We claim that momentum is conserved, yet most moving objects eventually slow z,y/-dnz-e ei down and stop. ziez e-y,dn/- Explain.

When a person jumps from a trkz9std:n0s;)0lns r see to the ground, what happens to the momentum of thess0:nstlzk0 r ds)9; n person upon striking the ground?

When you release an inflated bupkooxw 7j4t9avjfh (/i ufh+9i :9,r wt untied balloon, why does it fly across the room 9othjp9i7orj9+ ah4(x,u :/k wvifw f?

It is said that in ancient times a rich man with a bag of gt vj9;ue6kg 0 ;-j,hbxvkqpy -old coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so misegyqb6 tve -,uxjkvkp0;j9- h;rly?

How can a rocket change direction when it is far out in space1 2( hl5a9vw smvtfn 5gov:lk8 and is essentially 5so9nvl2 va1:hf lwgv(k8mt5in a vacuum?

According to Eq. 7–5, the longer the impam u,kiknhrba 2/6j 6j a:+n:toct 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 during an automobile collision mjbo/r6 +jakt ni,h6:ka2 :unand reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisionsr vhdxq)w-5/n(q y4o f. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantw4nr)do( yqx-fhqv 5 /age of this new design?

Why can a batter hit a pitched baseball further than a ball tosyf t 2d b0/6ks8vnsct4sed in the air by the battersyv46t/scb2tnf08k d ?

Is it possible for an object to receive a larger impulse from a small force u+hyram 6eou d:ouz atgz.8uef(4:/ *than from a large force? E eou:tz8uarz* /ad.ou:4f g e(m+uhy6xplain.

A light object and a heavy object have ijp.3n.w;y :rume3 n bet4hb wcg+e//the same kinetic energy. Which has the greater mom/p/ tje.iwbr n 4yn:bug e.3hwmce;+3entum? Explain.

Describe a collision ikr,.mlp9q )xfv 6fik;n which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against turbinbh6( krcp7 /zne blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be d(6 p/r zn7bckhesigned so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wallx79*rgd/k*mg3 j3xam e3 aofe 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 onto a hard steel plate (fixed to the Ea/ xb; 07xl:95z9ovla izr8l ;za ktypurth), 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 steel platptk9rzzxxibla;v ;0:98o/ 5ay7l zl ue.

Why do you tend to lean backward when carrying a heavy kg xgnsqou8 r8iq 73;5ne +.afload in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, where *.i8ockhmbp/as this is not true for youokb.h*c 8 /pmir arm or leg?

Show on a diagram how your CM shifts when you chr lw0gb ;kqfa wsj psp-o25+2*ange from a lying position to a sitobpsa ;-*k fp52+r0wg sl j2wqting position.

If only an external force can change the momentum of the w l-bstd0.:0fy ;ostr1pij, x center of mass of an object, how can the internal force of an engine acceleratefy,wdol 1-. 0 rtsipxsbj:0 ;t a car?

A rocket following a parabolic path through the air suddenly explodesuc yb:u ll6 o7+1avd-xy 9ha/v into many pieces. What can you say about the mot u/vld6xav a oy- +9:chb1ylu7ion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed of d-p n4x6ah-8gjvcz0z $8.4 \; m/s$    $kg \; m/s$

  A constant friction force obnktbt,:13 lxf 25 N acts on a 65-kg skier for 20 s. What is the skibl3:1tx k,tn ber’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hii 06 zsm f9o8-e/+lkf9yyauli t on a horizontal line drive straight back toward the pasy+lf9koi6yi /uz8 f el09 m-itcher 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 horizontac5 4s3aq 1lttk5ns :molly with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kkqasl31 5 4o:stc5tmng. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given tu) 4q ,9oubg c zbn ryk fb(mce64/95vaec43awhat the propelling gases are expelled at a rate oo/k4z6gc fe 9um4ac,ca n9byvreb5 u3q 4)(wbf $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback mov+mn8yq )7.yqd )frwxg ing 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 alod +viqg6*.h *-kkwgm zne on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initiall.h+ -dk**zw mqg6vkg iy at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveli0xo+w/9nxi: p,udpq ung 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 of 100km/h If thenw ciu5cv21r pn; dx-: d w2u xnr5c:ipn; -cv1air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum 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 speed of+i, 0/-zr j/ drx.uvxnsdrc)d 4yxjv: 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kryxv4xd)0/ v/: udi rzc.x j-srjn ,d+g/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 aig-am26ixl9q9 k . xqnt 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha partix9 iq2ka- ml9qg.n6x icle 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 it is emitted?    m/s

  A 23-g bullet travelinst8p6 7bo/0n+jqckfi: yv 6rs g 230m/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless nriq 6f6:syjbc+o vpk/st70 8surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage roc*z-3 tznbi na1qaa 6b1ket 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 outer sphc4tq)dmoc-: v63 hra ace with a velocity of 115m/s To alter ir d qthov):h4cm3- ca6ts 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 speed of 45m/;0k5)r,m:9v 8vpzpdngj dbxc s The golf club w x;)c npvkpmj8b9r:dd ,05vzgas in contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes to rqexx; f nj817dest in a time interval of 8;d jx e8n7q1xf.0 ms. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s ao6+-it )j6cu/iqp x rstrikes 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 automobip(gr9tczl v8 h, d,aal:jd66kqe *,pxle models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact 6:lgrjtp9zp*x,e,hk6a8 l cq, vdd a(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 eastmxne4 t/) fw)b and is stopped in 0.75 s by a head-on tackle by a tackler running due west. x mt) /4fn)bewCalculate
(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 0.060 kg) points in t+ s 22fpxycr3eq2) xushe +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estixpf2ssu )qyc 3+xr22emate
(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 heighote2:-t 8q h+/pap ou yi gqm/bcd9f2*t can a 75-kg person jump without breaking the lower leg by mo/ofh cdq tib*t q2p:p-/ag e289u+one of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of collides hehn8alok+*v, eku2 sn; ad-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.nlo8+*2kn sh va ;,eku440-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 p)dq hx889cb rggsvy0ui) 6w )a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elasti )8 vu 6)wgxsghc)r9i80pybqd c collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastic 8strne h:b*sy vpz6 9)head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, wvst )h zr:9sb8n *yep6hat will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides head-onw(vyo;kxfc ev 8,fme,eqh w o+*n5-l0 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 -wv+x qol ofkemn eh(y v,we;*,5 fc80of 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 moving with a speed of 8.5m/s co pgvse*f;3s,c meh td9: 3q*jbllides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7mvs;qem3hsg *, dc p9:bftje*3/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 ridefbl z/bv +hr ;,6mfl+u collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and6+ lzvfrb+lf;,hb/m u 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 9tmcrln0r)lgv9:pg7 p8 t4h vhe6x 9 telastic head-on collision with a second ball initially at rest. The secot gvl8ph 4 l:7 c60et x)v9g9nrtmr9phnd ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless io2/4emj,pur, 7 wtv1/zc o zqbncline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the ruoz/o/vzb14,j2mw p e c,7tq incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object o)pyoo*er-0 m)h1rrw tm* d5s(7fqmdrf 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 maximum height h o kb: yks3 k-;x.prp0yyy1z;pxf the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swi -kpzx br1y;kx. spy0;3:kypyng 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 ,jo7yw xglioi318 2-xq i 3lqu hn,)wf bt(h*b230m/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. Determine the vertical and horizontal compxq3yq l,b) 3 t2hw1nii *hbfgx(w7oluj8io- ,onents of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetne0x ( ol g2pnriv.vth7+pq/ev* (wxc4f1-t fic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into twoqm1q*v c fuhh-*+im) x 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 each piece acquire? (Let A represent th mq x+vh**i -fh1)qcume heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped m.c)lv wrs dx1i5x lchqe)6,: 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, calcsex5m1):hxd w,cci6q .)lrlvulates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and reboundse0yd8q8 r4xpdudk 6n; to a height of 1.20 m. Approxr6xkyq4d80pe8 dn ; udimately how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collisioa vyzrb.qv 7 qk501xl;n of two objects is the coefficient of restitution, e, defined asxblv51q k7 rqaz.0 yv;$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
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 9im*sc48 uj; 28uigwvy (dsu,d+mcrpinto two pieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecra 8r9*+u4pyiimc,j dwu2ms ug(v8;sc d cker 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 ,y.;hrdn azt4i )tld6zk uy/03( vtufthe +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x di t4ut;6ly0(tnv/z ,aduzy fd.ki3h )rrection at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a se*2dsjh:lam*ighui ma6 /-b 6mcond nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and hai2 * ij6*s:6hm gm/aahublm -dve 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 zs tuu6355juomegwi.b 3fy0:$m_\mathrm{A}=0.400$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 inelastio:/.yw3 hknun c collision between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial /ynh.:n uo3kwdirections?    $^{\circ} $

  Two billiard balls of equal ma:d ku;n)e3 mgbj-j7d ;mjgn6 tss move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with spee );m e7k3j;jd:jd-gtb gn6nmud 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 collisiono4)z wl, jhh jk:*odr7 with another atom at rest. After the impact4 7zk)wlj,oroh:*djh , 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 perf5g yotu6pmd588 mi c(yectly elastic collision with another atom at rest. After the impact, the neo om85ypgdy68i5mc u(tn 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;y: ftza94m.9po1m qc5jn xlnf 7h;lk three-mass system shown in Fig. 7–38. Specify relative to the left-hand 14x.;ojym :;cp f nl795hkmnt9af1zq l.00-kg mass.    m

  The distance between a carbon atoywy gp 5,e nqrm9r3fe *tf/,/vm ($m_{\mathrm{C}}=12\mathrm{u}$) 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 1e+a (gl, 5lmca050-kg car is 2.50 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 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 ga+5 lca(,elmhas a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of man1m7n2qs6 kx+u7 k/n kdzf6jwss 6800 kg, is used as a ferryboat. If thrk k7 unnmw j21 qn/s76kzx+d6fee cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides sw9.ykdjgt5 s 3ik ,(k$l_0$,$2l_0$, 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 identicg5bms6ed 2yzm4+ y ;zxal cases of tomato paste (see Fig. 7–40), eacby+g5;xsz46 med2 ym zh of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of rad1i e3fk5p fb j0smf.m8ius 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 positionfs.3jp0 8kmbfie1 f5m of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calcvz **lel) 8be u4o dmg0bzb6u8ulate the mass of one of your lee lbb*o* 8z)u4med0 v6lb gu8zgs.    kg

  Determine the CM of an outstretch380h ucbd 5z4iaz ohv,ed 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 tmld1)doc.ji*pgy / 9the position of the CM of an arm bent at a right angle. Assume that the person is 1l9p d/c. m)oj1i*tdgy55 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a pos:t38 bni 95d4dk grxudition such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CMdi3b rgx: d94du t58nk be outside the body? Use Table 7–1.

The masses of the Ear1ig6pnt4d9 d xth and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an yf wmvl+wn/:a(;:gja80-kg man stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform ca dnbog8. )h-s6q-sxm.5ibfq ylindrical 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 showns.dgm)o-. xq- ba5b6s fq in8h 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 un7au0r szovj06i lc25fiform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical 25vl zaco 0j 7f0ru6sihandle 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?    d    d

  (a) Suppose that in Example m3aok e3/-ro52e7l pdyq xhw 97–14 (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 the air and j1dj3s )w r4) mvxe+m.udpn*u 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 .1ur *upv)3dwjes4) jd+m nxmballoon. 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 i4j 3x)er 6z 8u1+xqk1zblvxyqs 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 contact. qqb1r+1lxz x4 v ux8k6e)jy3 z   $^{\circ} $

  A rocket of mass m traveling with sa w,yjujfx 474peed $v_0$ 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 n;oq a/do/ r5oy /b-rsthe corner pocket shot shown in Fig. 7–43. Relative/or;d-o/n5 /absyqr o dimensions 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 suit) acquires a speed of u7 fl 26vpatq*2.5m/s by pushing off with his legs from tuvl2q 6p 7*faan 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 v-bm1sh *i+cg other 80 kg, are initially at rest in outer space. They then push each other apart. How f-smcgb +v*ih1 ar apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a secondg1x)2hf/ hnl v ball (at rest) and rebounds in the opposi2hn /h v1glfx)te 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 an expert witqo elc ;56 q*syos6x3nness 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 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 (9olq;6n36 c5 sx*qso ey0km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight v+us00uwzzk6:in +t vof 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 differetzv6w+z0isu+k0:u vn nt 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 we a4:4 a1e:t mrd -it4ad 29yqt9cr aakf3*ihtood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s hoe9kt:eqa42 cra:ir9-4amt d 1ha 4tt3a* dyifw high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becog.gh5nxc50sst6b* hv mes embedded in a 1.35-kg block of wood placed on a hori bvg056hhs5x. st*ngc zontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other o k4f8l/k5pfog f 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 of the boat 3.2 m apf5fkg84 k /lopart 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 waskhpdo0qudoylpj- ;,0. 64 3sjrtef x4 about $ 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 fragmecy 17cnv87 sqr3r agh3nts by an explosion. One fragment acquires twice the kinetic energy of thh7v 83s qcraryg7cn31e other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 580-( .nq: p;r ywlkr 0,dykw9k.u +s$1.8 \times10^{ 5}$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 massesy128ncjb))b m0nmkm(qiaa72i l* g nj $m_A$ = 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 int1(.cv6thzu ny o an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed ozy.6hntuvc 1 (f 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)vi- y2yor; kv. 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=2.2kgfw,9w1p bz czi1 rmag98crf/ 2 slides down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mass m ifo99.l hstip0r7:cq ti it is to rebound from M, slide up the incline, stop, :90scip.ql7irhto9 t 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 shong:3lg, lvv9/ fz1vpl ws the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6kmlv:z1,lvl p3g /v9gnf/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