We claim that momentum is conserved, yet most moving objs/zx)z ob5i ,.ugc4 luects eventually slow down and stoxso ) cli5/4bz.,zu ugp. Explain.

When a person jumps from a tree to the ground, what happens to the sflyk0e0peibv vexj:( ))5 a,momentum of the p0jvxy)saf,:ee)l50b kepv i (erson upon striking the ground?

When you release an inflated but untied balloon, why does it fly acttq8r9n v+ob 7ross the roomnoqb9 tv8+7t r?

It is said that in ancient times a rich man with a bag of zmixv:fv cod8( .cr( -gold coins froze to death while stranded on a frozen lake. Because the ice wai-v .o(xcfr z:(vc8dm s 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 i5xp7l mtc+2 kge8q8:1 ybvvjss far out in space and is essentially in a vacuumk5: svtqbx8+c8mvypgl72 j 1e ?

According to Eq. 7–5, the longer the impact 1vp6/atcg p)m 9cl-ak tu je71time 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 value of air bags, which are intended to inflate during an automobile collision and reduce the possibi7 ctljg-vp6 /t9 c1)mpua1akelity of fracture or death.

Cars used to be built as rigid anaf)8fd,b1 oe z, b+ 6nx oek-9vjjti5s possible to withstand collisions. Today, thoughkfjo6oi n-ed) f, t,b ve8b9x+15 zanj, 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 further than a ba3zd2dwyt dzu:na6 am 516e7 la-gd5gkll tossed in the air by the battke56dng3md: w 7 gaaa duzz2y-1tl6 5der?

Is it possible for an object to rewxyh0ki0 ml37*l. p xtz nw*y;ceive a larger impulse from a small force than from a large force? Explaizi 7.xtph0n;k3y0wlwl **xm yn.

A light object and a heavy object have the same kinetic energyy lvasp( ,(z)uv7yx;y8+ :lhj 9lslrj . Which has the greater momentum? Expl y(9upz(,xl:l7vyra+ll y h8vs ;jjs) ain.

Describe a collision in which all kinetic ew(; lt8l. jdv2w -6ztd akzt/cnergy is lost.

At a hydroelectric power plant, water is direct uc51.ei8xakced at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water k5e1u8xa ic.c rebounds?

A squash ball hits a wamhxyq tzp2pcv08,n l (+/ *hqall at a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixed to the Ea cc6(c2zg6 ikqrth), 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 stee2 6czgk6ic c(ql plate.

Why do you tend to lean backward when carrying a heavy load in yy *wq*zsa-nzrx+5;setjlf ++ie g- + pour arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is not trui*y05 qw bwd*;kmgxs2e for your arm or l0*;y ik52bgdmq sww*xeg?

Show on a diagram how your CM shifts when yomjugx4 la9r4edy (bw/r0;a;iu change from a lying position to a sittinx;l uia/j(4w4ba9 yd0gr;rme g position.

If only an external force can change the momentum of the center of .qg 8/5vbpdr x1tuhd) mass of an object, how can the internal force of d rqp/xdhub1.5t) 8vgan engine accelerate a car?

A rocket following aanbcozdxf9m . f/9 v00 parabolic path through the air suddenly explodes into many pieces.d0f vz.9cfb0omx9 na / What can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed gm k/(ried(q2s23et5p7u arhof $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s .mx6h5sl ug4z. What is the skier’s change in veloci .564u xmgslzhty?    m/s

  A 0.145-kg baseball pitched at 39 m/s is 31jvd yq6f 28s lepnozu daz4n+(i 4;mhit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time between ba jo1l 6 vsqzn4emdpan4z8d2 ;(+fyu 3it 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 horizon5 fu5 aq;a)wsvtally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initias;5a u)qafwv 5lly at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, givew9ds2sqy qf81cc (d/pn that the propelling gases are expelled at a 2s cdqf1c/ w9(pyd8sqrate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving 1,c( img rxxel/ar b8-, xvzm;at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alonej0 +ji (y yt86ltw1 mmx 4x;:jtqdns*e on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’tjse( l+ ymqijw4;yx1tdx6*m0 tjn8:s new speed?    m/s

  A 9300-kg boxcar trav+emddck rwfm1;k.g( 9eling at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip h ( 9:m7hphqtqrorizontally at speeds of 100km/h If 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 m wide. Compare to the typical maximum forcrh(79htqm pq :e 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 con zk-fvw mh bh)v2geqqc) )tz o9(+se5;stant speed of 8.6m/s on a level track. Snow begins to fall vertically and fils2w(qv)m5e;f)t c)oh-bgz9 eh +vq zk ls 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 g unjf, vg+du3rh/z8 gm4q5e0moving at 420m/s emits an alpha particle in the direct3en+hrmu zgfgv0j g48 5,qud/ion of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling1izw koc( jv*0o ,d6vq 230m/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, (z od 1ockvjw,qv i6*0how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocff j( r 7(7yqv3ow:4(qq2higzuh1 hcxket 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 3180 kg is traveling in outer space with a velociu-dbhn 8m - ( rc:ubq5-oamz2yty of 115m/s To alomrzbb-2 cnam h (:q8y-5-uudter 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 -r3dgt 4vemr 8a speed of 45m/s The golf club wasr3t 4vredgm- 8 in contact 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 8.5mh m +05d;gthgg/s and comes to rest in a time interval of 8.0 ms. (a) Wham5d;hghg +t 0gt 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=8 bs (df.tvb:q25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashwort rm n7g;24tg(z nje7kuhiness 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 averagjk g2 7u(t7rz4nmn;g ee force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in 0.75 s byna f vha4*re n6j)0-nnajnn*) a head-on tackle by a tackler running due west.n-)v j e*nahnrn*4naafj) 06n 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 /gtudjxrpj- yu/.f6 0 on a tennis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a funct rp/d 6uyx0fj-/gtj.u ion 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 z9z ubt1e3y c9bone of either leg? Ign913 etcyb9zz uore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking 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) with a speed of co0)y0 2eghgy ps.qmwd* llides 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, ang0 q2yeg.psw )*0 dyhmd 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, movinss(2)j-hhq xi g 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 ss-s)h( qxh2j ipeed 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 per,:apv+ .fo+f5 or gotxfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in tt ox+.og vop,5:+ rfafhe opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s col phc zhx9+fn1in7u) +mlides 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 9ciu7 z+n n1x+phmfh)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 87c +e*0*6c oqfounq2la z4yf j.5m/s collides head-on aaq 0l+6fo2u4fozc*qjn*ey 7c nd elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elasticalle tz c1*g +mvkpft/c iob:+95oy as one approaches the other directly from the rear (Fig. 7–3 : fo1tkizpb t*cg+c+v95 mo/e4). 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 elastic h-09l qjnf*f k65vq gsjq,d5m zmth1g o: cjl7-ead-on collision with a second ball initially at rest. The secondmq *gj- :,ns7l5k5 hz0j1-lm vgfoq9fc6td qj 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 slides down a frictionless 4* z a7zkdwlcd5)nqi-rt ./ geincline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the iez/*rdn kw)7i- c aqg5.4tldzncline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an tu7;v 8l4rnjxobject of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in m o5 wn:ssik(,a maximum height h of the pendulum equal to 2.6 c(s5nsomwk i ,:m. 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 tvam dqi7b)w nf; *;i+wraveling 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. Dei*vb) mw;7ina w f+qd;termine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetiyb4,0 ;p9b khzivkiyv2 oi1 (eq) bqf4c energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into two pi(ubh wx. i3;nl)je) ueeces, 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 acquire? (Let A represent the heavier particle, and B represent the lighe).xbu()jhwen lu3; iter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides iw v.fnj0 *1oqj zb7:z s+,,tahoxpa ,into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at iaf1tja,j7z0,*i:+.wshxo zp,ovq b nmpact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height of 1.20 m. A7 zz m;/fc2yvnex: lr+ppro2 ef;7z /x+vzrl:nmcyximately how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two wed-i2:7ty kayy g.n5w7eu /cobjects is the coefficient of res5 7g:.twdwne yei7yu2 y/c- aktitution, 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 thr,s uyu*o8qco+p(6k loee 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- cyuq p*6+ooo,uk( ls8surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in thxs5cdacc0nz p w -)ging*117ne +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 i51n cd0w a*nngcxc zsg-)7p1 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 de/sdg hla3k s4x 8)wl-pcays into a second nucleus, an electron, and a neutrino. T 8h-lsw3xs/ld4a g)kphe electron and neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of ma5z5*ju fy/ n kn-9kfqsss $m_\mathrm{A}=0.400$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 objectx r2i3jf(i smmbn 7xnzte9*+ /s of equal mass, each having initial speed the two move off together with spe3r+*f /njime 9xt72( i sbxmzned v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal n+v3 wfg ;+co+hnpjp;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 co3j;+n;+wpv fp+ hng 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 pdam/ +daxdjl,a f5-i1erfectly elastic collision with another atom at rest. After the impact, the neon atom traia+a/d,xdjfl- adm 15 vels 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 collisionk q+ napg10ce/lf 3c71pdiiv . with another atom at rest. After the impact, the neon atom t pdq 1.k v7/cin0p+f3a1 lgceiravels 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.r t59zrppnp6cum11o . Specify relative to the left-hand 1 mzc16pr 5p1urop n9t..00-kg mass.    m

  The distance between a carbon atom (zw:ph;oq3ytd7 k7.a9wcxq xaz 0c5:i $m_{\mathrm{C}}=12\mathrm{u}$) 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 2.50nh( o8p 0aygc7r*g,j1r ow.q gcx e+/k m behind the front of the car. How far from the front of the car will the CM be when two people si/weax7h nyo 0jr*+ 1(g ocg8rc .,gqpkt 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, ote2nev- 6.exlny cp 5:f mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, dete -.e2p 5xte6n :ynlcevrmine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides )) a1aacvqenr*/lua 6n 6o-wv $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of tomato paste g) ddkw*:/wkb(see Fig. 7– wg*d/k wbkd):40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radiust e mis3e2t+7e 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 ce+7me 23itet senter C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1z3g/lr *s vv,u, and calculate the l3rsz* vvg/u,mass of one of your legs.    kg

  Determine the CM of an outstretched arm using Table 7–1.em(fr27g vxcll ns7b lt(25k0   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of t fxo:lo1l h n3 .ho+ l)kucyw5vf:2.kzhe CM of an arm bent at a right angle. Assul) o.y vlf2f+x kw:coh:lo1.k5z3 nhu me that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hanv1grw h+4m ii3ging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median lvrmi ihg3w4+ 1ine the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon arq93y(2 eeoib1l-h qrwe $5.98\times10^{24}$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 1ffzd0nksj 2c 4b.bkb+ e11e)m 0.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of(p 92m+pppe23yzawxqzmp (* 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 thpz+xy azp 2 pe 29(pprm3(mw*qe 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 6gew6w u7 wxf1of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical hawf 6 16wgxuwe7ndle 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– f3 e.ijh;-whjzv(6 /u:oea qj14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the ai ow)0 kqb9fk ,gl-idd)r and stationary with respect to the ground. A passenger, of mass m, then climokkg 9iqf )dwlb0-, d)bs 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 passenger stops?

  An 0.145-kg baseball pi0iyki(w6 t cewlo ;:67v(ydkbtched horizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball durinv7y(c6w dtei6k iyb(kwl:0; og the contact.    $^{\circ} $

  A rocket of mass m traveling wa/i7.0ise 5 uge p1w/lwj.otlith 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 wi.3 x1g6u moshyth the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give detaxu16m. g 3syhoils.

  A 140-kg astronaut (including s5he ff6w4d8hbpc8 m6 bpace suit) acquires a speed of 2.5m/s by pushing off with his legs from an 5 h bc6hm48e6dwp8fbf1800-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 nc5ij,mb l83.k lv)4pu g;nvv 60 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are thj blkcun v3iv n,vlpmg58. ;4)ey when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second b+zc;8),gto8vyxwkwzr 1ij8 qall (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its origr1xkzyq 8 o8gz)ji 8v,cww;+ tinal 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 wit5afux)v:1 lu lga*s m7ness 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, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was meax7af) 1 lumlva:*gs5 usured 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 steps v/2q :yv: 2xslgs i2ubof total vertical height 4.00 m. 2 ivg/2:xbs lsv2u: yqThe ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically e-xbda0+y9f ninto a 1.40-kg block of wood at rest directly above it. If the bullet n0xy9f-de a+ bhas a mass 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 embedd pr/p8c:/w.t tbimm :ied 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 to rest, what was the muzzle speed of the bullet/tipb wr 8m /ip:.:cmt?    m/s

  Two people, one of mass 75 kg and the otherfe2)d uf;3da p 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 dfaf;)pd2u 3eends 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 about 9srkht n,l9x/hi3 ub/ $ 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 apa1d4kn2 la (,5bj hf((mfydlkurt into two fragments by an explosion. One fragment acquires twice the kinetic energy of thebkladd1y u5f lkn2(,(jh4 mf( other. What is the ratio of their masses?   

  The force on a bullet is given by the formul k5g2/oizxlq3 m3fym:9vyz g( a 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 w:igxe i1*i3qz f/ *-*fjsehm $m_A$ = 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 k )rm 4 rotv,w*-8byqy-ll 2adinto an alpha particle and a smaller nucleus. What will be the spwqydt2 ,ka4ro )r bmv--8*yl leed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay n))ejih pem:u*o1sv8 target) is fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides do 0rqmmf: 7c.odwn 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. 7–47318 ;lcd qbsfk+,ibac 4pkyv6), what is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the q ,;ydbb af scckk743i 18vp+lincline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Fiiq02f m6n5wmx (5lo ylt1s:a dgure 7–47 shows the planet Saturn moving in the negative x directiotai n1 wo56ym20qmf(ldsxl: 5n 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