We claim that momentum is conservm, 3 v6,(zs:qzuqo qzxed, yet most moving objects eventually slow down and stopvoq zq: z,xzm,s(uq 63. Explain.

When a person jumps from a tress(s0qps t.r h *yf3u2e to the ground, what happens to the momentum of the person upon striking t ts .ss*h0yf 3(upq2rshe ground?

When you release an inflated but untied balloon, why does it fly acrvs-eo 8x:gxb0e w/c*r9i x)vgoss the room?x9g-:*xwg c0vbe er) /xi8vo s

It is said that in ancient timeh)rev 0q x5- jrk:1ndb j:kb5js a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he en)h :v5rbjx0j: kq r j15-dkbcould not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is :lx8j0dp2yrbgpq 3:p essentially in a vacuup:xpg23brypj ql d:80m?

According to Eq. 7–5, the longer the impact time of an i qhs93u-:t 1mf(aj -qdz8jfoj mpulse, 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 o9- h1qa-f8:tujj m qjd3(zsf reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand 3:q jw;lmsdef(jhj:yc:gg 23(v tm i 0collisions. Today, though, cars are designed to have “crumple zones” that collapse upon igg:sdjew v 3m:(0 mj2( yl 3jc:fi;tqhmpact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossei h+*p1t8abv fd in the air by the bv+thia bf1* 8patter?

Is it possible for an object to receive a larger impulse from a small force thy3 wkib izi.59an from iiy3 9kbi 5wz.a large force? Explain.

A light object and a (pnmz4ail/) fdp4/ xg 1lw 9ygheavy object have the same kinetic energy. Which has the greater mome)l14ix/ ggyfz (w4 mnp9p/ld antum? Explain.

Describe a collision in which all kineyls:l 6xus)tkrf 89opf(0nf (tic energy is lost.

At a hydroelectric power plant, water is directed at high spb80 vgqvc s7yvc2- m/;j vbg3peed 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 stop, or so thpc;b2bv3g8vq 7m- s cvg0v /jyat the water rebounds?

A squash ball hits a wall at a 45 c 50/:icfczavxhj8 8 m0p2 dy*3ud q,g nhjnn1$^{\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 (fixexj+idape,uw4xe/ pmto6o (n 6::7 dzz d to the Eart6pz:ejt7,n ea4o/ m:(xoz 6dp uxw+idh), 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 plate.

Why do you tend to lean backward when carrying a hea* j /nto-2)aexufmky h 6ye++rvy load in your arms?

Why is the CM of a 1-m length of pipe at its u(u4h(mzqe2)o w2 ,waeq8vo smid-point, whereas this is not true w qu 2mo(eh8 qs(zvowa2u,e)4for your arm or leg?

Show on a diagram how kp9+iesga1c-qgg 9q.4b4ibw your CM shifts when you change from a lying position to a sitting p- g9w441aqik.g+bies c 9pbqgosition.

If only an external force can change the moi;dk d1it7u t2v +-ekcmentum of the center of mass of an object, how can the inter-e1kdt7 cdvk t ;iu2+inal force of an engine accelerate a car?

A rocket following a parabolic path thro6,7ixnk v2bmmz jg0b j/ e/i6eugh the air suddenly explodes into many pieces. Whaj/ 207imbm/i e6ezknj xgv6b, t can you say about the motion of this system of pieces?

  What is the magnitude 2:/a:fp9x5 wni sxjfgof the momentum of a 28-g sparrow flying with a speed of 8.4 m/s i pgx/:f5 nax9fs2w:j    $kg\;m/s$

  A constant friction force of 25 N acts on a( d ;vs+op8.s-a: p9uewyxsyw 65-kg skier for 20 s. What is the skier’s change in velocitsyww dvy(a:+. 9-psx peu;8soy?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizo5)jc (b 5f j;jsb: bfub6jp 5g:z9mouep;7nccntal line drive straight back towbmf oj59bcj 7:;;je )njp5:cufugc(5b6pzbsard 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 ap8f1k4e59kp yxx0ce- rir :gpackage out horizontally 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 kg. Ignore water resistance. The velocity of the bo14 -ka5p 0gicpyx:rkfr98x eeat is    m/s

  Calculate the force exerted on ag +xj pjigb0s5+b7- +v: ypq(x*hig me rocket, given that the propelling gases are expelled at a rate of 1500kg/s with a speed * p5g-bsp+jg+vmebxy g:+7 i x i0jh(qof $ 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 fopy7 k7(yxq5jpr a touchdown 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 mutual speed immediately after the tackle?j(k y xp7pqy57    m/s

  A 12,600-kg railroad car travels alone on alevelwewji9m rtq27x; q1e3 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 speed?w eq1wim7r ;qxe9 tj23    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a s hv0. yxk9- 5bvbz.bboecond boxcar at rest. The two stick together and m0.vbbhxv-5k b.ozb9 yove off with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at spe2d3mekcr5cb( a/zx+ yeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimatcx3ym k+ /(2cre5dabze 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 cuegs* v6/m ( uil,h;ggoasts along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 minum6ihsv(e, lg/ *g ;gu?$\approx$    m/s

  An atomic nucleus initially movi scc1,7st2w7--p dmt xi ,oz iit*z0xqng at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha 2o,s-i7ixzpwt,-m c q0tc idxs7*1t z particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood9e.c2zgjc zvvg)-9e5j xb h:j and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move afte-vcjej c52gzjg xhb ev .9):9zr the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling agpm.e)ys 4(3ul opep: wg5-s+shl1el77 vbpgt 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 space with a veomq. l r* mt1)b6/ gogpm,4cqylocity of 115m/s To altermg4qpr tylq go b.*1,)mcom6/ 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 speed oz1i52 cul y9o*o 7e(eziyf5vuwe/ vl2f 45m/s The golf club was in contact with the ball fouvi (2uvcllz2 5y1e/fey 5eiw*zo9o7r $3.5\times10^{-3}$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 o7ud+q ;yo qlp6f 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the n q u;6+yoplq7dail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes a wal, p zgerouq71-l 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 engine;ymsdw tm2v e+ r;zzac.a* e7g4n1eh6er in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model oe;acetw ey14m +; 62maz * .rd7hsvnzgf 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 sto, (rwp9ctd. ndpped in 0.75 s by a head-on tackle by a tackler run 9n(d cdr,.pwtning 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 tennis ball (m+srzjy6c v 6jj8 waw +.8yngp7ass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimagw jsy6cr68azyj+ jp 8nw7.v +te
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking the lower legiu -r 94awr: 6cav+uxj bone of either leg? Ignore air resistance and assume the CM of the person mov:xw r-j9 uiacrv ua4+6es 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 +v bpz(o3v6 zkmoving 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 represent6vbzk(p o3+vz the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-on collision nucdx/ (stk +8with a 0.900s(8/ud+ cktnx -kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-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 max+jdf lg q9)f2ss undergo a perfectly elastic head-on collision. If one l)qdf 2fj+9xgball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving 7 3obm/ tqb t;wx9:cdowith a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away fromd3ot : q;bxc/ wtm79ob 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 t5m icrrc3,a8collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounce 5c3 acr,m8itrs 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 elasticallmyda-n6p 0 xx;rs *xi0y 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 approac6x*xi n dp;0-rsayxm0hes 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 headfjt7 p9w;t4vnp w u:+d-on collision with a second ball initially at rest. The second ball moves off with half the original 7;tfdpvpuw +jn4w :t9 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 slidessn2o)v f(k4e9s d q(3pf gmmw;qv*3ib 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 qs;onep2mb3(9 )si4 3 gv*mkqd vf(fw90 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 o b z/ 8/bn(vq5bl efhbxa.51omwd63hsf 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 maximum height hj;n; 9o*skw zu h4ru))h1 oplpei6a i* of the pendulum equal tourp;s eiw*hn za1k;9oj6 i4ul)h p*)o 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-kg pendulumyc q 5 us:+)vimyp18gm hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal componentsq1 up y8m5s)vmg:+ci y of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinettcaef5kw2i-t 4/r 9n qic 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, in9vx :55o 1uuxkqe:knm2:ph* fj z(dx nitially at rest, into two pieces, one of which has 1.5 times the mkuz(f*h up 1d :2jvk59 :xomxn5qn:exass 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 collid 2v4fwj ,a(hw3m ogk0ues into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient ow,jhuo(fg3mv k0 aw4 2f kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height of 1.20 m. A: n:fd-2s wk)jg ,rdmjpproximately how many rebounds will the ball marjfk) wsd2j:mn :d-g ,ke before losing 90% of its energy?   

A measure of inelasticity in a he ivmq8n,lpwut7//d ww q/7n* hmq3kz2ad-on collision of two objects is the coefficient of restit m7w ql/q//ztd hw u7qni, kp8wvn3*m2ution, 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 int/o(eynhkyp owe 4h q78zw*q(*o two 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((o qw hph8eke4*y /*onq7zyw 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 heafx 5re(af 51)w,ag ph; vtlj,iki;+c dupbl( 7d-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of e ge(r 7jlltdi, 5w,ix)pv+;fa;1( ahubfcp5 kach 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 second nuc5 f+e,vmxauw. leus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have moxue 5mw+a,vf. menta 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 3puv-gx :7j/pa2 /rvqgzdms12nj 8 lf$m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two obj387pe 5 bqfadeects of equal mass, each having initial speed the two move off togeb8e5afe3dq p7ther with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the origin op7 cf1igb(u8 h5qdb2 e gdw3/zf an xy coo dif7q h/dgz1c w3gu(8b52be prdinate 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 direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with another atom at res d br0o74v nusbxk46c:t. After the impact, the neon atom travels away at a 540crx 4knvb:s7oub6 d 5.6 $^{\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) icl:g .f,e -vog43p abmakes a perfectly elastic collision with another atom at rest. After the impact, the neon atomep:fic3,v g.g4a- blo 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 t2zwt3 nlk6r+ arue,aa:u k-j-he three-mass system shown in Fig. 7–38. Specify relative to the left-hand 1.0aw3ae-ru z ,-r:an tku+kl62j 0-kg mass.    m

  The distance between a carbondcw/ gf(-:nom8vr8d0 4rm 5ld wx o/hg 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 2.5mqf.*fe( l8d0ja gng (t6cl0 i0 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 dfl8e *6q fj(gm(galit. 0n0cthe front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 hp7y(( rrf5 k xw7:hj4vrc/hxm, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, ar:pkrh w75r( vj/4 yhf7x(cx hnd SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides9q sup x(2(ntt $l_0$,$2l_0$, 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 ir6d7g.af 0ej:u f1vs Fig. 7–40), each of which is a cub10i.ja:76f vugs d erfe 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 ) ,r0dzkbhl9v+4rd dgradius R cut out of it. The center of the smaller circle is a distance 0.80R from the center v )rlrgd4dhk,dz +b90C 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 those in Table 7–1,i (lut9eiqy4; and calculate the mass of one of yoeuq(i y it9;4lur legs.    kg

  Determine the CM of an outstfs1 :msut1597gk nlc oretched 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 6s/ dyve0.axu the position of the CM of an arm bent at a right angle. Assume.ey uxvda06/ s that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position suchh uhrnx6+8 c5u that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate howxr5u6+n8c h uh 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 andak x:w-*wzfn;/ xdby8 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 80-kg man stand 10.0 m apart on frictionlen* 3q:;*fvvqi 7d ex9v5p xvwwss 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 mass 2.00 kg and a diametej3y/ p 2+yy7)iri)tgmqb+oigr 0.0800 mqyp )or3 +/2y)b j7iym+t iigg mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of vudee44t e6(2+mb uqqmass 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. 7q uduve+4te(bm 4qe 26–42. 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 7–14 (Fig. 7–2 c3)j31je33j4fz :xkbs :p nmskast(g 9), $m_{II}$=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 sta.r, o1gkx;h/q) x(pjve1 r pezb65 teotionary 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 (rele;et6eqp1 (,bhrx v/. jg)5x kz1ooprative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes *-qrm)s zb w5va bat and is popped straight up to a height of 55.6 m. If thwr*bq zs)v- m5e contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with f z9-81wxmeoe 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 shown in Fig. 7–43 :uy/jxfd-p0) v88f9ztqu hbfv6 0foe . Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in wve8vt ozph90d-f0b8f yju6u :)f xqf/hich the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a spe:nu8a h6zprh ,v3i)j)-nhur ned of 2.5m/s by pushing onj -6vrunhru)az8i)3 hh :,p nff with his legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are initiallyb, xb ffn63wb5 at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 b6bn3bfw5,xfm?    m

  A ball of mass m makes a head-on elastic collision with a second bka uoc,5+y4 t;a9cuvx all (at rest) and rebounds in the opposite dirkx,v u9c;o 5cuat+ ya4ection 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 cou hkgcza6 y()q2rt 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 wheels6 zkac2)q(gh y 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 ,k)e /qjw v 26g,s jt:erupg-eof concrete steps of total vertical height 4.06gusp-ej2,e v/qjr k t): ,egw0 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg blg ns4k +ety f28sw:f4zock of wood at rest directly above it. If the bullet has a mass +8wfn44yszkge 2f:s t of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood plac3wws opjsl: d;qte.vr(c+ ;3sed on a horp:w ejdvsslq3+c;3 ;. tsw ro(izontal 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 ud* gu3v5ofn;8.ozkl:)d ayz and 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 in what direction z:d) ny ovd;ko.3f*u5 a8ulzgwill 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 d-pd27(/ckw(n .4klrwxb cyhabout $ 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 intbk nx/6m98j icto1 2zvcft;m(o two fragments by an explosion. One fragmext(if8o cvbtz9m kjcm/ 1 ;6n2nt acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 580-(l+ex1b-/1ysyco:azk zcu p5* $1.8 \times10^{ 5}$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 masseslorzvi,k8 1a v8w 4 mp).:atuf, 9atqj $m_A$ = 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 radi:+))ei zmfftam q nhvs +f9x;2oactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the spee+emthmq+);9n :zif sf) xavf2d 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 t jj.o.iq-eoz -8jq5f) is fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30 nsacj- -*b4ex.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 masn(k/mqw/m t 3ms m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collintmwmk(/3m/ qde with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slinda4 sunha 6m c,b).r1qgshot effect. Figure 7–47 shows the planet Saturn moving in theqr abuhm)d,ns ca. 164 negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s