We claim that momentum is conserved, yet md 39klrpn lb7c:- gq;dost moving objects eventually slow down and stop. Expla rkdl3 : ld-;cq7bp9gnin.

When a person jumps from a tree to the ground, what happ3-u8oaekypc-*m fu.2*ly muxs5 jyl2ens to the momentum of the person upon striking thy ucp o mxe.-l5fas2u l*-y2* kyu3m8je ground?

When you release an inflated but untied balloon, why does it fly hk 45*ru/luhx across the roomkh 4/5ulx* uhr?

It is said that in ancient times a rich man w:qci ufg x::rft,c-joa8m 9lu -h3 /nwith a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he :g-x cnu ff/l3m:qwt:ouci r8j9-h,ahave done to save himself had he not been so miserly?

How can a rocket change direction whe5i+y u;fqn op ):4du)a:idtlen it is far out in space and is essentially in a va)pioq diu+45e :fudalytn:;) cuum?

According to Eq. 7–5, the longer the impact time of an p:6a5 * +0;eku-1 xuaiw raouc)cldc zgg3d,limpulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fpg*,kd:zc5 +g-uc r;e)a6x c1o3laladiu w0 uracture or death.

Cars used to be built as rigid as possiarbzp/*xy-)(td5c m68ybu. 2eo jlwible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon imjy lb/y()ou e*z628 txr.i pbwcd -ma5pact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed im zr 5/lqt.oy7a-ex1 rrog svv6,a8o(n the air by 6q(vrrl t,sox/m5e.v8gyaz1o o7a-r the batter?

Is it possible for an object to receive kk o)alxel5,9 5lb6oma larger impulse from a small force than from a lal5o9k l,oe6) lxk5 mbarge force? Explain.

A light object and a heavy object have the same kinetic energy. Which hase1if 85x0:)k, nj 7cuxg bkr g:chxn;y the greater momentum? Exn :g1ibjegf7x n;x8)5 cy 0rc,:xkhkuplain.

Describe a collisionuas3sb - (w1yz in which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed agnfrp36d3 8hc(+y to5ldvl 9 ksainst turbine blades on antnk3yroldh6vpf+ c3 d59(l s8 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 rebounds?

A squash ball hits a2hr a9(pwkr btz 1:ts7 wall at a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h h s2:x0 ;+mdfo;aefz f dc2o;gonto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during w o 2fa of:ded0c+;x;2mzfgsh;hat 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 .3wfrubxahjj**7u)r a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this i .sxsgu7xbxde-s*6;v s not true for yourgx.*vsbx xds e7;us-6 arm or leg?

Show on a diagram hoi7qw;;f/9:kyx 2xim *tzy sz rw your CM shifts when you change from a lying position to a sitting positiok:q 97;tf mxwyiryi z;*x/2szn.

If only an external force can change the momentum of the center of m s19r,u0kva bx3s:y swass of an object, s0urby9s ,:k vw s1ax3how can the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air sudd7v sfps mj 9muw,w940xenly explodes into many pieces. What can fvxw p90 mw 9us7mj,4syou say about the motion of this system of pieces?

  What is the magnitude of tgtv0mc35 *,uf1dgqk4 bey2m t he momentum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 xb/h q .nsk c(-o sn2*juz38ils. What is the skier’s change in velosu2n.n-i *zh8c/ loq( s kbjx3city?    m/s

  A 0.145-kg baseball pitched at 39 m/s istr g30n+uucj 1 py(xl6 hit on a horizontal line drive straight back toward the pitcher at 52m/s If thxugc nl u6yr ptj1(3+0e 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 oe5-b fu)8skgd /qzs7mut horizontally with a speed of 10 m/s Fig. belo-5gze qs8m7u)d s kfb/w Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that thyi6bs f r(djenm5 7a6:e propelling gases are expelled at a ratesn rd6(f 6may5bei:j7 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 movnq 1,al 9z+ y23(jdsu*wdtvo cing 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 car travels alo):ifg tl se+ota3j3r5dv; 5c bne on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new spr3 l b j5setto;)d3+ 5fvica:geed?    m/s

  A 9300-kg boxcar tracj;n .s,r3lrflj 0 o4yveling at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds or-+.p :lgyomd9 ou 2nwf 100km/h If the air str+ romy:g9-2 dp.nuo lwikes 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 wi:7nvm,* dfqtwth a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car amq dtnfv *7,w:t 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 emits an alpha park gn(8c7gz/ lnmq0 lt/ticle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a0mgzg8q(l7/ knt l/cn mass of 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/s penetrates a 2.0-kg b-9rc.,t r ftaodd7-f hc64 wkalock of wood and emerges clean f-oh w7c.r-ka9ttr ,f6ddca4ly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rock .uaa e;xs 7tr: 87mbtu.91qsp9sxuleet is traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in oh )vc8(u:c1q8lpd r keuter space with a velocity of 115m/s u8qph:)cel8( 1v rdckTo alter its course 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 sper zt .4u jl7c)gp:ac-i9ty5o puo4ps*y0 d4jyed of 45m/s The golf club was in contact with the ball oz-7upj).s lyj9g ct dyoatp4i4p 4c:05yru*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(:q 9utqoamr9fuel ,35 pgm.k velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nai. o(r muqfl:5m939 qk,ge atpul?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg a)v e fs7ka; * y4q0yrdlq*we5und 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 new automobilk7z j+k -c4q8w;h zynle 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 kqz;c4z7n+lhw - yk8j 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 ru /fe0 5vpai)*o7et+qy hyy *pbnning at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tacklebi7hyp)5 v+p y yeea o*tf0q*/r 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 teumlhw5 0jfr id4bjmu)*) .p6v nnis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–3w jm06v 4 jrd5ui*.p)hulmfb) 3 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking z)bo z e4bq9c9the 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). Ass )q 9ze4cbbo9zume 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 movinglfaja4ks0 u wa6 6* +egvt55nq east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg batl 6fg j*4vaq6n a5ws+k0a5 eull, 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 ecq7 7m0b d g .7qbyd/+p jx)u,-guouvpast 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 vuq70 p , 7gdgx+)d/puoj-yq .b umcb7each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal w dzcs*zz2n. rz+ /h+bmass undergo 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 +b.dzzw/z+ h zr sc*2nat 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 o x x/crf;lj :dedw03y)f 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 perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent0 c 3xw)d ;xe/ljfr:dy the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with pcuo (2wsyz,l*4* wema speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming 2*zwlc ,u4s( om y*wepsoftball 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 elastirjdly6qg1.u2z80ba9 8vk lg fcally 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 1z80ll gu86drqvgay f2 bkj.9 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 elastic head-o l7: laxe kr*8nym)z5on collision with a second ball initially at rest. The second ball moves off with half the original speed of the first r:x5nez8ko la *7)mly 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 cuo;xd: 31h,quo9 qwu dfbe 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, where does each cube land? [Hin 9:wxh3d uqu;qofod,1t: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an objec-xlyscqx0 ,e 1t 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 maximu37m,u lf1egt 7ia;q eim height h of the pendulum equal tol ,gfie1qi; 3eum 7at7 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveloklg ls9w zz),8-p2h.1zp qzling 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. glzk zzh1.l, 2zl9ow 8 q-pps)Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the frpp bpnt6so;z*1h2wm x x+ d;(uaction 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, i8b45v zke-3qk e.wm wlnitially at rest, into two pieces, one of b4e lvz3wkme .5wq-k8 which has 1.5 times the mass of the other. If 7500 J were released in the 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 a 2300-kg SUV rb t;/ln hunzt*/in6. 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 the speed of the sports c uitz/ l. 6/t*brnn;nhar 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;wm abz:ip,w zwe:9+zs3lr2x m and rebounds to a height of 1.20 m. Approximately how many rebounds2w3zz,rlswx a;w:mi epb +9:z will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the coeffici c7yulxh+ jl9)ent of restit9 yu)jc+ x7llhution, 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 twoa5 dheo+.rzlmhf1b-.o m1:+w 6glj xz 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 56.wlxel +m+g.f1z hrh1m:bodo-j azthe block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/sov, g7iqn- y2b collides head-on with a 10.0-kg object moving in the -x dirgo y2i q7,bn-vection 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 decaysk91deycs 1 x:(xfdvn- into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right ang:dk1 f1y(-xdcn9ves x les 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+:kmfn*utx 99:3 bz5pkccsj v $m_\mathrm{A}=0.400$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 idg j;cx7/ knid) oc-(vnelastic collision between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle betwc;)7njdi cg-k(ovdx /een their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles andsf gn.89xjgv/r0, fax 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 axijxn,80 v / ag.xg9rfsfs (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 n fs* qhex ;89qur)qzn*(9vswa perfectly elastic collision with another atom at rest. * s s(9;xfr*q)q8uewq9 hzvnnAfter the impact, 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

  A neon atom (m=20u) makes a perfectly elastic collision with rayoovudo( x1;u. * z(another atom at rest. After the impact, the neon a (dy;z1ua.ux*(vooor tom 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 Fosbz(d7 /l7xw ig. 7–38. Specify relative to the left-hand 1.00-kg 7b 7dsx( /wzolmass.    m

  The distance between a 8gw ;d-1ro+8 v4b08fb 5 unyup ksoirrcarbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of the camret62 5ti k3qw ds*ga64r0+d bu g3tar. How far from the front of the car will the CM be when *6 +bd 33ru6qrgskae4g2atm it 5t0dw two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by )n2k 9jrqwac 118 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE,n1) kw9arqj2c SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sideslwer(g-p8ew9c djg -/ $l_0$,$2l_0$, 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 cases of tomato paste (see Fie gkuh8 /b( hrb13(ippg. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping uibh(b rehg/ p8(13kp it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius :l 6glqw.yekmi7 x ,4q pa91 x0m)xxcg2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the ce m14:p9 g6)l qe70gkxayx xmilc.xw q,nter C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as tq3 ujuqh0iix5 :t.. monfmu9b8enz. 8hose in Table 7–1, and calculate the mass of one of .35uh08 . zi nf m:tmq.9euqj 8ixbunoyour legs.    kg

  Determine the CM of an outstretaea0 (cvt0hu-r6a;a) -efpesched 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 anx*zy v/dh.x 2a arm bent at a right angle. Assume thayzdx x. ah/*v2t the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are happjcay 1yw*d;vvz63( nging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Tap;j*6 w(zd y pc31vyvable 7–1.

The masses of the Earth and Moon k.ub k;ezvg5( 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 stand 10.0 m 1set9 o bf 1):qt8yq6xy.gorkapart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of massor4 0kwokfrnfeb0lx /c,4 / (/yssp. c 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is thkp obs ey0/fwr4/oxl c4c 0f/s(.rn,ke point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindricav( d ,w,glvcp kvctw21 wp*)g/l head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectowvg)l,d* gkv/c,(p2cwvt1 pw ry?    d    d

  (a) Suppose that in Examplhe6vqekiyi y61(n2 k2i1au0xu b 04t ge 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in t/ t sw);tergjm: +mjoxj ct219he air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens ifm;j: s wt9)1 /jtr+2ctmgxjoe the passenger stops?

  An 0.145-kg baseball pitched horizontal2-abrdj.c 1sv ly at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the co csj2rba-v d1.ntact.    $^{\circ} $

  A rocket of mass m tr vg,gijre-. 8)rdiov )aveling 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 cokx(b;c 56z ;4tl) 5f dbjtubovrner pocket shot shown in Fig. 7–43. Relative dimetb5 b;4 u);d65jozctxk (bflv nsions are also shown. 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 suk3lumo7 f+4b xit) acquires a speed of 2.5m/s by pushing off with his legs from an xu4olm+kf 3 7b1800-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 mamksm)if +7i. ess 60 kg and the other 80 kg, are initially at rest in oute )si7i+ekmmf.r space. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision o+ g (sp ofmn019muel0with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speedp (1ommgl0f0e o+u9sn. 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 involving3euuy)8lt pd)l m8i3s an automobile accident. The accident u)ip8es8ld)lt3u my 3involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a fligh(i*8du+tn oxf t of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the hord8otf+(*nix uizontal part of a different step 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 vertically into a 1.40-kg block of wood at rest directlyi 7r: *hrtwrk6m ;;uod above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will ri;*;rmd6urwhok : t7the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strike8,uia,x:xfshmj q 9u+ s and 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 betweenj, shu+,am8i9xu xfq: the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of /th+58mnnk+ .cc8a)r vjtjd a mass 60 kg, sit in a rowboat of m k8n+tja hcc/r+ 8)5.jmadtnvass 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? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was ab6-.ow/2gg f sufn-4luh,1 (nx(d bstcg5cy ijout $ 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 fragm2qw 0otgy z(3xez0 oo4ents by an explosion. One fragment acquires twice the kinetic energy of the other. What is the rati 4023(qotx0 owez zyogo of their masses?   

  The force on a bullet iswwtd1g+5gk+o q e)(e v 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 massesd :az cs(1tyq- $m_A$ = 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 aepx,m*+/hwyg xv*asss6j - *l n alpha particle and a smaller nucleus. What will be the speed a*y mjvx**s6lp g h,/se x+s-wof 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) is fired avr0j y*,glygb*mu0/vra81cmt 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 de(bkhjiv1, .qziei q5 ,; xnr:mj8 2llown 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 th 5::ql lxigx0ww rg4*ge upper limit on mass m if it is to rebound from M, slide up the incli*gwx:gg: x wl4lr i50qne, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shbm9ks arjlkxoh+-082 ows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is+ko 8rsl h9x0am-2bjk $5.69 \times10^{ 26}$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