We claim that momentum is conserved, yet a qnj h 2*pr8);g4m/ng l)lrsvmost moving objects eventually slow down r m84 nl)q ;pv/ aj)*shngl2grand stop. Explain.

When a person jumps from a tree3d o9xogtc lx y9yq*z94k/j1x mn ,4ad to the ground, what happens to the momentum of the person upon striking t/noklyoz1j*xxyct q4mda 9g 43x9 d9,he ground?

When you release an inflated but untied balloon, why does it fly d(53k )gajcis(wffp 8 across the roomk)ws f(3 (g8dicaf pj5?

It is said that in ancient times a rich man with a bag of gold coid3hkv/mf f3: lns froze to death whild33/fk h m:flve stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction wh kzv ya9tuo/*quj/667; a.l 3tqzoxnwen it is far out in space and is essentially in a yz/*oaqtoq 3vn6jz9/taw7l.;xu ku 6 vacuum?

According to Eq. 7–5, the longer th6-b*:rf9:whxc/ v/e yvzba lte impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the valuvaex/ by *:c6 zbrfhv9- :w/tle 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 rigidpmjyp r(lh3e5g 6xn 4 iib6ta;5pr l4. as possible to withstand collisions. Today, though, cars are designed to have “crum;53np yma 6lb4 h( rp4r6ijlgie.tpx5 ple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball 6az8 mhh,k fl isl-/oij0y*y:o eb/-r further than a ball tossed in the air by thelhyb,a*emi8 :osro0hzyi/f6 -lj k /- batter?

Is it possible for an object to receive a larger impulse from a small forc*dc*eyow5z+ i5mjlvz 0dl z8oa5a1)fe than 51l**i) ev o0zj8+ozmzaf5d5c awd ly from a large force? Explain.

A light object and a heavy object have the same kinetic energy.lxkw)3i x:td9 kt4k )nzf6mq. Which has the greater momentum? Exp) zxx kt i3nqk.9k6m)dt 4flw:lain.

Describe a collision in which all kineti z2ij1y( i.ya;8 x7gacdbv m)ic energy is lost.

At a hydroelectric power plant, water is directed at high speed against turbine dn h 18frmy3so z+y)lum)(y,ublades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be desi 8 1 ummhsny)yz(fy, 3urol+)dgned so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wal:c9cr/; (r j5l kxbypeq5r5 udl 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 from a height h onto a hardww2i/l8 ).ir4b ; zj;sppk8q e feh8ll steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we cons88 wie8/lfqhj2eslirw p)k4;z.bl;pider 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 heavymy:oik7h yre)s:n-vdp cl7yo+36on ) load in your arms?

Why is the CM of a 1-mdsey8 ym;t: cn/46g cd length of pipe at its mid-point, whereas this is not true for your arm or legt;:cse6mg d/ 4dny8cy?

Show on a diagram how your CM shifts when you change from a lying posi n6 g wguhi7lmb-blj-8+wsh lue:e8::tion to a sitbm l6hunu87s i+w-ljweh:gb8: l g:-eting position.

If only an external force can change the momentum of the crq/ 5 ) yfv.* geh;;sulpuoojgea7;c)enter of mass of an object, how can the uh.;*e7s;r caq)) pvuo lofj ;g /ye5ginternal force of an engine accelerate a car?

A rocket following a parabolic path through the air sudzebr;1 5.jtwg7a 0 kfxdenly explodes into many x0f. z1g 5waj7;erk btpieces. What can you say about the motion of this system of pieces?

  What is the magnitude of the momeny(fwo6h* ewb +*88u zra f,qhhtum of a 28-g sparrow flying with a speed of 8.4 m/s+ f,hbzo8 q whurywf8*ea6h(*    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg sk k d7aqf(,y.ge//or uxier for 20 s. What is the skier’s change in vel7u (,aeoy/q /rf.kg dxocity?    m/s

  A 0.145-kg baseball pitched at 39 nw5 qin 5,wix )mtrz ;r)am *1gqw67kxm/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time betweenka)g75*,ri;xr i nww wz5qmxn qt)16m 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 horizonr/5 8k wa(skeasgarv4+a k5j 0tally with a speed of 10 m/s Fig. below Calr(v4w5k ja0g s kaa8+s erk5/aculate 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 boat is    m/s

  Calculate the force exerted on5fs.,+e ry*gkebcrwj 5zsj2 6 a rocket, given that the propelling gases are expelyej+25 ec*5gjk6bzswfs . ,rrled at a rate of 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 apparent breakaway for a touchdown isv 3fw.ys2d0f, z8abzx tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/wfz,ydxsab03 2.8 fzvs 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 track with a consqx 8t *.g1:l2nejz lvkm0zi l 0(r*tnwtant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the caxe*il gl0 tktn* zmlz021.8qj vn(rw:r’s new speed?    m/s

  A 9300-kg boxcar travelin a4 y6)av-nk7nnj ms7 ydx42uzodc 2*yg at 15m/s strikes a second boxcar at rest. The two stick together and move off wi nn)s*a2dy47 x zdau-yym2n7j ck4v 6oth a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speeds of 100km/h If h(v0sgf1;vcs7p4 jhc the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 jccs7f4v vh0 p1h;s(gm 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 al9zt(8w) pf 8;ctmuu5rs hwxh76, ho rkong with a constant speed of 8.6m/s on a level track. Snow begins to fallxzwkorh,u7psm)8t;8 9tw fr6hu(c5 h 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 alphafm c a r.tx*y8wx:nm2; particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha partic2x8tmmy*: ; fwx.rancle 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 penetratesrk1 8t,kz4l hfu6,2g v(plin m a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is n l4 m1 ( k8gpiltvkzh62r,u,fstationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speedt ,3p3)cvag)y+lq pbr 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 ebl zdrm7b8ww 4f6te*m ,ne)/velocity of 115m/s To alter its course f t4 mew,6eb* wzdn )rb/m7e8lby 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 6393 sym wdttv 8m1uzq9e/mqwgolf club was in contact with the balmdms69et vw1q3q/y w 9uzt m83l 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 av0ge *5a.v:z m/g 0z,(a t.ctj akkkp9yc: pzof 8.5m/s and comes to rest in a time interval of 8.0 ms. (5 ,v kv*a0(k:.gka9/mc.at:tp0z caj g zypeza) 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 strik2:k la3 q/heb9 g9hpvz5.td swes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charget)ij*kn)vy xpnnr)0)lc0 0svl a,* kq of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/hqt )ln0ayvcx)i*0)k)0,v k jsn nlp*r (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 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 runni;pvgetk6 ;ro +8hd;ktng at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tacklkv;et ;hok p g;t68d+rer 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 (mass 0.060 kg) points in the +x di)lz3jq vh )9s 1uo-f 0opuxcw5rection and sqo pxwcujol)1v03f 59 z-u h)is given by the 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 h+j+7 x lfd1qhthe lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fallxhdj f1h7+ q+l). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) widyzui9sy.8u, w-e mi 7. fico.th a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, whatcusf8meid-y,uyw.7 zio .i 9. will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, movink6zlytrg yv6k(b45 r0*/b aspg east with a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.9vgz6k06y*5 ks(yrl p/r 4bbta 00-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 elasticvb.yi2 ;sybh2yb9 v(5klu f9t head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving atbfyksh uy2vbit9(5;y9 2 vl.b 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis balay9v*v1 f q+g0u,ryof l, 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 perfe1fu0 a 9y*rfo q,vyvg+ctly 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 0.7c 7vbv,o1tuo9hxo6v 220 kg that is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the ino,v7xvo v617o h9tb uccoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as one app;:d 3leygddg*roaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to diff3dde:l yg ;*gderences 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 elastic head-on collisionqsc5mr34f/m teu 8bt 2 with a second ball initially at rest. The second ball moves off with half t2qrcu 8t 5mtm3b4es/f he 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 c n r*q,fuq74c v1xppbnz,7x)pube slides down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom,n nf1c b xp,)zur*qp7vqp 47x that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of macbl8k)a :d 4fyss 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 exp al 9sa;5wqas.eriment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A s9;.a qws5sal aecond 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/*5 jr4gwbhbg 1s 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 components of the ph1 bg*brwjg 45endulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lost, jk9 jl5;v .(yw.c 3mqplbjv9n $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into t4/yhs 3msv*zvwq p/xd; e9jx-wo pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acq4hd3-jxvwemq9 ;/*pvs /zy sxuire? (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 svo co)4vdwe2(nd w5.vtopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculatend) 5.de ovc(42ovwvw s 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 e3:i kdv3a 3kymcs1h +m and rebounds to a height of 1.20 m. Approximately how many rebounds will thea3e3+d3hvic:s1kk ym ball make before losing 90% of its energy?   

A measure of inelasticity in a u6hn2sopj b4/- cc0mahead-on collision of two objects is the coefficient of restitution, e, de20ahsn4o/cm -cp b6 jufined 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 pit+7va nti9:ep eces, 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, and the fuse is lit. When the firecracker explodes, the two blocks ne 9a7tt piv+:separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on witr(nx8at. ue yc(g q;s/h a 10.0-kg8 nutr.g/ yc(;es(x aq object moving in the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, amz v6ilcrg2x84b4i u p79vv)w n electron, and a neutrino. The electron axbv9rilvu4 7m)w8g6p icz 24v nd neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of masc uvq+.-ncyzty (ks-3 s $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic colli4e wq9rk44t uzmoo -a:sion between two objects of equal mass, each having initial speed the tq4o 4kazm-9 ue4two:rwo move off together 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 orign0n/*b6wm7h0lp koll abu3dx*4+cyc in 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 A3/ ah7y dll 0l*mc nobkp0xuc6*nwb+4 fter 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 ov1nc; - bl7 n6frn*wucollision with another atom at rest. After tw71nf*rcnu -nl6b ov ;he impact, 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) mak3m5t6mlgy:h c v aghzt4: 5;mfes a perfectly elastic collision with another atom at rest. After the impact, the neon atom trav5 l hvm:ctgh:5; f gma6y43zmtels 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 sh9asljjv y3e;f /ve+1vown in Fig. 7–38. Specify relativv vf3ya+ jvlj; e19/see to the left-hand 1.00-kg mass.    m

  The distance between a carbon a6*rb5d na: nkvtom ($m_{\mathrm{C}}=12\mathrm{u}$) 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 behind vq8 (ch3nz x:wthe front of the car. How far from the frhwvzq(cn:8 3x ont of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used ai t lgehp,1az.d.lv *vha43u/9 1kas r p.oap,s a ferryboat. If three cars, each of mass 13/lz .14 avpatp,.krha.ig olh v,9* u pd1esa200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of siden6 ap;);g rdbks $l_0$,$2l_0$, 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 9zeq upcs39 +uad-bblpz:9jdmh+ f(2 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 gravity in the horizontal plane, so that thju -f:(+hqbd2csme bzza9d3ul9 9 p+pe 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 r *5 od)j8r ,9hbpqkhg/ (llmpoadius 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 o8( kl ol)5*pdqh 9j,pbmh/r gposition of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the sam+v b/nnvip k:u(nec 4+e as those in Table 7–1, and calculate thn kep:nv(+u4+i/ ncbv e mass of one of your legs.    kg

  Determine the CM of an outstretched .yj 8 lrx.ovg4arm 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 ar w-3btv961mnkaw b 6a)ow1qpq r4h3yim bent at a right angle. Assume that the prmai wy npqa3w)3q 6v41t1b-h ow 9k6berson is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such tha61obeyrfe 5v,* 1wdonu az. 4 (oa ag+zyrrd)4t his arms and legs are hanging vertically, and his trunk anr4 *.grw rdoev1andz6aa+uye z4o15b,(ofy )d head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Eac:r2ia+e7*fl/ql nmq t s12l frth and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on fricti1eki*azemp b am92ax;.b5,d k onless 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 uniforkapw.fm5rfd6ri du phyloj+7, x5t0: hi6 ,)rm cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown i0i, jkt.,mfr ifxdyp 7w):pa6+556o rrduhhln 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 dya fjzpzv*;/e 09r+r mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajector y fe*/9z0r+przdva; jy?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–2)yl-b bbk5eose;b6: x9), $m_{II}$=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 iw d0 o5er;az8y1r0uv2gvu wb1ts gondola, 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 ropa00;wv2 ub5we1z8 our yvg1rde 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 passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is pprgd usr:7 2z;n5i1n gwa8 r-sopped straight up to a height of 55.6 m. If the contact time is rr n17 sgws82z:-na ;du gir5p1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travelib pfr8fc +w3r*ng 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 shot shown in Fig. 7–43. 2iu(b2qa8qkn;s- c.pkgu la uq* 0yb *Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also.*uc yqu 0qgbpn2 qu;ai s*kk2b-l(a 8 fall into a pocket? Give details.

  A 140-kg astronaut (includi 4.i39boy*m b*cfa sc06 lsyyhng space suit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-kg space capsubfbh yc 96icaym4ls0.**o y3sle.
(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 initially at rd9acj+cda9:8.k f.awmgpqz) est in outer space. They then push each other apart. How far apart ardqp+ cmfd8j9ga:w9.ca. )zkae they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (at reszykek- t6.q-/ to.sf pt) and rebounds in the opposite direce zys.. 6k t-ftk-qop/tion 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 expe-m0m6w lte8w.-kdksr rt witness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision,0k8d.wrm-6k tl-msew car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight od2f1z:9ayh x9 dy:lyn f concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, e19l2yyyad: nz:x9h fd ach 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 *-pp*5:z-kbdpb tt6n i)sszg(a m eg 2block of wood at rest directly above it. If the bullet has a mass (imkpzeats*b*25)d: n- gpg6 s bzpt- 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 pl54ap 1a:xmo)e:n qr gcn 79liraced 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 thoc4i7:nqa:n erp5r9 g 1ma)xle 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 aj5o7z +b4lga, 6rt q8ra 7ownvnd 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 q 58r +vrbazlao7twjo 647,gnother, 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 g*ch j+fi3mkp9kw i 19ag)sp3was about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly brvt- o1js- w )zg 2jhmys5ov8t48o*bac oken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their masses?mot5 vjtzc*g) 48 o1b- jsvo2yh 8as-w   

  The force on a bullet is given by the formula F = 580-( ,rn6d ct/vi*x ngtc.1 $1.8 \times10^{ 5}$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 q;o ep1q+c-blz cl0) r$m_A$ = 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 deca6pu b*-x- 7mx*wkvknjea yl94 ys radioactively into an alpha particle and a smaller nucleus. What will be the speed of this6*u- 7yln 9bm-kxp*xa4vjw ke recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fm-fbr/g - (dkoired 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 qgl:,, o;luk ljx6u;p 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 rebounddxh;/x,.uij m kk4ts-;ytqgxmtlhvt3 0) b) 1 m 3;x1b-iu)/sytht)tmlhg jk0 v 4;x.tk,xdqfrom M, slide up the incline, 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 7–47c*,q xgpe 6mppwa5ut9gw1 58 l shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) ofptx,5aec 9 ugq5g *lww68mp 1p 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