We claim that momentoxnaz96o +td , u+gf0 r fk3jigj7(6wdum is conserved, yet most moving objects eventually slow down and stop. Explain. 36zr (dx,gjjkg76af ndufwi+t0 oo9+

When a person jumps from1, 3 yt fzodn3ct5mj7j a tree to the ground, what happens to the momentum of the 5t,j zn 3o7fyt1j3mc dperson upon striking the ground?

When you release an inflated but untied balloon, why does x7mra 51lp ,seit fly across the rooms 5lrxmep7,a1?

It is said that in ancient times a rich man with a*ppf70a vf3awimi: :l bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. Wpimi ::7afa fwv3lp 0*hat could he have done to save himself had he not been so miserly?

How can a rocket change direction whu ,fhbxcp8n-1 en it is far out in space and is essentially in a vacuum? f1- ,8pucxhbn

According to Eq. 7–5, the longer the impact time of an impulse, tqe 7fcvo,gxxkr k4.34he 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 auto cvk7xgo43xe k4rq,f.mobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. zjy46ei g0g3v Today, though, cars are designed to have “crumple zones” that collapse upon impact. 6ge4yiv0g3jz What is the advantage of this new design?

Why can a batter hit a1g.eb 1aeem3xx( u on: pitched baseball further than a ball tossed in the air by tm1aox:( eun3xbe .e 1ghe batter?

Is it possible for an object to receive a larger impulm juc hu/cr8*5se from a small force than from a large force? Exp*jcc r /hu5u8mlain.

A light object and a heavy object have the same kine*)grk0rlouizl3:, wctic energy. Which has the greater mi)r3ol z0k,g: w*l rucomentum? Explain.

Describe a collision inhgm+ +28)pfc yz3/h; kxs:ti m0ct tni which all kinetic energy is lost.

At a hydroelectric power pli 0),gccx g3*wbgk(e/iostq8js4n 7 jant, water is directed 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 waten)xk 7s o*s,t0ec8cjwgg/b q(3 i gi4jr is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a 45 uu k;:zu +)y t 4wswhyd+y10jx$^{\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 heightsc6y p5,whso7 h onto a hard 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 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 t7,cwp5s y o6sho the steel plate.

Why do you tend to lean backwk5cbstm p+f 4c3wcmv d 4w6.jdi72xd*ard when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas ur 9fwszo ww 5wr)xn94fr1(e450 mdwv this is not true for your arrfrv49rod( ef 1 w4n 5mx5 wz90wu)wswm or leg?

Show on a diagram how youdb 77mg+g wcxq9(lks:r CM shifts when you change from a lying position to a sitting pm+k9 l(x ggc7bd7q:swosition.

If only an external force can chauwy x (tj,2qi0brk/8dm (c6hznge the momentum of the center of mass of an object, how can the internal force of an engine accelery,/k0 j( zmwq8d6c huibt2(xrate a car?

A rocket following a parabolic path through 7vg0xx8byim yz(mw**ko:3ow the air suddenly explodes into many pieces. Wo * :m*w3xx ym7bko80(vigzywhat can you say about the motion of this system of pieces?

  What is the magnitude of the momentum j3bpi. j gwj8;nr+0 wkof a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts onm5o1c4,,,vnn bjyxs4 :sp xxgkfn0 :c a 65-kg skier for 20 s. What is the skier’s change in velo4,osx1mpvnky0g4, c::sn c,xnx j bf5 city?    m/s

  A 0.145-kg baseball pitched2 o1ve;xo 3zxgt jz(5f at 39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time between bat and 3ovxefg oxz(zj 152;tball 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 pn6 no9h05f1u6s ) xqvfsg8mfqackage out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child ifn061uqs5xo 68g sqf h9m)fnvs 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, zp.mo+ce5y/ pq yr1uz, zk0b7wh+pbj: g -si*given that the propelling gases are expe/sy:k5m yep,c1 b z+uzpbiwh qz*-. g07p +rjolled at a rate 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 ax6 ehe39 sz7qvbww1.ht $4.1 \; m/s$ 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 alone on alevel frictg - /chau,q 4;0k ;r 8epmdviptlg:*lwionless track with a constant l-ai plru:* 0,k mce;hqwpd/g;g8tv4speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at a;p q;t;g,sjq0/hk( u a:revy0( )khx*j lhqz$15 \; m/s$ 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 horizontally at speeds of 100kmhng + *mbpz:,e99gxsn/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate ,gs+n 9n* gmzpb9hex: 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 .d9 jhjg+b )gi2 e1:uisl8g yfalong with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring 9iu2s8 ggdj l if+:)ebgh1 .jyfriction 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 alpha particle i v uwqon1x98 crr+ptt1+ + nb-o)frk1dn the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when k9++)ptrnnb+-8t 1ruqo1o c d rfw1vx it is emitted?    m/s

  A 23-g bullet traveling a) dp3+q 6asem230m/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, how fast does it move after the bulletqa)ep a 3sd+6m emerges?    m/s

  A 975-kg two-stage rocket is traveling at mc6: (tbvf iqw 5tslol)5kg+;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 xa/pp/fausa a;+c5qmt35 e: ga velocity of 115m/s To alter atsu+pqfc5 e xa3aag 5m:p //;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 p2tqtwd 55c quzpko( /gpk+ e-l):b.wtee at a speed of 45m/s The golf club was in contact with the balkqbp+q5: ww5t opuk(l e 2-)c. d/gptzl 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 m:fv try66xcnt: 0 ;flto rest in a time interval of 8.0 ms. (a) What is the impul;6 :yvtnr mfft 6xlc0:se 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 wal;th mjb,xbn70wh0do ; l at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthiness of new aut f/zdwt9r: :3jbpxo/,miyik1 omobile models. Cars are tested by smashing them into fixed, mas3/ifoizj 9w prtyk1mxd::b/ ,sive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force 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 0)lbc ,vllfavl1n .rfm 1su2 ah q:h0+running at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler run l,01).2 aahcb r:svlvmfl1nf+u q 0lhning 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 -+jfz,,ndruq a tennis ball (mass 0.060 kg) points in the +x direction and is given by th u+,qnjd zfr,-e 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 withouxui,k pn)y*ob */+ocft breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the p * po)x*nfk+,uicoy b/erson 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 ci :lep:fr q i0a*-vlv5hwg 72kollides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the s- piwvfrq 2lia7e:0:*k hv5glpeed 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, moving east with a sgtls8.i ;xtl1peed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will bltxgi1l8.s t; e 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 : 2yg/mu lni :u0uv; zca8;zfgelastic 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 thc/uf; 8z0m2lg;g:iuva: u nz yat 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 spno g;h2e7m(k z8sb f5feed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away fr ffm (h;z285sg7bnk eoom it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is movind46 q+dmitm9zg with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incominzdmqd+6m9 4t ig 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 approapmfp s:a gz sx 1k/15ny 71u3/2nogcyoches the other directly fo/m1 n7:3agcky/s n xpf5z1o2y sugp1rom 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 elastic head-on collision with a second bdt 5c)a4w+u/ ljy tqa o49oo4sall initially at rest. The second ball moves off with half the original speed of thojo doql4tw4+c 5s /a4)ya9u te 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 cubenddcu) fvi 8820abx; y slides down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom d2xc0 i)dn yf;8va8 ubthat 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 ooa.y4a-kn5 -gr/t* g m)c scwjbject 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 experima5*a ar+tn4i ment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pea t+r4*nmi 5aandulum 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 231i i*6kxzu y8x0m/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 components of the peiuk*1z y 8ix6xndulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lost, 8w*y2ng(yhla $(\Delta\mathrm{KE/KE})$ 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 restczk: - pj2hdh0, into two 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 acquire? (Let A represent the heavier particle, and B represent thecz j:k-h20 hdp lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stoppe7 :ec) j mttnjdwp--y-d 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. --jpdjntm ey-:c )t7w80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height of 1.201k c:s7p+) xoj4nt jce m. Approximately how many rebo+nc14jo:p se t7jcxk)unds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the coe+o:9k ek(t;*t1 rlftl6 xbida fficient of restitutiontdtf+b69:1xi ole;tk (al r* k, 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 tf1s ;tf)nr: zaej8 up6hree times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can)fu:ens6tp 8fja;zr 1 be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object movins-fn (jciz:uxq ,8wm eh 0k:c7g in the +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 xn- :qumih fc:(c,swjz7 ke0 8velocity 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 seconl- j.xrj6r kj93 mx4gsof+j y(d nucleus, an electron, and a neutrino. The elecrjl(j3-4jxkrs j m9y.6x f+g otron 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 mas6 (z4dso 9quius $m_\mathrm{A}=0.400$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 eyb.n +vjz;+foqual mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial directjbo; +fn. +yvzions?    $^{\circ} $

  Two billiard balls of equal mass move at right anglesffx v+tkn04k7 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 xff+kn0vkt74 ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with aar ,9vb*0niycnother atom at rest. 9rinyb0a,v *cAfter the 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) makes a perfectly elastic collision with another atom at ro 7y8jhhtw5 1r 0*nvxhest. After the impact, the w x5*vrh ty1n7 jho80hneon 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-ma1 +qmf 9kv;w7a7m9;;j nylkopicttm3ss system shown in Fig. 7–38. Specify relative to thi wjfotkt9 vp;+ 1kcm;;am nlq39m7y7e left-hand 1.00-kg mass.    m

  The distance between a carbon atom (: it9dvu lybp( /xw.7ibn1g7u $m_{\mathrm{C}}=12\mathrm{u}$) 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 the front of the car. How faroy 5 :9 qrvwfg*vm4x+i 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 seat 3.90 m from the gx5iwfvyq*ro9v +4 :mfront? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft:hpd1sv du6 w*, 18 m by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of thdpsd * w6:1hvue loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides 42ozrj 0ibcx9wyrf65xyax zv53z . 3w $l_0$,$2l_0$, 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 oh*zk00 wxm km6*dqb j)/yhosy08jr1t)zdc3h f 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 the crane operator can pick up thw0*zk 0)js1mj ort0ddh q)k6b3cx h hm/yyz*8e load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of ra21fxn* po 5w(tvxm4 fvdius 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 the larger circle, Fig. 7–41. What is the position of the cen xf(v5wtnov4 mp21*xfter of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Tabes bvu76;r ej-le 7–1, and calculate the mass of one of your ;-vu6 rj7sbe elegs.    kg

  Determine the CM of an outst5r)*9ztpn a u5wn8hijg7 q5xfretched 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 Cv6gg.am/t9ylf ea 3a, M of an arm bent at a right angle. Assume that the person is 155 cm tall. f63,laav a9m/ .gy get$X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position suc;c z(v, mtrco8 /mzm3zh that his arms and legs are hanging vertically, and his trmzm( 3;rmcc8, /zzv tounk and 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 Earth ang -0l/nswyb: h 6okpv,d 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 fpsj)i61 ko h*arictionless 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 mk0t+ ymd s4-x:t+zxi qass 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 parakd40xs:x-+q+ ti mtzybolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a 6 bdrv*6 vr:zmdiameter 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 parr6: *vvbrmz d6abolic trajectory?    d    d

  (a) Suppose that in jlze67h b- m3xExample 7–14 (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, o ly-,qc hq(j627; r:v.z)n vvoa nnyqcf mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured 7n(2y; vhvcqr c,jo .vaz)qlyq :nn-6 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 an-mzg(fw iff 5vt-yv2 8d is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average forczf v8fgmy52(-tivf- we on the ball during the contact.    $^{\circ} $

  A rocket of mass m travelink9 d*58p f(fqcpj,y gfg 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 Fs 1n jzj g:g,:,:kd*nj/r5em jpwm 1unig. 7–43. Relative dimensions are al:snu*gw:11n,5ekdm:g/jnmj, jr z pjso shown. Should the player be 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 space s h66x1pb,tj4b8 b 7 mq8ywpjzuuit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-kw68p8t j1p7, qmbjybh6 zbu4xg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg an foqwhvu9k7)c :6v8li d the other 80 kg, are initially at rest in outer space. They then 9ufi86cok7l) wqv v:h push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a se 8icl aod-6 0zbj..erxcond ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of tojce0-d rzl 8 .x6a.bihe second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involvp*k4 7k,xwosxing an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver,ks*4 ox7w xpk 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 measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total vertk8o jtj ;cw(s,3d k(jcical 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 al(kc(;d s8wj jk3,ctoj l 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 block of wood at rest dire tp)p i(3wme4vctly above it. If the bullet has a mass of 29.0 g and(4 tp) mvwe3ip 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 placedotb tx -(ew8pyryy95hf )zcy3 p:/f0f 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/ yytoh0cbz-fw)9fyt8p fe: p3xyr (5 block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the othg m+x kh.,xh:+:p 5e ycdmxw)cer of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat movecxdmw.)kxhh yp+e, x:gm :5+c? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was aboutnof9pyg6l qs+t p3z-1 $ 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 54ci pa.jzz5ezp/z:f apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is th5zpc:z fj/ p4aiz e.z5e ratio of their masses?   

  The force on a bullet is given by the formula F f2i(e( hha. uy 7/hd (rjq8w u/gxh9rj= 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 masses5.3kzmp(uz9ttm n9v/*aq afk $m_A$ = 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 decawy m)hq,m4dyw-t j. v-ys radioactively into an alpha particle and a smaller nucleus. What will be the speedwyqm-d4wtmj)., v -h y 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 target) is fired at an anhl/0yx/pr mes)+ yu.sgle 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=2.2dtefa, l*xspr;,t ; w7a5ye( zkg slides down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on -ea4se vd1q 4i/aeku 9)5ioc w833ogq kzgkg 3mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide kwe-goo9ea /34e qcdqkauvz8 5g3 gk1)i4 is3with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. wh dii0xi4/h*b6i. dt Figure 7–47 shows the planet Saturn moving in the neg4 i *idw./ t6ibihhxd0ative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s