We claim that momentum is conserved, yet j3dmo- rj+qh.d 5i40t)vu ldd most moving objects eventually slow down and stop. Eiqdujo3v5r- d+dltj d.4 h m0)xplain.

When a person jumps from a tree to the ground, what happens to the momentum ocs-t x4mha3) sf the person upon stxtsm)a3h4sc - riking the ground?

When you release an inflated but untied balloon, why does it fly across the :7acyw-s tt ns: 9cq2nroomn9s2aq: -sw y:cttnc7?

It is said that in anciekqv8q1gv4gxp8,kiz 3s0 qo9 p nt times a rich man with a 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. What could he have done to save himself had he not been so miserg 9ip vv04,8oks 1 kzg3qqqx8ply?

How can a rocket chang4 /5n0jwpwuk le direction when it is far out in space and is essentially ljnuw05w/ 4k pin a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller t;4wysn d /: vc3n y1izxe8bmr5he force can b ydcv erzs34:/5yi nbw; 1n8mxe 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 possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Today, thou w:n)jfq/d tt5gh, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage t)tf/q:jwn d5 of this new design?

Why can a batter hit a pitched baseball further than a ball tossedb1f en.bk(tm8 ;nt v+bg/r+zm in the air by the batter; bb tzn k8mf(+/vnbr+1mg .te?

Is it possible for an 5yo h )equzp/ dgrirx7+w+g, lt80ff 6object to receive a larger impulse from a small force than from a lhe uytgf, )x rg7+w +ql/08rzi5 dofp6arge force? Explain.

A light object and a heavy object have the same kinetic energy. Which has theqijs1mv:y+p .)fy/k he u)mf3 greater momentum? Explain+k)s )fyq fmvje:31.ip m/hyu.

Describe a collision in which all kinetic energy is lo n:aeo aa:,rjmj /rd4xzve999y) gd)x st.

At a hydroelectric power plant, water is disbpelzh 6/ 04prected 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 e0 hl4bpp/s6zthat the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a gq (ryypu 0u-9r jf(b1wall 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 plat3 0iniq.5xzr te (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 ofi.0 xzirt3nq5 putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy lo 5 r;gpq/mt.anad in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this lguy jeq+)tzg5c*6*yis not true for your *y)tj5+zuq* eyg lc6garm or leg?

Show on a diagram how your CM shifts when you change from a lying position to a i5gq-jz:ge0 q e vf9+s59sg qj+f0e givzeq:-sitting position.

If only an external force can change the momentum o/hgkgj dz2.h8 1qcn y7f the center of mass of an object, how can the internal for1 h2ch z.g8k7gn/jdyq ce of an engine accelerate a car?

A rocket following a parabolic path through the air suddeu lz*f,cirk,v)+/dj inly explodes into many pieces. What can you say about the motion of thi)i c*/r+kjz,uvl fi ,ds system of pieces?

  What is the magnitude of the muz 3fx(, indd+omentum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction budk ,3 cr :21fr.hxgnforce of 25 N acts on a 65-kg skier for 20 s. What is the skier’s change in velr2rku 1:,x.f bhg3cd nocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal liner n9yz yx8+o4yuejq:7 drive straight back toward the pitcher at 52m/s If the contact time between bat and ball is q8o y79yj4r+ n:yxzu e$3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package3et,k +y ,b r+3jfmsye out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediatel+ tkesy,f j 3ym,reb+3y 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 magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases arewb ry ph9ag96 33cp*r7xjxl8 w expe jawp y8xgcrh7w936pbr*9xl3lled 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 movinvkl c) x;da2z:g 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 railroadt/b,o t5spi* f+ c7enf-kq6rk car travels alone 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- e 5qncr7t6kfi/+k , ptfo*sb car’s new speed?    m/s

  A 9300-kg boxcar traveu, yya-d9f4/qlf:sbi5;j6jo/ kk k yiling 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 f.yo4ulksnic9l59 b 6p40zb qhorizontally 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 force ofobcl5l4fs6 u0 pi4kbn9y9z . q 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 nlq6)( b*a yquconstant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0(q) q6aynb*ul min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in the dj ezi*eld w :3im67(acirection 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 (6z: id3l7* aijewmce 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kusss3vh:45i ,v /pd dumtd0j) dhbz:-g block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface d shh0: s d-: dvu3,dm5b vzsupi/jt4)when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is t ggw+r,,k f598 elybburaveling 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 out+umt2g;,wsmb y4en e:er space with a velocity of 115m/yg :,w 2bm+se4tmune;s To alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a spewn2 vgcxzpw/(7-h*/jj/ipa ued of 45m/s The golf club was in contact with t /gzc-pa u n/i h*w2jwx7vj(p/he ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s l1kdl:* cw f eou0fs;q ohbh.6-1u,ksand comes to rest in a time interval of 8.0 ms. (a) Wh k of; swusq ,0c*dl6.:u1le1khb-f hoat 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 sl*atb :qp6w 4ktrikes 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 cdd)h , im-vrav.aqn3*rashworthiness of new automobile models. Cars are tested by smashing them int-daqdanm r. ,)hvv 3*io fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force 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 i vwxmp 9w/,rf,n 0.75 s by a head-on tackle by a tackler rufm/w9pv ,,rxw nning 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 kt4-bp3jt qzr0g) points in the +x direction and is given bytz -3pjr04qtb 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 breakt:)sya a3 +jjlvbq y2:ing the 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 fall). Assume the breaking strength (force per unitb+:ql3aj2:ysa y )tjv 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 direction4*ulvuxv t e2z5qgxp-4hdj r,23 v2oe) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each,2 5vth*2dqe4urx3 p glv4uvox z e-j2 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 om)9+hlr,ca a )m0ind4kf )ttspeed 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 ob )f+r))4at ao09lc tnhmmidk,ject after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastic head-on collisj7q1cxvnw: ra*i+q : hion. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direcq qj:rwca*xvn:7+1 hition, 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 the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving withzp lva 3,v d-w3l(*pwt a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)lw,w3(d ztp -va3lvp*v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s collides head,bhd(5r asu.sczfds 2avi,84 -on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s d84,s.dbh(sfz iavcsu a2 ,r5 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 elastic e49du,kbrqv(p0nr5ba z8 yv5ally as one approaches the other directly from 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 3.7mb09(zv,5pkba uq5n8e 4y vrrd/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 cn3/u,mhb/ n sae d0l,sollision with a second ball initially at rest. The second ball moves off with half the original speed of the first3mns/eh 0n,u ab/sl, d 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 incl*uaj b5uz9og1; qalm.ine 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, wouz9q l5gm* b;ua 1.jahere 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 obj0chlrsh9 3g*gnn31mkh4 9b duect 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, jt6 z+iv f(v2ry*0 5qg1dek/- hgwovt projectile 1 results in a maximum height h of-gg6fv/ k2ve (qh1jyvztrt i ow*05+d the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet travelinv eoc 1g-pwu*0g 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displaceme g-e*ovp1 w0cunt.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fracxnsiqg07* cn, go.f*n9lj,.(g psjc rtion of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into t h4hpoqwe(w1b u xi),n*c hq-5wo 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 dihxhiho-4b*(q5e) wc,1uw n q pd each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rea*4v fyun2zt;;; fh2aq bg+ mper 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 betwee;f;ah +;n qbguvze2 4*2fmtpyn tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and reboun7m6a r 1q q/p anh.l5* oq8o3ijwu-eyhds to a height of 1.20 m. Approximately how many rebounds will/h1 6wryq*l5n8ohaqe3a pju7omiq. - the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects ist +9+f7kz ,cpl 2qzrna the coefficient of restitution, e, defin9f7n q tp+az+ z,2lrcked as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the mass ofuo fg78vov95l 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 se go v9l78vf5ouparate 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 collidj ey)yc38zb w 74*xtakes head-on with a 10.0-kg object moving in the -x direction at 4m/s Find they k)*axt8j zwbcey743 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, an electron, a 2-qdvwem j8loljuma 2e+7v6 u)3d8ej nd a neutrino. The electron and neutrino are e d2jvw7eoe8l) jd-6e qmu3 j82uvla+mmitted 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 mass 8dbm l8o. psv7$m_\mathrm{A}=0.400$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 b u+(;qi.gs is.h3toi tetween two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial direciu;t.is+h.i tg os3(q tions?    $^{\circ} $

  Two billiard balls of equal mass move at right b dk,8y+ -cbpwla98yrm/tj d 6lo; b;cangles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/ o r - c6ktlb8dmy,dc;;p/b8 a9w+ybjls and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elagg,w)y9j owlo0 l5 h5kstic collision with another atom at rest. After the impact, the neon atom travels away ogh5 5,llo90 jwwk)gy 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 anotheru. rc,fgzdh( q 9nibbq6/rzg3. td39zd jy+t/ atom at rest. After the impact, the neon atom travels away at a 55.zfgytn t/b6.r 3ij,gdr.chuq93z d +z q/d 9(b6 $^{\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 thrc18cu9 iysb er/cv0b,h+i0kr ee-mass system shown in Fig. 7–38. Specify relative to the left-hack0sh0cu8 c 1,e/rb9i +vybi rnd 1.00-kg mass.    m

  The distance between 79y6 c9yayn 6iv3gt6i0to ti va carbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front o-dl.:;vd vpp-tak2r7 iu,4 j3ey xfiff the car. How far from the front of tkj.i; -f ,av 4dxyvetu:3 if 2d7r-plphe 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 68y67f f 6b;u 65x3 yj55rd xbwlkq*xzxm00 kg, is used as a ferryboat. If three car *zj5bdxx5y6kqrlw5 3u xff b766m;y xs, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side/ /:b xq1ftc7 .c2qsmyne qhp*s $l_0$,$2l_0$, 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 casqzwprr wi:3te )*94 jkes 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 that9w 3rw kzp*iq4:tr)je the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius*9xbzn9u5 *2u:mzumduu *nry p; 9cuz 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 d9u9*5u; mc*uznz*zu29np: uu rbx m yis the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the se4h . mn qmj.32ku;q 1mot:bssame as those in Table 7–1, and calculate the msm j.t:k 4qqob2he;s.umn13mass of one of your legs.    kg

  Determine the CM of an outstretched arm using Table 7–1. :)su:hgtg;wuixs 4f7   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the posithq(xx af67i s*ion of the CM of an arm bent at a right angle. Assume that the per *xfx 7(sqi6hason is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such thnz(egrr(go f+6 i bz:;at his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the znbf z;:ge +(or6r(ig torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon ;if,o,;vmgf fz xrk(v f8wm ;5are $5.98\times10^{24}$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 a5rxxbzl1erd l p7b pzwum p7)08.*x 2mpart 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 cylin i.j ogzb:1zezu;t4/rdrical 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 in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom ofj ;r.zo u/b1 :ei4zgzt the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindreel8vouri +p 5x32 c 4-zx0mgcical 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 in Fig. 7–42. If this mall4 o2ume5p3v8exgx il -c +c0zret 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 7xm;hl+qrjc cb rqp.6+.r5d f7–14 (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, of mass M, are in the- ;pycu0td 5hb air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed meapcyuh0b;-t5d sured 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 strikesxz7-8zenqgg0np 30 fr 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 during the contact.-rn g3fzz7 0x pg8ne0q    $^{\circ} $

  A rocket of mass m traveling with ngv0o 3;.9lh o(cdl/qdohd;qj0 te.h 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 l *pgd3 c0r0hh)xm3u3xfoo 1 qshown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch qh0*dxo3cm )ol0fgx31up 3 rh shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by pus;t9j ej2dsj2fo)kn8e hing off with his legs from an 18jseend ojf)298 kj2t ;00-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 vo+m8c;e;ikump i )+7 9mmsatof mass 60 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronk motm;sci89u7emmva+ +i )p ;aut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second b et3wrpqms(bu4-0hy*m)hb, 2bp 4rxlall (at rest) and rebounds in the opposite direction with a speed equal to one-fourth p2mrb, bhptu0xb)w-4 3l4(h yem r *sqits original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving sru l8/nz.0)fmhu b54l 7ksij 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 measured to be 0.60. Show that th0 u) 8hln lzfi7bk/r4mus.js5e 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 8g86ghc 3ycgas0 cy-y flight of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, eac6ya0 8ccc8gy3sy - hggh 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 block of z0b ,c*utlob7wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block ris7uo,z b0c*tbl e after the bullet becomes embedded in it?    m

  A 25-g bullet strikes an/ed pqe16ars03cm ld28t /rsnd becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and t 3rslc a0d8p teq r26n1/edm/she surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kgv94r)p7 jnb9lzarh a00lw/. /vlq tbt, 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./q. vr t9l9l7v0trzh) awbj nl b04p/a 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 am;/ kw3mw.u ndauh mzk7lz7;)bout $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into cs+.)8m e6hilpxqxlupw2 d7) two fragments by an explosion. Onsx mlh) l+7pe u26)w.xipcqd8e fragment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 580-f2w.zd (dx 0lzxgvb7hq6 5(bp( $1.8 \times10^{ 5}$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 massesw .3 ey-rwm/9t.dpdwq $m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha particleeavr 4; g.nk4o and a smaller nucleus. What will be the speed of this recoiling nueg. o;4 4rnvkacleus 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 tl rdav7dku2)4 zx 0 /vq8fli5aarget) 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 down a 306s ym qg+gf//m d-u.gc; eq:mq.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 ij6s /hw y9pqw6(sd xw-t is to rebound from (whs9 6/j6w qwdx-sypM, 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 slings .so9ok/ uifp:hot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is o9ou:pk/ ifs.$5.69 \times10^{ 26}$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