We claim that momentum is conserved, yet most moving objects eventually 5 r,rmlc jc-a 7/xj)6 xrnch*qslow down and stop. Ex*a r crl6x5 cj-/xcr7h, )njmqplain.

When a person jumps from a treeu nhhs (+yih:;pty9beop2/1 c to the ground, what happens to the momentum of the person upon strih/;s2(uhphtb9:e y n iyp+o1c king the ground?

When you release an inflated b g(/ d, 40k9 qrr6lokvf-nkjdmut untied balloon, why does it fly across the roomrq/krg,0 9d(dm 6-lno jkfv 4k?

It is said that in ancient times a rich man with a bag of :mt,b5gq3by8fr em2on c q:*egold coins froze to death wo 5qf3 mte2m:b q*:nbcyeg,r8 hile stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space a3jbm qbkl 0ca 68d*0 asyr+drw +*/lldnd is essentially in a vac blka*lb3yd+ a+m8 drr/sq d0wj06l c*uum?

According to Eq. 7–5, the longer thesw1kym v3x1azjs :7l5 impact time of an impulse, the smaller the force can be for the same mz753lvx 1: sk1jyamwsomentum 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 withstanw3fk8k3z7w(ypd , nv+1s m bdid collisions. Today, though, cars are designed to have “crumple zones” that colld3zy1psb( mwkwf nk v7 i,d8+3apse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baser*)vqvqs9* geball further than a ball tossed in the air by the b g)*sq9ev*qvr atter?

Is it possible for an object to receive a large-nsmdr8q 2lc-r impulse from a small force than from a large forscm-ql 2-8dnr ce? Explain.

A light object and a heavy objec.evkkt3u-0y zs* nyk/ 1bq*ntt have the same kinetic energy. Which has the greater momeqzny kv -ybkte. *k/snt3u1 0*ntum? Explain.

Describe a collision in which all kino7pkx(giw/ubv9f,u g+ksd 0t -xz7) qetic energy is lost.

At a hydroelectric power plant, water 4s,7x+ihcekq)o / szg 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 water is brought to aeq his74oxs zc) ,/+gk dead stop, or so that the water rebounds?

A squash ball hits a wall at q;ugyo/ z 3vi1 zd:o)c)fv,yl 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 stee 3 hy3,m7xd/ ,poyrzopl 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, durinr dz,/,opy3x37hom yp g what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean bac j0h(o)dilc :5+l.ruszv .*g; hk iuoakward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe ats4vk: l+b d:,zc6qda g its mid-point, whereas this is not trueda ldk, c+vqbsg6 4::z for your arm or leg?

Show on a diagram how your CM shifts when you;b ff.dkqo 3n tc,vq44 change from a lying position to a sitting posit4fkfcqt4;3,nd obq v.ion.

If only an external force can change the momentum of the ce6uov vk4 ba0h:nter of mass of an object, how can thev0 bvuao k64:h internal force of an engine accelerate a car?

A rocket following a para/ *ipgp0txx1 yqac p+b2r7q*4tfo- efbolic path through the air suddenly explodes into many pieces. What can you say about the motion of this system of pyq xprbc1epq/x0o i7 f4+tt g*2apf- *ieces?

  What is the magnitude of the momentum 5mh/qpt8.lkn iyb+zc5+v dlf8k1 l0nof a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What is the sp+rp n jz(yskn 7e e:ja-f:(1vx4+vjikier’s ch e y rjavzi::+en(v 47-+1pnj(psfxjk ange in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a ho80t,yg*x g kur /yk;pprizontal line drive straight back towarpy8g rkx ,;k*ut/gyp0d the pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontallg 9i0b))a ,;btnw wm:zl qnifisr3b-6mdk;1d y with a speed of 10 m9b,dlmt0g 3braf6; di:k; mwbwnsi zni1))q- /s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted:gs.pien1a)y(a+6mjf *qfl s on a rocket, given that the propelling gases are expelled at (pf)smsef.gajq 1l*:a6 +yi na 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 81x pcw2wrp4jfc-6x eat $4.1 \; m/s$ 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 aloneti ;1qtfnkuv4 droeo*g /7x.r 5xc :1g 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 c1qx:e4g *kfi ;vt/gdt15x .r 7uocornar’s new speed?    m/s

  A 9300-kg boxcar travelin54fw p8ph-p7tlu; h rrg 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 horizontally at speeds of 100km/h di uhij++ n o .bi-9,n)1dahpfIf 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 forcd+n1odinf)p9+b a.i,ui-hh je 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 cars a63 +ugzrdr;8yu-ul coasts along 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 friction with the tracks, what is the speed of the cg8+-sz uyrua6r3d lu;ar after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in th( cjh 82ocuf ck*(xxq4e direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha partc *ofq jx2c84((uhxkc icle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg blow ,h7my69gf72st8qtwnt skmo/7n-f x ck of wood and emerges cleanly at7 to8ff6ymwn9tsw 7mhx7kg2tq -s,/n 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is t ib3/e8hcq5 ptraveling 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 3jzcmw-p -s4 ldf *7t.js1x5 hh180 kg is traveling in outer space with a velocity of 115m/s To alter its courhlc7-ds541f jxsz-mp .htj *w se 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 atl7y 12rxie4qw/t a95c6 b uxks a speed of 45m/s The golf club was in contact with y 5 a7ls6xxitu91re2ck/w4qbthe 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 veloc mjt,,6amcp4j ity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What i,tmjmc ,4a p6js 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=0.06,b8c 5tfc)biskg and speed v=25m/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 engi5(sb+x62(o )f) q c sgustxem0gua/aeneer in charge of the crashworthiness 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 ss+a (e bf/xcu6esmog au05t)xqg) 2(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 in 0.75 s by a hqivz)h a*mb,-ead-on tackle by a tackvbzqm ,ah -i*)ler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force act ixf -up+ky) 4noy*y6eing 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 function of time. Use graphicalxouyn)*4k-ep f6y + yi 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 brkx3v*5 y3eg,kool -dteaking 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*g-3to yexk5ko3vd l, 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 movi*ky qs6ok qrf2 ).9rdpng east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, .qq2ps )d *rrkk6 9oyfand 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 speed of 3m/s 8kx/unh)be twd,j 0f4 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 dnu4)bf8wedk0 jhxt ,/ irection 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 undej f)6zai g,v4hrgo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite dhjga6i4) v z,firection, 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 with a speed of 2.5m/s collides hea/34 7qyr2 w+idopoh po1 3 ,lg3nrrmxod-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectorh /1 3 w7mi4po,dn ply2 3rqogorx+3ly 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 moving with a speed of 8.5m/s collides hex.esyjsivbtjygz.4;; v--ep0d:l ( had-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate.zph s;0e ti:y jgd-s yj.(- x;v4vble
(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 collid,sa,csha *13 lv,jopse elastically 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 3.7m/s calculate ajh *1pa l,s3o,csv s,
(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 ball4f wb// acy5n.fc0qed initially at rest. The second ball moves off with half the original speed of the firsqce. cab nfy f0/54w/dt 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 incline as shown in Fig. l 1vpbe x) 1t7)fq;nad7–35, and elastically strikes apq )bva n1;f1)l 7dtexnother 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 incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an objectgm*(sa i-m*k w 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 experimenhsw mceub adpp53xh e,6k/u.n1 ,vd4,t, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A ew1/xmp.kha,he, vs4 duuc 65dpb3,n 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 traveling 230m/s b;0 it:09xmhund2ru;xvz2*g o x tpf-u uries 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 pendx:00;on rgux-*ph9z tm u iudx2f;2tvulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for tlxr/g sn1qh()5yb 7 jgyh 1x)nhe fraction 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 twog fw -.+oprdq: wxinx:+gre1 4 pieces, one of which has 1.5 times the mass of the other. If 7500 J were released dfi 4+xn:xr+ewgpr-g1q w .:oin the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV nm4twpoot46kc( fat .8 y*:y astopped 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 roaa:n.y48o wtfk to4(t6a *pc myd 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 rebounds to a hei-fvh g r*p. eop(i6a12 z0dfg:zsof(rght of 1.20 m. Approximately how many rebounds will the ball f.-gp*6rph drvz(g f o: is201(oezafmake before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of :nkqyc07 )yvctwo objects is the coefficie k :7qnyc)vc0ynt of restitution, 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 three times the mass -yyzn:x1sy)2d -qrc -pkcbq * of the other. A depression is madeybn1x 2-s z-cq-yrkqyp): *dc 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 separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5me9b:,o xvcr t.9bmh+yhler 5;/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final ve +ry9x; :5h9br bmhtc.,elovelocity 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 dd15 oi)s.5px qvgk*gat rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emit d ggx5isv1k5.p) o*qdted 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 mas: 1ugf9drmro58hlg p*s $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two o3iq4mc :*f ortbjects of equal mass, each having initial speed the two move off together with speed v/3 What was the anglqo3*4mi cfr:te between their initial directions?    $^{\circ} $

  Two billiard balls of equal may*n/ 9yu,eh lx+pt/yhss 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 d9+pt ,ley/* yx ynu/hhirection 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 pe-o:pzws+okp m .jb2i(rfectly elastic collision with another atom at rest. After the impa-2wo+jspboz: .p i(mk ct, 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,tniqxr))g 7; ;vf hwud+dgvb pe q28) rest. After the impact, the neon atom travels away at a 5 )gn; )d;)u7ve8p+,dwthgf xqb v2qir5.6 $^{\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 in7,mzw zx-dcy/6yni hvi 3)ppn qb1 )(q Fig. 7–38. Specify relative to the left-hand 1.00-kg mqyq-)vn1dcwzbn (i/) i,hm7 3p pzx6y ass.    m

  The distance between a carbi kii g)c.t*(won 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 of the car. p5g:biy w5 lfsq6,a+uHow far from the front of the car will the CM be when two people f,6ip5sqwl:g ubay+ 5sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is u, uu s1;aiz(dpsed as a ferryboat. If three c1z upsua(;i d,ars, 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 sides hmk nh0x-.89;l 5jj4lne hjq 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 uuki6 nd t17783uz fceidentical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Finuz c61tednu7uik8f 37d 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 radius 2R has a circular hole ofkcfm m*bnx.6/o( ;jlo4c5lw 2ioj qt4 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 6 t( c 5ojbo fql/o2mx*m4;jlkwnc.4i position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and cal5k2pns: n-sfm ec0z:mculate the mass of one of your legs.m cepnk:n: sfz5 s0-2m    kg

  Determine the CM of an outstretched arm using Taaorc9hcm1fg (-gc szh3d ln*hnv,.6/ ble 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the posbu)hh meq i+5d io00y:wk;ll;ition of the CM of an arm bent at a right angle. Assume that hlqe0ib+u ilhw5) yo0:dk;; mthe person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a pojbdv9d jdf3/tqq *w1zczl/r 4; j9m5z sition such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculatedq9rvbz9j / 3m5 ;jlc/ t*f4qdw 1jdzz 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 Eaiuh*g;f 4 p25 a19l+yzkinhpdrth and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on frictionvb6 ow pk.2:vidy :3bsless 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 mass 2.00 kg and a diamefr 6.jsm i1vk8ter 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 mrvf.1k j 8s6ihandle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform c1 jd +7)fl,vim r4hvbfylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of ma 7m+l4vr ,jb1dif)fv hss 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 ((n+w88e.p4 w(1 r t9lrfas *nuh doluhdejh9,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 air and stationayw :p(u7t0l1ccsat r )ry with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and directa7uytr(: t0lpccs)1w ion (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strxx zj6-8)*f t;eh:axvdfp lr 9ikes 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 thevjx*zater9- px8hx l:ff)d;6 ball during the contact.    $^{\circ} $

  A rocket of mass m traveling w)lc d yw 5mvtt9,288jbdpc(jp ith 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 shc:aozr/9mz/ ft a4/veot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch/zat9afv:4 c/e z r/om 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.aa(g)3jua90k sq b bv pushing off with kv3(9ba)a b0 . gujsqahis legs from an 1800-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 60 kg and the other 80 kg, are inib-gseqor6vfz8:n5:rpp)fuqz 55x +) i uua.gtially at rest in outer space. Tho5xripu )-qzvfn f: bzpg:qr58 u .)ua5seg+6ey then 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 hei1e hz v4im)h(ad-on elastic collision with a second ball (at rest) and rebounds in the opposite direction with a speed ee v4i1h(i)zmh qual to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as k)yr+z vd iw+vnm 1m.o;t.+zj an expert witness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels.i++rky v1)wtmdn+;v. ozz mj 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 0ioes31+q bgl of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of thoqeg3+0 i1b lse stairs?

  A bullet is fired vertically into a 1d;qvrdo oao; 0d)vv51.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the )qva; ro;ov0d d 1d5voblock rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes andu ha5x +qj bw6gw(px 4jv2m.fa n3jb/2 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 . jabg3hnq bfwu2 (45+j 2avpmx/xwj6the 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 an9 l5))utmye tjd the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart fro)j ey)5 l9tmutm 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 1 0hho.2: 8j3ridq xg,vugamiabout $ 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 tom.x(osy/ a w11 datg*wo fragments by an explosion. One fragment acquires tos(ao m*/wd1x.tgy a1wice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullei 57+opx/sao)m,g;li ljvd c +t is given by the formula 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+ 0v3aen2 k lwsl;b6az $m_A$ = 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 r4nk nl4v .u8+r y3plk9ee5auhadioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the a ll rn+ y9.kvnup84heku54e3speed 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 (claeqjh-5*9bze ay 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 slidt7, )h2t 2ta xrrjwgo+es down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mass m if i,y69jg lq5 xlqpv1f(pt is to rebound from M, slide up the incline, stop, slide down the incline, andjq(f5 q,l y9xpvpl 61g collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn moving 3 /rlv),l 9owee9: b7nuxssawin the negative x direction at its oxs 9w7b:ea9)e 3nv / lou,swrlrbital 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