unrn(bfh yu d- 1v0(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 mas (e-3vo2kp)5hkrmboz h; *rmws 3180 kg is traveling in outer space with a velocity of 115m/s To alter its coure2(rp-ho 3r* bzkmk5o;v)mw hse by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speeye7 5- +nvjzhvz8fdr0 d of 45m/s The golf club was in con+vj-r5z 8fvdhn0e z 7ytact 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 n)io20 7gwdq6 qnm9qh a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given mqow 0 )h92qn76 dqngito 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 x: n+ :u:3gkcdpej q0fa 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 automobiled879r hm, 3jldv q6dxx models. Cars are tested by smashing them intl,8vqx dm rh639djd x7o 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 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 easc zyq8roab6,* 8z9jwr t wk*u-t and is stopped in 0.75 s by a head-on tackle by a tackler running ty6kz q-c*w, u j89o8z awrr*bdue west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.0wfgq9e j01 i*h60 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical me*efg09 i1qhjw thods 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 lohde/2 5,l nfxt+h) gcmwer 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 hx/gd)c5th + 2 nlfm,estrength (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 directionvzz7*jtaa4 r b7v4ew ;) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and directi4 v betar47;z7awjv*z on 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 hacdw hy)jr.2.rg a82 kjs 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 represrjw cj2ah.rkd8)y2 .g ent 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 undergd/,p:kjj5q b7;sl kij o a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the oplkbjj:s ,i ;kj /q57dpposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m 1hg -fazx lz:c8 (yyxss8g9e;/s 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 represex fzcgx y(eha89 s18g-zsl;:ynt the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is movi3z . 7mysjoah; qc.-bvng with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest.a3.ychj 7s- mboq.v z; Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as one; i:kzfmc/pb a*d-b9w 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 fcidp 9; b z*mkba-/w: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 makes an e 8wzb , .x8hh+(lxgvgxlastic head-on collision with a second ball initially at rest. Thehhvxlwxg (g+8 x8z ,.b 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 cu6t ajcv w8c247m+a7mj(4es,rsfd( 7 til potebe slides down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, wherest76p(f dea4t2va7 sm(j4cce 7 t8m li ojw,r+ 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 ofd h h 7*adhcuhaq 2,9skp16yk: 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 expe rt,r32c nb4kbp8r 5glriment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the g4 5 rc32 rrlbbtkp,n8the 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 235or quk3wzyq)u n1k9 ls,m,e70m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in qk3q5,mu wu yzek7nl r ,1so)9an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lost, qyscs5ctdb+ 4vr0*f4 $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into two pieces, onedpsc8 0vos dh* s*yxph60d k(9 of which has 1.5 times the mass of the other. If 7500 J were released in theps skdy(6xhd0* d vspo*0c8h9 explosion, 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 collides into the rear end of z9e8cinbkb 0l;f) 4 opa 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates tcz ;90) febn 8ikl4pbohe 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 o3rfgbzd7+l -5 +mm .lxyyb1cif 1.50 m and rebounds to a height of 1.20 m. Approximately how3ylzbi+ -lbcm1x.gfr+ 7y5 md many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the coeffici4 htm9t90sxs2v rb )cyent of restit trs tsyh24)c9bm09xvution, 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 ;tbuyec 3u+ +n0f;fonv tg 1-xtwo pieces, one 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 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 a+f t1-uotyng0n3fcx+; u eb;vnd 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 f5e4c-y; j g-fp0v w a/fozn*sp*py .hat 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of ea-hywzvgnf a .cp*; y* - pj/e50sp4ffoch 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 seco)a7hu1 a ,1avz k6 txxria55unnd nucleus, an electron, and a neutrino. The electron an auu, xv17i556a)k a1h xzratnd neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of mass twl10pd- zlf3 $m_\mathrm{A}=0.400$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 of equal massz 7iv zb/(mrw1ry-6rw, each having initial speed the t w-zimzr1 yw 6r7(b/rvwo move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move atw-et)ds4 xx2l 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 the right ls4d)x etx-2walong 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 another atom x )jda.f, 6cps7o7cbkt veq/6 at rest. After the impact, the neon atom travels away at a 55.6 7cxtfspovbk e j.)a76/cd,q6 $^{\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 elastirot.c/+gpl wwn k.):tc collision with another atom at rest. After the :og.k.t / pt)+ww clrnimpact, 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. 7–38.a2pji ip-yemt t86g7iv x/v98 Specify relative to the left-hand 1.00-kg mv e 9mptp87tv-yx/iig68aj2iass.    m

  The distance between a carbon atom 9 lml+r;m c)na($m_{\mathrm{C}}=12\mathrm{u}$) 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 ca.ab7ln)k dk (/5mw2o,8mgr- )crlo mi mxs-mx r is 2.50 m behind the front of the car. How far from the front of the car will the CM be when two m l,i)(.kwx7)b ad -olgnmsk-/r2orx8 mc5m mpeople sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 yiu3u8c e)85 gmn)qeqm by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loa q mce)iey858guu )q3nded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side4e :x5/xi xiqzef5g(mbv b 92ls $l_0$,$2l_0$, 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 ide jifppcpzlf -kq846 1nd.47 gsjs2n 5tntical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of glgz.iq21 fs54kn tp8jpjcs7 -nfd6 p4ravity 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 circul8jn8,gjky8ett8-b isqa q-t/ - ao-cgar hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What a t,t-8 ceg k-qs -gt8-bo8/n 8yqaijjis the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions arzodtqb .d ;0:ly txet38p)kld3px .c7 e the same as those in Table 7–1, and calculate the mass of .ptcd; d)0bxtx: d .kl3 zq8y3o7epltone of your legs.    kg

  Determine the CM of an outstretchrz0ei9k+bj xi72 q pw5ed arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calcw1;47l;( oqycby 4mu hsbbi8s* y7rs lulate the position of the CM of an arm bent at a right angle. Assume that the person is 151 7lsbh b4lqiyc;sys74( ym8*ro; u wb5 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a 9nyf msfmjx9n5z)pif5/; e. bposition such that his arms and legs are hanging vertically, and his trunk and head n. i;ff5 jm)9x/bfp95m y ezsnare horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moongl3ttc si3w/: are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stanntjvu;lmw2 36(-jce cd 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 c+knzmu 4ekl c9h.o(9 tl c7ik;ylindrical head of mass 2.00 kg and a diameter 0.080t+lc9 czni mh7lkkeok.u ;(490 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 parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diamegmg0t /:.c ti2ii9awi ter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and leg /aiii.t ictm:2w 90gngth 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 nr;r 2d5uj,t o7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, ofw0 cuf4*i dmg:8 u g6tcxbu(v1 mass M, are in the air and stationary with re fc*1(0v8d :wcbx 4uugigmu t6spect 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) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is p3j zdrx() y3f ,vq2hrfopped straight up to a height of 55.3() f ,xzjrfdh3qr 2yv6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speee. pa8w-6/i0fl far2gq1 ljv sd $v_0$ 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 i(p0f3j6)d 9ng e1)mbw u+qa bzw ,lmtFig. 7–43. Relative dimensions are also sho qmwbm3fjn(al6ewt9b1)g,0 zu+ pi)d wn. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s t:a0sc i1l dyzb+ :rs q/ik6e9by pushing off withb6q+:k1t ziyre l sci0da/:s9 his legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80z gdp cv354h8q kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighq 3dzp5gv4hc 8ter astronaut has moved 12 m?    m

  A ball of mass m makes zdo +(cxg6.fj a head-on elastic collision with a second ball (at rest) and rebounds in the opposite direction with a xgf +6oz.jcd (speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving anz6s qsc ky;9:w 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 d6 :kqz w;sy9scriver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off t0c6o1,6zlsi mxf+e gjhe top of a flight 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 stepfsji g6,e6o0 1 clxmz+ 1.0 m lower. 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 verti55buu::gox mscally into a 1.40-kg block of wood at rest directly above it. If the bullet has a ma5x b5:u om:gsuss 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 aw8ma 6l1 oix9+ukwhp uy,ri 4,nd becomes embedded in a 1.35-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 6 wu4uph x1k ,r+ioamw9li8,ythe block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowbj1h fam;d,)(v + otqpkoat 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 (jtv1 d+ q,kmfh;a )opin 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 twh 7; bwdfw1n6,x sx4oa 3zi5$ 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 uc2 lm sdzj85)suddenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of thescul52zm8)jd other. What is the ratio of their masses?   

  The force on a bullet is given by the vxqc+0 l6 x3)0kcersb 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 massest5qlqa.)g 6+se rmlkj )b +;mf $m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alzv/6q8 u6 1/9nsx y1pu5hrnwwy(u ibtpha particle and a smaller nucleus. What will be the/9b/s y1w quy( i 8w 5tvxunuhz6nr6p1 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 target.vhdo7(s ubs 671 g fc z-awbckq6p(x8) 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 ds:t96iga2gxq2x t gh/own 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 tm7vvrtd g/b.y j)o*x 0r5:9 zve:rgzho rebound from M, slide up the incline, stop, slide down the incline, and collide wib9j r v:v 5rzh0)r 7ye:*vdogzx/ gtm.th M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingrqa u5,v 1y6trshot effect. Figure 7–47 shows the planet Saturn moving in the negu5qt r6y,a r1vative 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