We claim that momentum is conserved, y)b6 8n o1murrjet most moving objects eventually slow downmb u8r 1)onr6j and stop. Explain.

When a person jumps from a tree to the ground, what happe/dmt ne. 9sv0uns to the momentum of the person upon str m v09us.ednt/iking the ground?

When you release an inflated but untied balloon, why does it fly acrou z)o 1;asrzq 0(v c*qd)kbqa+ss the room?vcq*qz1 ao0)duqa)+s(;rb z k

It is said that in ancient times a rich man w,,)av f gfvqx+ -t)cmsith a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push hgt )a ffqvm,s,c)+-xvimself 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 far6oq20m2t+ugg zujl; m out in space and is essentially in a vacu2u2go6 zm+0lmg ;qj tuum?

According to Eq. 7–5, the lon i2m 3kg4npkw)c mx.8ager the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the kni43w mcg28x. ap )kmsmaller 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 fracture or death.

Cars used to be built as rigid as possib iy i6ay v7oms3.:5zf g(xdj;ple to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of thiadg . mpovijy i:(yfs;5z73 x6s new design?

Why can a batter hit a pitched baseball further than a ball tossed in the agy+ el)t hhwlg+x*.8 t.9jjrnir by t9lt8)gy. .+grjxw l+hnhe j*t he batter?

Is it possible for an object to receive a larger impulse fro ypz ,f.c3bb9om a small force thanp,bfyb 9. 3ozc from a large force? Explain.

A light object and a heavy object have the same ki b/ zvlz0z;;(ub ,vilznetic energy. Which has the gr;z;u,il vbz0zl /(vbz eater momentum? Explain.

Describe a collision incqmfv jlyeyz g)*u22m7y /zj /ta .1)yj v2fw0 which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against turbpyy ,+ okoohp7(mn-r1 ine 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 ty7opnr1+p ,khom(o -yo a dead stop, or so that the water rebounds?

A squash ball hits a wal dg h 5q6bki(/q1qza*ep9 t;myl 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 droppepaa u*yo21w /bd from a height h onto a hard steel plate (fixed to the Earth)a po2/1b yaw*u, 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 he n0,5wev c*v+u 1khy rho+ h6:juus-gjavy load in your arms?

Why is the CM of a 1-m length of pxl;x+h8 o f expnm;).xqne2 h5ipe at its mid-point, whereas this is not true for your arm noxh pe8x;2+l5;h. xe )mnf qxor leg?

Show on a diagram how your CM shifts when you change from a lying pnl 282qpsei2h cqw-g .osition to a sitting position.nwl8. 22is 2-geh qpqc

If only an external fb umt t-;,w8tdap)4 xyorce can change the momentum of the center of mass of an object, how can the internal, u;pwt 8ym-dt )t4bxa force of an engine accelerate a car?

A rocket following a parabolic path through the air dzo g;(wxl5:yn (tl-hsuddenly explodes into many pieces. What can you say about the motion of this systwd:t(5 hn-y ;x zlog(lem of pieces?

  What is the magnitude of the momentum of a 28-g sc otzz(,fjp0 m uyoo* x:ci8( :/hqmh0parrow flying with a speed of 8.4 8y0z cj*h( c,i:z:opx uom0( hmq/tfo m/s    $kg\;m/s$

  A constant friction force of 25 N acj9-1 ecyzzu9b: huwq,ts on a 65-kg skier for 20 s. What is the skier’s chazwzbj 1:y9u-uhe,9c qnge in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horibp/pj+0tk6r 8ok j5:sn npq:izontal line drive straight back toward the pitcher at 52m/s If the contact time between b8kbo/ sjpkp jt 5n+r:nq 6i0p:at and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat thr 7hh1jyl-b8b thx a06lows a 6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, lah1 hb07x8hb6 y-tlj 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 exerteyrrc5uhoc;2,m oflra,2dqfq,+kng 2 s0 uj,+d on a rocket, given that the propelling gases are expelled at a rate of 1500kg/s with a speed ofr 2hos0gdlr+ck,,+2 n ,u2my qrf;a,c ou j5qf $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s onx nzceg*xpy/(1c- 4li7 0fbr b an apparent breakaway for a touchdown is tackled from behind. -/gfzn7rib*ce p 0 (x4 cxlby1When 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 frictionless trac6 5y1qmzb9r 6kz/hwihp2qgv ,k 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 1vkh2y,9r w6 5gb6mhq z pqi/znew speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a secon)t3aeiplv sbz a ag ;*,0;ue/cd boxcar at rest. The two stick together and move off with a speed of 6m/s What is the mass;*3e 0/b,zi ) avaas gclpt;eu of the second car?    m/s

  During a Chicago storm, winj6e3m2d0good7ap qw - ds can whip horizontally at speeds of 100km/h If the air strikj da-27gmp6o 30qedowes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of 8.6m/sjg*clha3b4(f 0llzisbk. /k+ mcc7x i:84k fy on a level trac/ki z l4.37hx lk* g8aibcc: k(bf lmj0fs+4yck. 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 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an ;c/kz a.x8kryalpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has y/r kaz;k 8x.ca 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 emerg5 ki75jwicw,w 0v p2p+cwq- j(xkhcc6es cleanl5,7-q kipccx+(5kv jwi cpj6hww c0 w2y at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rock r4 qjk82l1tf+u o1srnet is traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 318wrkc+tvbxx m1( 59-eb0 kg is traveling in outer space with a velocity of 115m/s To avrkwb(x+ e-bt5x9m1 c lter 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 of 45m/s The golf clcqc,hc 5qhfspj ( )0c9ub was in contac c)fp(jc95 0scqhhc ,qt 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 rest in a : em d/8mv*ex6qvvqn-time interval of v:vx 6vmde-nm8qe/q *8.0 ms. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes a wall ae :7t-r qd,1fs4bqgaet 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 cfpch7 *b8570wdapk0 yheb 7virashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new modywk0 api*850d b 7hpvb ecfh77el 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 andvlw/:t:w27kh b:zf6j6h xcqm is stopped in 0.75 s by a head-on tackle by a tac vlj/ qbx6:w2f mhzkw ch7::t6kler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (massiwlz :ruw1 34o 0.060 kg) points in the +x direction and is given by tw 4wroi3z1l u:he graph 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 height can a 75-kg person jump without breaking the lower leg ktzjv67j)3qo 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 sq z6jtkoj3)7 veated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x directiol8o)8to g stk5o ba wrqh76 *ew/g-p)an) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent th)p6brkh qot-w*la wg8set/ooa)g5 87 e 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 em5 w w)nqo)6gll+i3vr 4oq e;gast with a speed of 3m/s has a head-on collision with a 0.93 ogqlo)+)w5l g;wv6m4riqen 00-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 mass undergo a perfectly elastic head-on collissi4rtn)q aj nos356s h; x5-ofion. 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 repr) -nar qfi5o6; xsosn5j3h 4stesent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a 8d( bre9g*8bzisp-ld9 s2nkwspeed 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 colliseprd w*l9dsbs2 gnib8-(z8 9kion, 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 coo(jly8,c 6bcgae/7u, ia7xtih q 5zj7llides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backwii7jqa(cgy 67lea,xt c 8b,o u5j/ 7hzard 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 elastically fd 1upg k) 5*5bvs0u siwyp,-xas one approaches the other directly frvkug 50s)1u,5* sbpxf wid-ypom 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 ball makes an el,d-a k51o(l o5fcod+akv + dftastic head-on collision with a second ball initially at - +dotolacod+(faf 55vdk 1k, rest. The second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube s gqrbrl4w 2kv1f6or 8c6:n -ehw( by,jlides down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only f18 r lrw ,wb bcjk-6nh2vqoge r:6y4(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 incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an ommiq i(z02zw +i41vd55vbuc o bject 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 pendulum6 h 5uqch;e65t qp*x1xsfbo1rh6qd;y experiment, projectile 1 results in a maximum height h of the ;hbh6c1q ;fhqx5 udq r *s5teo y6px16pendulum equal 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 travelia*z1 ll 7megk5ng 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 comagkm1 *5ez7ll ponents of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraca 3-2:-+m qpdmtikak jtion 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 break;h z ;d42s vy1fwsobg+s an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, v2yz+sfgs4 ;w h1;odbhow much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV pk f(wf)zw):x5rdff2 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 frictio(fw kxzwf5f)2fpr )d:n 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)23nou yim+jvtq76s,yz x jf2v6 / cdb of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rnof26/b it+x6 jv 73muydy,2c szq)vjebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-onn2rpysll-)e63 e )h0hmh p8m l collision of two objects is the coefficient of restituti8lnm6y spe)r3 )lmp0 h e2lh-hon, 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 intox jdx6rwzgrw/54u14 a 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 in it with the block reassembled. The reassembled block is set on a rough-surfaced table, a1x64zg u 4/arrdwj5wx nd 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-qn,sqaze h)5f 67hslhh f0n ; 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 i z;hh -haehfs,f)q 7qnns05l6f:
(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 aqqn b/fok7z m3g +y;z umh6d+9 7bf1am second nucleus, an electron, and a neutrino. The electron and neutrino are enmkq1/9u 6mmq+bbof3g+ zy dh77a ;zfmitted 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 m-la09ugupk p7 ,k k(xmy)whv39s1 xplass $m_\mathrm{A}=0.400$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 equal mass,3 o19wp3l zhk+ii ;jcr each having initial speed the two move off together with s9 3j1rp+iwhi;ok z c3lpeed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls or:;y a:f;sxh ff equal 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 direction of ball A and what are their two speeds? direction of ball A:ff a syr:xh;; is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makee87vjm k f;2hjg9.i hjs a perfectly elastic collision with another atom at rest. After the imj.m jfi kv;hhe98 27jgpact, 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 coghd54jhw2z6 w fd7pr sq -4-jjllision with another atom at rest. After the impact, the7j-g2 dhjh5jp644zwfq r -dw s 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 shown in Fig. 7–38. Spi s,ovy 98p5zy30ll/k qs:xctecify relative to the left-hand 1o:8l,lxz 0ysvy 9qkpt5/s 3ic.00-kg mass.    m

  The distance between a carbon a2aje6h ;jwd l)-oq6yu s rp*0atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m lykw+*lla -b48qn1ru bk 3 9ftbehind 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 sab 1k3 yuf4*q +wl9k-rtlnlb8eat 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, of mass 6800 kg, is uset8ga -zmp wq46m0 8gszd as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the 8 6zwmmz0t g-gpqa 8s4loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side t18n4a0pm n u05vuwais $l_0$,$2l_0$, 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) palleitu+ b) ge f.1e yf-aw2:edu6pt has a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravitugp a-)twei1 :6ef.yuebd2+f y 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 plat0*l1e 6zvfidl4yclq t); d9l. qj qk0ue of radius 2R 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 th* l6kc lu ef.0i9llq01jdyqq;dz4vt)e 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 inb) .av0l 60fd*y0lkz 5 xyjor.cu0eyh Table 7–1, and calculate the mass of one of your le 0)lldh.6y0bx .j0ycavez rk*y 05of ugs.    kg

  Determine the CM of an outstre( 4zgzyr jii0.tched 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 a sw363 m/0g ctaagc3bfn arm bent at a right angle. Assume that t0s33c wt3 c/ga6gfabm he person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his zsm*vn+lv8wb * + *xcul3xd -carms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line tvvxxc8s+*lcudz l*n+- 3*mb w he CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and M1c:rzh (6fip ldjc, )m,c8(u rc to3eeoon 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 frictionless icbbv(k1/tf v,fb /* vqde.
(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 andpo) bk 77j okk2qpbp/- a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg an/p opq7bk7oj) k2bk p-d 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 mass 2.00 kg and a diameter (a(hycrvi5vd:; hey50eay;v55 i (vcd(:ryh h.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (15i xo ex,.y,qci6k imFig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass v:vsd ql -x2/qM, 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 direction (relative to Earth) does the balloon then move? What happens if the pas/dsqv 2xvl:q- senger stops?

  An 0.145-kg baseball pitched horizontally at fe*nbo3)c(8n8t ba 9(n kl urtstrikes a bat and is popped straight up to a height of 55.6 m. If the contabn*8al ub nefkntc 3 )(9(ot8rct time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travelin -ctm+ux (l3njg with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shoc2ns/2 2 lgujkt shown in Fig. 7–43. Relative dimensions are also shown. Should the player b n kcu2/2gsl2je worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including suu4 o5tf27e +*jb xlnepace suit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-+el7*f4 tn2 buo5ejxu 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 60gp6g xtra 4x(6 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter asa6p4gxxrg (6ttronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (at rest) mbn5icue+ hp:u3n n)3 and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the second u5mnp 3 3b+he n)i:nucball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving/gf568cecttuam41:y xa jbt ) 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 fe :fmgu ta)/8y5ctxjtb16a 4criction 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 con1u, ag, urf8z9rtn1bo crete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a 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 ooafgr819z, rbut 1,n uf the stairs?

  A bullet is fired vertically into a 1.40-kgq.iyil7u8 1 rrz37 ewewqh;)e 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 8qwyueh w;1 3 )7e irqliz7.rethe block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and bemil 06 bx5i1jfi*e d;q-zqwl+comes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes timf5dq+ wz q-*6ixlejl;i 1b0o 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, si ah,x95 5ckvq+ ykz huj/snh85t 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 will the boat move? The boat will move+/ k5h8z h,h9u v yqkjac5nx5s    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abo 09 g blwpxm:hln1/8qjut $ 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 an expgbpb2))h(v o wlosion. One fragment acquires twice the kinetic energw 2op))vbhbg( y of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formulav*zfr;d :3 8uazjf7+oa6w zka 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 )h f0odfzanrp x**,v+ $m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha pm f-w -vz9kwu:ep:d 6farticle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle isfu6w:km:v9dp --zwf e $ 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 firedr r6s3-,x,9cx rklj5vso5ekt 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 slid31/dsu z gdtjc0 vmq/6es down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mass m if it is to reboundolkk+t yx.r4 0 from M, slide up the incline, stop, slide down the incline, and coll k0o4tlx.k+ yride with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational sl-*l3up4 k y ds6m,z)i7c10 tbvx qrt* bob8xvlingshot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction8 to*sbl7x4 u ,tqi01)xml vc-pr k *yzb3dbv6 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