We claim that momentum is conserved, yet most moving objects eventually slo)bd 2 g3y i9sy ok85rmjpkr*n)w down and stop. Exy98dkgn2k5mbor3 )) pjrsiy *plain.

When a person jumps from a tree to the ground, what happens to the momentuue 9xvm acn pf *3rwz4 pdn8n83xz),4jm of the person upon stfj)nu88x4rxdmnepz a* z 3cv9p3n4w ,riking the ground?

When you release an inflated but untied balloon, why doel.x mhp:o9kfk,3s *a knyf(l0yq:1 bys it fly across the room?l,:sy( hlka0x9p .3fbn kok :qfmyy1*

It is said that in ancient times a rich man with ;vgf ziwyil- at1 ik4a-1u3w9a bag of gold coins froze to death while stranded ont;-akfiawu v11 -4l9 iy3g ziw 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 miserly?

How can a rocket change direction when it is far out in spa)(5glmx/np moce and is essentially i5 m/x)m gn(lpon a vacuum?

According to Eq. 7–5, the lon sq-3m6awff4ar2s:tl*a * vnrger the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deform *:-tasqff34*2rn ralv wsm 6aation 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 fracture or death.

Cars used to be built as rigid as possible to withstand colli oil7ulnp30+yb2n3vu sions. Today, though, +7vl3yn0n luu3b2p io cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball fuakses8f9* hk9rther than a ball tossed in the air by the b9sk9fk eash8 *atter?

Is it possible for an hjfk0x:;yrn3onz q2x f 2c,p3object to receive a larger impulse from a small force than from a large force? Explain.f03n x;yoph ,3kc:q rxnjfz2 2

A light object and a heavy object have the same kineti) gz p9bpuo65c9a4bx uc energy. Which has the greater momentum? 6z)bp94b9xc uo apu5g Explain.

Describe a collision in which all kinetis +f/st:z 0-.v1nqk5lb9u mfmky gy y.c energy is lost.

At a hydroelectric power plant, water is directed at hil)v*z sm2althb e1)c8kg nihb)8 lq;fe-bv 85gh speed against turbine blades onl k tm88clgnb;ehvb)q)5i1sa )e l-2b f*8hvz 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 that the water rebounds?

A squash ball hits a .fhl xoxp.uod6 pi6g d1 x)j: o9wrq.1wall at a 45 $^{\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 5p za)b/ 5ruwzxz8fk6from a height h onto a hard steel plate (fixed to the Earth), from which it r6r5zzz5/ apwbfk 8 xu)ebounds 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 x, 7q6usl+kn ha heavy load in your arms?

Why is the CM of a 1-m length of pipe at ickk3x:e-rs) u ts mid-point, whereas this is not true for your ak)rec uk3:-xs rm or leg?

Show on a diagram how youo0q )u0 ) ve s;pc-ea1totm5lpr CM shifts when you change from a lying position to a sittp em aqouvs;0)o e-cp1)50 ltting position.

If only an external force can chang.ynu 6hdzak81f b (w6qb)f:ud e the momentum of the center of mass of an object, how can t :bq d (zfy661fu .wdabunk8h)he internal force of an engine accelerate a car?

A rocket following a parabolic.ik,g lzc c , pvh:ervw/.nto(y6rg 8( 5kuhi- path through the air suddenly explodes into many pieces. What can you say about the motionkel o(.c /gihv8n:vuk rhc(yig- ,tr ,w65.pz of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparro8.n op,q, yg ey5vnq.xw flying with a speed of 8.4y5en..gvx q,8npo ,yq m/s    $kg\;m/s$

  A constant friction force of 25 N 3dxb-q)sjpqk4v i 4-pacts on a 65-kg skier for 20 s. What is the skier’s chq 43x spk-qd-4jp)bviange in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive straqe3ssq +;o ys 5xpir1)ight back toward the pitcher at 52m/sr135sxeiyq o ) q+ps;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 speed of 1m a 3tu dg9jl ds*-5oil.gmf n4r5qj 5yu7o*5y0 m/s Fig. below Calculate the velocityjmlngy35 duiu-m syftg5 7o q5j*a.l dr*9 4o5 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 boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases are ex:w. (r jsw8y5 7zjs ol ;rkxiiwh:4bw8pelled at a rate ofo84lrh w yw:i5(r7w;8skxjb i.z: sjw 1500kg/s 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 apparentb+ f +rh)c/npx 6pbav jj0,;4q.wkkf:p1lkdf breakaway for a touchdown is tackled fh1dj+:akf6vb)pl fk.0 w4j +qr; nc, f pxbp/krom 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?    m/s

  A 12,600-kg railroad car travels alone on alevel fzc ;k-b)ox +vfrictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the carfc+ok) x -z;bv’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar at (de yfmmn a2/ u*ri(0brest. The two stick together and move off with a speed of 6m/s What is the m /brm( u*fya(iend2 0mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speeds of 4me(rgo 5 ns4zydn0e/100km/h If the air strikes a person at the rate of 40kg/s per squarem drg4( n4 5oz0ns/yee 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 v sv+t d8k(zv*coasts 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 speet(*vz d vs+kv8d of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially movins q ji/3k7 itatoggbtj e*(54uxy051 vg at 420m/s emits an alpha particle in the direction of its velocity, and the reyiki5gj /(tt3 us x voj b15t*7gqae04maining 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 penetrates a 2.0-kg block of wood and em slkvemfrp9k4r cf 7j 8,8d5d/erges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bulle pdej fcr/ksl75,r 84d9mkf8vt emerges?    m/s

  A 975-kg two-stage rocket is travelin0j ,nkq wm( wvs+h3b2rg 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 trav bjc543 qihxhn)q0.m beling in outer space with a velocity of 113x 4ij.nb )qb0mqc5hh5m/s To alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at wio cu ,ox9,(rb-; mcja speed of 45m/s The golf club was in contact with tw,-9ojco(ux;,rcm bi he 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*k w.lw) ts1x,,zncxd velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms..,sxc) t1dwwxnz *l k, (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 strikes a daolz0pdh8sox-+k. 7mno3y+ 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 engin4 7- rc fomg.d nf r*jz.tve6*hyr;a7yeer 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 of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exertedr . ctfy7md.y7v;*6 n hrzoer-fgj* a4 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 57e6 5eool+zssi e3nqa head-on tackle by a tackler running due 5osqe s+e5i nl73zo6ewest. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) pojkkybw4hj2pey6,.o8:. h f,lr h /dbcints in the +x direction and is given by the gh 8 yr:64w .e/fjp.,,kkyjdhlbcob h2raph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum heig:qzjl 2mu+g-ght can a 75-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and ass -mz glqg+j:2uume 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 m hpj2+*o5avieoving 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 ea2+avhi jeop *5ch ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-on collishund ii4v4o-0 ion with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object huni 0-o4v i4dafter 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 h .eh.ld 3dg (fmv-+jqu8rul rnm mh)-3ead-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, vd38 g +.u(-mh.merludqnr-)jm3lh f 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 bal8yw;snyx2kp8 m*ri4ce* e w0il, moving with a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A repr;kcem 0 y2w8ew8p4x *iinyr s*esent 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 movin , 7l/(xv0 0zxci16fbfxedqzmg with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming ix0/fz bfml7e,10vqxxc d(z6softball 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 elasti xuhyu k4j,* 7ur7s8dqook(4 luy2.mgcally as one approaches the other directly fromlm,d u7x 4ukh 8uqko2su*ogr(j. y74y 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 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 ballpm,/8b n89gg/ hqgl yl makes an elastic head-on collision with a second ball initially at rest. The second ball moves off wm8 pg/lhgq,lg 8 /ynb9ith 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 incline)3 u 1 fo;gmec j,qi 95f )yondeduxe(ysf6(d5 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?ui,yyuo5mnf6dq)1e9)cgdd ; ffsje3x 5(eo( [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object o88z aq+s-pfq ajxt1:uf 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,1,0krfcyx7y i projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice ,x1 k0yiyf c7ras 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 traveli2hj+: vxnwes- ng 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal comp2hwj:nxes+- vonents of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction .)zc riu4i4s,f.h baq of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an8efe)ndc )6 yk object, initially at rest, into two pieces, one of which has 1.5 times the mass of thecedfy e kn68)) 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 jth79m fangy f5k39rr/z:dd * 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, knowzn9tryrh 9g/ a73dd fk5jf*m: ing that the coefficient of 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 hs26hug gzf.)veight of 1.50 m and rebounds to a height of 1.20 m. Approximatel26fhg. vu )szgy how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-3i(ogya0sz1)p,r ;jv w )0a* iaseowi on collision of two objects is the coefficienjg ai30)w,*(er1sw)oiy 0avpazi os ;t of restitution, 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 the mass of tuj u5 ovq-xta5f.+2ex4)fu ighe other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distauuxgj5 )f+ uvf-q54e tax.2io nces each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the s.-poetu fxiqbb2 pgz:.y 88; +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass iuqtz .psy-:p f8eo;bx.bg 28if:
(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 ele d9gj)lvdzwant):ue2qer+w))q4 iz1 ctron, and a neutrino. The electron and neutrino are emitted at right angles azd a4)l 2j+ :nwq)r) g9q1)viezutedwnd have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of mass ee0ow:28ih(1 c,demuj8u nbl $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equ(*no 4yw 1( w,xawbivmal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial directbivao4 wxw1y(wn ,* (mions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meexp1q6 7d axqxn: (ujc1t at the origin of an xy coordinate system. Ball A is moving upward alu:6x d1cn qpa 7qx(xj1ong 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 collisionr 04q5 zi(d el*1hvva2u iqsu5 with another atom at rest. After the impua v4vu5ie s10 hr5q(lq2zid*act, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision with another at) n6 ri1mt k5-notwxv7om at rest. After the impact, )w1v kx- 56nmtrotn7ithe neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system smui-zk h+,7 quk(bys*2 +e 0mhpy ;pvchown in Fig. 7–38. Specify relative to the iu he*bp2u q0-kzm syh7k(vycp+;+m, left-hand 1.00-kg mass.    m

  The distance between a jr:; 1g0,favk hs7gsk carbon 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 1-e.m*iby7vas4x* fw3hn+k 2rgcedj 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 ic- em*n*1is3h b.fyjvw+ 4g dre2akx7n 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 m hqlue h08/i3x, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaeql3u 08/hx ihded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sideswei ;6 9bnk:fvj 0cgwd,oqf3 - $l_0$,$2l_0$, 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 identl,.atky7*7or n*d d loical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane7rotd a, 7d*l*ylko.n, 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 ofhltxmu/qiuhuvh9l0t5+ +z, ( j/ctc( 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 (ul++/c5/tlth0mc h tqizh uux v( j,9of 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 caau7n dq b81no,lculate the mass of one of youra od7nuqb,n18 legs.    kg

  Determine the CM of an outstretw uzzqere(pfc 78,8(a ched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent at a right*bdzz x/;kg8 n angle. Assume that the person is 1xgbz*8;kzn /d55 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs ke4qaj -f s:z iogy*8.q.tp (ware hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. .jqzq :*yo w.( et-fk g4ap8siWill this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon are09 unt lqzk.x/.btv l; $5.98\times10^{24}$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 frictionless ice. s-:rtxsbcn. nk ,0x -uwmhk:80(o nua
(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 masmwdc/ r)a;kpf/6 vjk r wq0km)n8ey;4s 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, intwwy/6mv d c4e rf;jqpnkak /rk)m80 );o the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of;q 1-,tnwpitfa 0 *d: ng6vtcm a uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m ni:cgwt1 d, pv;nf*a0 tt-q m6mounted 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?    d    d

  (a) Suppose that in Example 7–m6xrq(0. ;l.; li9ys ryya cid14 (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,+ubl., ajwl4d of mass 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 w4,+d l.ablju speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and ise5j ox-bxy 1 6u;g5uvf popped straight up to e ovjfx5-;1gub5y6xua height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speedlb; a+ 0juh )nn7pafn- $v_0$ 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 corn lblgij. ba6-2er pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this-2l lab6ibj g. being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including st7w/ omvoa z8b, zm:q7pace suit) acquires a speed of 2.5m/s by pushing off with his legs from an 18 ,mt/ 8ao zbq:wvz7m7o00-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 a;-c;9w, vf(weiw xhi und the other 80 kg, are initially at rest in outer space. They then push each other apaui;,fh-v9 ; xwwiw ec(rt. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second bals:ruzpn 5. 9y+mze+0j4o bzjql (at rest) and rjyz+jub:.5 rqn 4sz 0o+mepz 9ebounds in the opposite 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 witness in a court case involving an autazslk k-:-zv*ir7(z: pd/qotomobile 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 kiniz::z7srdak --*zo/ql tp(kv etic 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 concrete stt-pj0 q;-m0 nc c4qfajeps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking thec4ft- jqjqa-m00 c;pn 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 blo c/jqo ,zjn qqkoyh9t/:i5l0ge1f9 )hck 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 the bullet becoiolq 9hk /h:/ ,1qfo9j5j)gyn tec0z qmes embedded in it?    m

  A 25-g bullet strikes n7uwc 9-t9f iyand becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficien- w cift97ynu9t 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 of mass 60 kg, sit in a rowbobjgqbib*x .rdy7 e.sk6 n9 d3e/y..elat of mass 80 kg. With the boat initially at rest, the two people, who havey6ql9.3 b esnyd er.i7dx*kg. /bebj. been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was ab8x(x*r *ncfkz3rw 7p tout $ 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 b jbcap:ozij 7grme5(cn. 44a) roken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What i7zbj4j. c:goer)4ipm a na5 c(s the ratio of their masses?   

  The force on a bullet is gi :n u1l*6r4uc1 v b79gllnp acroc.gp-ven by the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses.gai a +lt:5+sx6ovga $m_A$ = 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 deawods ifv(2r) cv3y3.cays radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the ryfiv3v 32)(d osc.w aspeed 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 aneki 8m8p)v :gm 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=2.2k29 ve29xjsk ab s)9 qgk7kz-xfv2ftq(g 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 up8; 3 ,:euh inibl(y m: yai/5gcpxc)uey9 aay6per limit on mass m if it is to rebound from M, slide up the inclincae6g)y;h38y5nu yl9apic,m : ib/e au(:y x ie, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure tpsjom+ mx37n/ig m ff+f5 2y,dw3k w-7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) offsjmwiyx ft732++ 53ndo-w mg fkp ,/m 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