We claim that momentum is conserved, yet most moving hcx*5v,y +ejo3a8n ua)dr jxmd l4.w0objects eventually slow dowclx5)o +xvm j*ar ed8nu,4dhy 0awj 3.n and stop. Explain.

When a person jumps from aqs0c+/6li qld jzr39t tree to the ground, what happens to the momentum of the person upon st+ j3lq6 0c s/qzd9lirtriking the ground?

When you release an inflated but untied balloon, why does it fly across thek+ 43 wlns-cw1jqxn y6 room?s n1q6wc4 ynjl x+-kw3

It is said that in ancienti:za8lv:sya ti r;fv-u*c*,va dc9dhyh 68 8 r times a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserlycya i*l zuvc9; *sdid-hr:vhat fv86ayr8,:8 ?

How can a rocket change direction when it is far out in s ,+heqba m9f*: +az+a hyzp/eqpace and is essentially in aqzya hbf9a p/z :am*e +h+e,+q vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smalwy qw;p9u4995m ntvuller 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 fwm ltq9upu ;nvy 59w49racture or death.

Cars used to be built as rigid as possible to withstand collist59f8q4z1l 0pd-u ;rp9d lqsofr tr-j ions. Today, though, cars are designed to have “crqdp5 d9 1r;f-8lftortr-0psq j4 9lzuumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hitr: gfrns:+ q.bs55 tkn a pitched baseball further than a ball tossed in the air by the batterrq b.ngr t+ kn:5sf:5s?

Is it possible for an object to receive a larger impulse from a s +e y wccnloo21l*0z)jt 1xej;mall force than from a large force1ylc 1eoxnwj e+tjzl;o)0*c 2? Explain.

A light object and a heavy object have the same kinetic ep19f; uw9: r-mcrfrcy nergy. Which has the greater momentu:mrf;-9pur fcc19 r ywm? Explain.

Describe a collision in which all kinetib5 g( p1 su3(ffqc:hycc energy is lost.

At a hydroelectric power plant, water is directed at high speed p;0fb8oy:bv -oa0q0te b wqv(against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead fo80;v a(p wtbb0qq 0o:e-vbystop, or so that the water rebounds?

A squash ball hits a wall at a 45p-p:,qok 8 -abkcn8 np $^{\circ} $ angle as shown in Fig. 7–30. 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 (fixf97m9dn0kwotd1 zg, zed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticmnzz,9 dw7t9g0o dk 1fks to the steel plate.

Why do you tend to lean back-ug t769 (ai w+w,y5mhmnbiikward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-pointv+oqlic3a 30g 9bs8 cw6dm d*t, whereas this is not true for your arm or gd+3owdmsctbc v*36 al809qi leg?

Show on a diagram how your CM shifts whenfu1;)wcs5+bc1 g(f ym-pkhnk you change from a lying position to a sg(n1b;5) +u-cpsmkh wykfc f1 itting position.

If only an external force can change the momentum of the cent8bxu-v1 zpm; der of mass of an object, how can the ;xp8-d b1uvzm internal force of an engine accelerate a car?

A rocket following a parabofq dmo r+ , g0dz4 2 -e-9o98,wknupjv*joykeilic path through the air suddenly explodes into many pieces. What can you say about the motion 2onkdmpofed4e , -9o uj,*- qykg90wi vj+z8rof this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed ofky2cy)oicfu huy 3sd nh1h ,; ,06v;gf 8.4 m/sh,)y03 2hfvhiuyyu dskc16 ;gc nf,; o    $kg\;m/s$

  A constant friction force of 25 N acts on f+/ ud7;y7m q3 0ww2gbrse:0bmnwxr va 65-kg skier for 20 s. What is the skier’s change in velocitbxwvm3n2bqyg7s; w0+md0r / :7 eruwfy?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive strat fnelsa.pzoxx *7)b(c ac9 .+ight backx)z7p.b xsl(+.o na* tc feac9 toward the pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a uaio4m; 00tq*jxqyc 1v.h ff9 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 h*014i tjofq0fva.yu9 x ;cq mchild is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exert0c ov25s6:bb5(4ndwgchdvv g ed on a rocket, given that the propelling gases are expelled at a rate of 1500kg/s4 h b dbsgv2o5c5wv0dn(c vg:6 with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an apparent breakaway for a touchdownqgayrm5 *7kp(wr)e y) is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their m erwyp*) mykq()5ar7g utual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictionless track with a c bt3(a9cv/gupq.stjh hys5* +onstant speed of 18m/s A 5350-kg load,initially at rest, is droctsg. 5vhbsuj +a 3t/( q9yp*hpped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar at )p3 ukx5hp,za rest. The two stick together and move off with a speed of 6m/s What is the p5h k,p) zx3uamass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally ,zdtje w8cv40msk(d+ at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square m+,z(d0w tckms 4vjd8eeter 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 with74 v:7cdevpeh a constant speed of 8.6m/s on a level track. Snow p:747vehe vcd begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle ine1v-i /: x/2vn:x plkxcf3 gkg the direction of its velocity, and fc pgk::ge/1x l2/n3-ixxkvv 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 it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates8bm,.tx hn.h(wdzu/ vrkbk 0( rkr4u; a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does hd;rt,wmbuknr(r (v.kzx/ kh0u 8b .4it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling ajwpxg; b2q92t t 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 masxzx 1-f6meg. ss 3180 kg is traveling in outer space with a velocity of 115m/s To alter its course byzxf. xs m1-6ge 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 eiv; ppnecxz4,9 1 ld10.045 kg is hit off the tee at a speed of 45m/s The golf club was in conta,e4n il 1devx ;9c1zppct 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 re5 joz-yi(p - )x:ug(n;a wqpmyst in a time interval of 8.0 ms. (a) What is g xwi-yy5 p) qn(pa:-o j(;muzthe 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 s4 + y1rzie y0p.zyki*hpeed 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 crashwortxsz4,+ u* t4zn 6fvukg xsej6.hiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30n,6us+ xz vf6xgz k.e4j*t us4 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 east and is stopped in 0.75 s by a heh(u.k6z8 sh/ kija1ay5qua kkl7em:4 ad-on tackle by a tackler running due west. Calculatej8hm7 u1y ks. iah4la:uq5ak 6/k ekz(
(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 the +x dix/un ps(szp, /rection and is given by the graph of Fig. 7–33 as a funn(s,s / ppzux/ction 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 witnfyf3px8 kdi 5**nhdp +ft *p,hout breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking streng i ptn*8yfh fxdp*f*3+ k,pd5nth (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 m; zbo6 .c+ lnrxgb8tx7oving 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 an6o7xl t bg;nx+zr8.cbd direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, movins 77g *rmvvvz+.dzj 2sg east with a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be 27vv7vs zgs. m rzj+*dthe 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 unhzpksy7vn( sz- z ,(e*dergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the posiezzvh(n z s-,k(7ps* ytive 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 8 .2ojec6 v:;iq:x wtvbcg sh4a speed of 2.5m/s collides head-on with a 0.090-ksqogb2t c 8j6vh:iw .cxv;: e4g ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent 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 colm.3a7 axv0c b1bm+.vs qg5v sklides head-on and 5ckv a. mx gqa03+7bs.vbs1mvelastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elasticalqht3j,:( hmmnx :ssh ybaf.1 4x yl5p,ly as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 m(ty,5.hm4 s qn3s:x, h jbypxl:1fh akg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ba 1av:2m8uais fll makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with v2fs ua8:mi1a 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 2 d: ur2,bzmfdincline 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? [Hint: Both leave the inc:d d2,m bzuf2rline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general casefwz6k/fi)grn 7, ct9 p of an object of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a mhv xk wop-0 g2n(5nwe*aximum height h of the pendulum equa5o h g-nx*(2wvnk ewp0l to 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 traveling 230m/s buries itself in a 3.6-k;d / z i.xy 1wrtufj72vzc:;bpg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward cdtyz7p2 u;/ rzf xb: i;vj1w.in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of uoezuc ;5d ywg; ijr/tb/mw:* v ,eg+(kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest,:el(cjo9mkrpn 5z +3 q/q3fd j into two pieces, one of which has 1.5 tidc: rj5ef(p/zoq9qjn+3 3m klmes 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 deoeg2qd /ibj e fij96 g06 *b+0,qjnlSUV 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 o/0n0j fq2qj+dj dbgl iee,ib*6 eg69sports 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 g8up mt -hu1o-1.50 m and rebounds to a height of 1.20 m. Approximately how--o8p1m uthg u many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision o:)svwnv6 x7 7fdo dv8jf two objects is the coefficient of rd8:sofjwn x7dv )vv 76estitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times tvt qcty2 bh0w+8wau29 he mass of the other. A depression is made in both faces of the+tw y0a8wcut 2hb 9vq2 cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-ofqi c/ /;dmwpm;cq-n2n with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass /;mi-f /p wcn;mc2dqqif:
(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 second nucleus, an wlmdk*r kz h::mj:13u electron, and a neutrino. u3mlk:h 1zw d::j r*kmThe electron and neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of masqy2i)s,fk a 2zndp8s.s $m_\mathrm{A}=0.400$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 colliswx4e xjqj4dv*j/pw.9.s gy)w ion between two objects of equal mass, each having initial speed the two move off togetherjj*/xxy g9 pww 4qsw .).jved4 with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equalwup*kt -h5iz ; mass 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 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 directi;zpt i-h kwu*5on 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 perfe7d/.kxob, 2 qjqma *nyctly elastic collision with another atom at rest. After the impact, the neon atom travels away aq7axb,o/ *.q kjm2y ndt 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 another atom at rate4td5i1t9n2 n2tqu est. After the impact, the neon atom travels away at a 55.6 4 9 2datnuqttet21n5i$^{\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 show /m+khev d99:c bcohg,g8 3dywn in Fig. 7–38. Specify relative to themc/kdv 3hcewy, bh g9:+od8g9 left-hand 1.00-kg mass.    m

  The distance between a carbon atom (5hym0 e2oj i9v qxebuv40bx 44;n-fnz $m_{\mathrm{C}}=12\mathrm{u}$) 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-k9f2uz l:aen 2m..yg-r +ozjvqatz)1yg 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? Asza2vuzn +rzaoyt2fq9egl.1 m:.j y)- sume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 68g5c62 qc 14hqb5svey4j/ q vn 8m2ikta00 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, de5vn6/mjk4v qb12qsgh2 8cc yaiqt5e4termine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidezsb:6 7c)o i)mstbh d+s $l_0$,$2l_0$, 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 casesljl br(v*yaa;p;5 ,ck of tomato paste (see Fig. 7–40), each of which is a cube of length lpll ( j;ac5k,*yab; rv. 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 20jgubqv+* rb w9su 9.zR has a circular 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 is the position of the center of mass of the plate? [Hint: Try subtractb*9 0g u9+s ruvjzqbw.ion.]   R

  Assume that your proportions are the same as those *4n)of gd ctt,in Table 7–1, and calculate the mass of one of your legs. tgndc,tf4o* )    kg

  Determine the CM of an outstretched /ts5xz2vu*m,a , nipzarm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculatewd t;vv 441kk(hc)k1;ipl b mq the position of the CM of an arm bent at a right angle. Assume that thedvq p;wck;14k) bhkt1 (4 ilvm person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position sucqwsuom, 3 3,h5 l*s u fp-pg9u8gjrr;s y7)ydnh that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculatemgsfh ysrlu3;-w8dqn 5) gp7 us*3,9jury,p o 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 Moon are 54mv.lbm:x /rpp rr8u$5.98\times10^{24}$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 apart on 4qhthbx 97 3yjt1gs5hfrictionless 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 uf4uc;2zev ycir:4pza8j (y(bkme g5 (niform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of (2 (y4 gefik5;j8a mpcvecz y r4uz:(bmass 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 un1 zbm,o(p l a:7d7bxiak ,8ar)v-df0xpezx7kiform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet:bkd 8 d7) ebz-lav op0 (xi1faakr7px z7m,,x 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 Ex-j ovy30r sdsz5uw .(. a)htbn0,xutsample 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 zkjy1b m74;p jmass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and dirzmbp 7j4kj1 ;yection (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 popped straic3tq,0+cjs + 3vfsfk fght up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average kct0s3q+3cjf, sf+fvforce on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling witaom-ixho+t 4 4h speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot . 5n q pptsyr9x)srnnf8wgqe/ y620 z:shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will al:p692n n) fty.ygq /8w5s zx0rper nsqso fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5mzbg1u8 7sl lm//s by pushing off with his legs from angl8/z7 mu1l sb 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:;hv y9qigdh0mr .q yh;ty+2w the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when 90ihw2td: hq;v.;yy +hqgm yrthe lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on ela1pp*z ;j4ypkemjv k -1stic collision with a second ball (at rest) and rebounds in the opposite dir*pzpj-k1; 4p k mve1jyection 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 witness in a couw o30x gz(o2te 9mhgzi 0b9jd2rt case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary carhm zwgebtd 3o2ox90(i g0 z92j 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 flight of concrete5)fvw(mr fd- g steps of total vertical height 4.00 m. The ball hits four times on the way down, eacf( -5)mdrvgfwh time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically int2vqm5hb o .iru r+*h5l-wr1 in.0y0rnnvm de 7o a 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after thiv0udb5vr2 *mni7+1whr r nqo0e..n5mr -hly e bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1 vwuttvff p )2l j*u8(w 00/j+f6laqdg.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 the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bultjujpwf t)g(v0v /6*f +80qad flwu2llet?    m/s

  Two people, one of mass 75 kg 3b ibujl5 )6cd08llfrand the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and)ril6 ll8dbj03cfbu 5 in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was about :l4;29 t k ox) am97pmh0qsjki7kcwkobxy.f 9$ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments by ( i y97dy,)qqfv endg:1l5d qjan explosion. One fragment acquires twice the kinetic energy of the other. What is the ratidq:5) vjy ni,efl9 dgy(d17qqo of their masses?   

  The force on a bullet is given by the formula F = 5e9r*sw2uj sv580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses df, 7ibhwvb3v9c 5-y,6xpven$m_A$ = 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 fcx0 th+e fg7a/x.uu(decays radioactively into an alpha particle and a smaller nuclextf0u+( e c.ug7afxh/us. What will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angle of 30uu: p04n mvk;p $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.yn mqp(y.29r m0 $^{\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 f*hfu +traa1:fbq71h4 .fqj ythe upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide w74+y.rbjh11a h*uffa: tff qqith M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 t ulg -+f1xo*tqr5rg(shows the planet Saturn moving in the negative x direction at its otf-1tgr5l*ogx (u+ qr rbital 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