We claim that momentum is conserved, ye/1dihhphbcyu 70p)lbpd71 o ;-8i;a4ow h wac t most moving objects eventually slow down and stop. Explaiy hapu/c7ii1 ;dwo8h4o;1)p d-pbach07lbw hn.

When a person jumps from a tree to the ground, what happens to the .m2 3k6ph 1a hduif2wtmomentum of the person upon striking the grom kwa 2 hud.6hi2p31ftund?

When you release an inflated but untied ou4f, g bul+i*r:vdfltkc886qf s s d)1mt :t;balloon, why does it fly across the roomd:tm ;*vf81f:ig sbf)o4 8t,6dul lt qkcru+s ?

It is said that in ancient times a rich man with a bag of gold coins br mp6gy7c(y7 ;(jrbt froze to death while stranded on a frozen lake. Because the ice was frictionless, he couldb m(tb 6gy(7yr7jp c;r 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 5n1xs0y 6zb bt.*wfhlfar out in space and is essentially is*x.t16lbz hn 0b5f wyn a vacuum?

According to Eq. 7–5, :hph;ke ky0qe2tiv,y. f u07) owwdt ,the longer the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, whiw;.k he7:ph 0tyeiuq ,dt) yk,v2w0ofch are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as ri05 7qpvbnw- qv am9g/ugid as possible to withstand collisions. Today, though, cars are designed to haamb 50p 7-wqvnvu/qg9ve “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further jcasfd9p2iv2 1 x3+xcxvuxo i5 ; sb2)than a ball tossed in the air by thaf 22xiucvxb39v;5+cx dj px 2o)s 1sie batter?

Is it possible for an object to k rsr6cpuxa 1t(d2clem ;* 7/breceive a larger impulse from a small force than from a large force? Exp/c k7p2lrd e*mtxu1c;rb (sa6lain.

A light object and a heavy object 7a t+y-xa 0 s3lgs fmniu25o+nhave the same kinetic energy. Which has the grei03ouna asy +x-g+fs 2m75ntlater momentum? Explain.

Describe a collision ie2; 26firij7: ou dgb:o8fntw n which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against bhk 9k.3o-iqp,*odd j turbine blades on an axle that turns an electric generator. For maximum power generation 3j.- 9pdkkd ,io*obhq, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall 0 /kch3m5e)836wp atdmulued ; cgrz(at a 45 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped 9b0h2 o:*o-d dnhu;js g olmuff9i-u8from a height 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 h-ogi*o m9 juufs2l0o :fd8hu9bn -;d ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load iaa1eehj/0 fh*;:.nq br2 smpqn your arms?

Why is the CM of a 1-m length of pipe at its mid-point, wherea9m bhnsff: hr;1sv 4e3s this is not true for your arm or leg? s h1rbff3 mh:4vn9s;e

Show on a diagram how your CM shifts w*dzw zbr6b7i 3hen you change from a lying position to a sitt73zzwb*rdi b6 ing position.

If only an external force can change the momentum of the center of mass of an:u gy w;ha*4l)r ku ;mbeb:0sj object, how can thwk:yb;bsr:*ul4j )am ;eu h0 ge internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly expz52twm7p0 cw vlodes into many pieces. What can you say about the motion of this syscp02t wmzwv 75tem of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a idqm p a9*s4h2speed of 8.4 ihqasm4 *pd 92m/s    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What is ta azkgg,yh-tt (w9*z,he skier’s change in veltz zy-a k,9 ggt*ahw(,ocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drwec( 5 /t 86b9 rnug0 gvwqpv(j*y(qfkive straight back toward the pitchb w* cg jfwn(6u 8kvevq(5t0rgqp/(9yer 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 outem-tt9 h+o6 jn 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 is 26.0 kg, and that of the boat is 45.0 kg. Ignore eh- j9ttmo+n 6water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelliugq 8/71f ):dkthasm eng gases are expelled at a r8dhmgq saf:t1 )7keu /ate of 1500kg/s with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an apparen n.wv) 1;htm ,mk5qyiot breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual speed immedi; koq1vy5 mit.nw)mh, ately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictionless track with tk sz.rof3 h3prs :umqg6 xmh7x 6(i61a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto theh6usx7t6 3:mg.r3 im1rpzx6k foqhs( car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a secih sensd s0:4a3p lpv.xa 29n;ond boxcar at rest. The two stick together and mov a9avlssp.x23hs in4;dn:e0pe off with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speeds of 100km/qvb,mz5j fl52*xgk/ zh If the air strikes a person at the rate of 40kg/s per square meter and is brought to rmgq2 v5fx5,zbj*k l /zest, 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 of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along wi5hh .3acz c6v4uob:lnth 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 th: 5 a6obncuzh3h.v 4cle car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in the sx;m6 cz p1sr-direction of its velocity, and the r6 rc s1zm-;psxemaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0 8pwx6:6)vh gqp;zeho-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fasz: h6x6g8wh )qpovp; et does it move after the bullet emerges?    m/s

  A 975-kg two-stage rod t6yjw-9vc+6-flz9 qvx b qu2cket is traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a velocity uan8 l((6shhkof 115m/s To al(6h (k na8lhsuter 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 speed of o.e*n0oebrq )4 m7xjv)g .tmb45m/s The golf club was in contact wi)tbe7g.v *4o. )er qmmbn0joxth the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocityu1468 boo nw1zx vxx5q of 8.5m/s and comes to rest in a tim18zvxw6ouq5o 41n bxxe interval of 8.0 ms. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.0f.w dp ,0m6qoa6kg 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 engineer in charge of the crashwortx:l5xbupl.- h .m:rtcp3i (w lhiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph).:xcpl -(bxih.: mwtul3.pl5 r 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 in 0.75 js ti zqpx aq8*u+v l*whjm/vp-29,j3s by a head-on tackle by q* tx ps9l3w-ivu , /*mp2zq8aj+jjhv a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) point47x: crwwp3n( 7ff;lyfx) bbls in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methodsf:wf;(ycwx 7rp)l347xb fn l b 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 ca3kp)naw.u*nzam n(:v n a 75-kg person jump without breaking 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 unit area) of bone .(va :mnzuk np)w*na3is $170\times10^6\mathrm{~N/m^2}$ 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 movid b7 (8zr*hev3o - eeah;ps/klng 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?eheao 7ds8b*pr/zv e- 3h(;kl 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 w;fjd4 q*d,jlzith a speed of 3m/s has a head-on collision witj4jd zf *dl;q,h a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-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 4,qmjay9 cafs9 od)/relastic head-on collision. If one ball’s initial speed was 2m/s r/adq)jsy o9c,f4am9 and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, movingo. qnd mjnit85 k asm)(h/y6bq/v +m8b with a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a 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 l8vqi+q. (/js5mab y)6nbmntko/ mhd8 et 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 efbaka,9an;p/s0 8bp head-on and elap8,/ 0;abeb9p snafkastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as(kyb9 jw l8l6m/7hq ygoet w9/ one approaches the other directly from th/(b9 lkyjy9e7 gh lt 6/wo8mqwe 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 sect*6.- mau15vbnjp fa qond ball initially at rest. The second ball moves off with half the origiq5f*-p1 ub.tv namj6anal speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frict 8b shkxj+f,wn a*)*yzo(uwf:ionless incline as shown in Fig. 7–35, 8w zfko)+fbsw u:x( ,nyj* ah*and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of mass 4mg6vi2k1 oklg9 9qkn m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a maximum hbf3rkam k*o0-a fjbkf; -,g2meight h of the pendulum equal to 2.6 cm. A 2k;jk-gab krb,3m-o*a fmf0f 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 buries itself in a 3.6-kczn jc9ak;w - 5gc:zmqv;r3 i9g pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizonci ;99aq;-c35 jzn ckzv :rgmwtal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lost,dv yw/ ba86ki2qyzaz-2rzt-; $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into two pieces, ouzdw-z+gk : y7ne of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic ener dk-7:u+gwyzz gy 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-kh 58fx0qac j y80,mxyng SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let xymj0hfa 8 5 x8c,yqn0A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.5aq v; y+cxw+(q0 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 9 wy;x(q+qa +vc0% of its energy?   

A measure of inelasticity in a head-on collision of two oba;kkz( imr:+t-yx y1qjects is the coefficient of restitution, e, defk; (tza1+:rmqi -xy kyined 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 piqlyip(p51q qiv+xc, , c2rwdux4 )j h/eces, one with three times the mass of the other. A dcwpqy,+ hp1jl/i x x4)(iq vu,r2qd5cepression 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 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 dire 7smtqctkl0ym c52 xjw3:b1j7 ds*. cwction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the f sct*xm k. csd53 01bm72lj7qcj:t ywwinal 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 /uzt;z0y8k0c h(eazc decays into a second nucleus, an electron, and a neutrino. The electron and neuc/z y(t 0kcazhzu;0e 8trino 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 massj+d .set n0mt:c l2b2*sm(2 z,do kjtp $m_\mathrm{A}=0.400$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 colsj+p+a6uovef1t ;e7s . fz1 fllision between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle1vf+ z1es; 7s fp+.eafl6tujo between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meenjqt /i3b* b fb3c6dc3h +hnplcd-ci(sr5: f)t 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 wi -cf :n3q5d)p6/jb+ 3f3ni c(ccdrblbs hi*htth 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) l q.3 wj h0:kg8 hsz6yl0t:ypvmakes a perfectly elastic collision with another atom at rest. After the i.g6h q0kz0ll:yh:8svtp3jwy mpact, 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 withyaf kn+c1+y-h02,svq /uus nn another atom at restn-2qncsyu+k+a 1h 0/y nf,uvs. After 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

  Find the center of mass of the three-mass system shown in Fig. 7–38.bsr/ c fmtk;o ,ck/02l Specify relative to the l cr,sfkmk2;0l/bt o c/eft-hand 1.00-kg mass.    m

  The distance between a carbon atomhl)660*:lg8y hdf,gyzi +na l9i uw zx ($m_{\mathrm{C}}=12\mathrm{u}$) 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 a.x;3 jl/cnl wvlh:,jl 97ujicar. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the fronta9 ./nlxhl7l3:,ji ;vujlw cj 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 0b;qtjl-xf,et l1- hv18 m, of mass 6800 kg, is used as a ferryboat. If three car xjvtetl-,hfl1 bq;0- s, 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 l92wy;nfij f oo68yub0c p*r;$l_0$,$2l_0$, 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 loadt m6dxw0f/et; kph n*: of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load wtdte kxh0*;w 6pm/:fnithout tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole oxf- pfg m 5zuss0+x/1of 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 center of mass of the plate? [Hint: Try subtractiom f/5xgus+sof0p- x1zn.]   R

  Assume that your proportions are the same as t5wlq br 5zt syl60-2fuhose in Table 7–1, and calculate the mass of onsr25 z0bt6 5fulqwl- ye of your legs.    kg

  Determine the CM of an outstr a.c.c 6oof,ibetched 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 t k t9;3*hb:nat h c6rqdt 6u:w4zrtq+bhe position of the CM of an arm bent at a right angle. As ttr4tqka:c q 3dbuz9n6t:h r bh;*6w+sume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is inqgr - jskqw)vd6 4(0 wtb1icu6 a position such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will j tq(6 1 4igw6k)s0rcubd-qvwthis CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon are b2dlkbxy984 x$5.98\times10^{24}$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-l or(qgd.;6n3ic1 d9bh:jpkdkg man stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of aj3d6y5exc61 r v+g2hizlpen;h oqj;. uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in . xpecd;;jro66evl32 5hgiz1nqj+ yh Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head alp 2l2moz1 e:0.yv jqof mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle i 1ja:lzp2 le.yvoqm0 2s the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Ex0 m+zny*15t zy u1wzvjample 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, of mass M, are in the air and stationaryack f0x4,g8h7xk1lnke c+ q7i 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 direction (relative to Ece8qkf xc h7+n ,k kl41ax7gi0arth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a b lzow;0xiq -s8ikfh)o1hj/ on jv--p:at and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculat z-sokjo/)q;holvhxjf n 0--i wp:81ie the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling wdh;5hitq4lb .4d5 dhwith 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 c y6/2+l )gavpd-qjsvcc;p 1:qzhiis -orner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the pl-;vdp6s vaq l gsc z-cqi1y:)hi p2+j/ayer 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 suit) acquire4aoa vv l+p)*nm;h9g gqb*4hk s a speed of 2.5m/s by pushing off with his legs fr4pmh kn;vgvhl+)*gqb4a o9* aom 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 ot v(,,.zocny s q/j+1zslr zdq4rf(,m mher 80 kg, are initially at rest in outer space. They then push each other apart..+zjq,r,l zs/ oc vmsn(4zdr1fmqy,( 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 du31kiyfo t7lq; e9/r second ball (at rest) and rebou1fe3or7lq/ kd t;u y9inds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving xk4g z1+yd0*exzy f e 8b0d9nqan automobile accident. The accident involved car A of mass 1900 kg whicd0*9 gx0yn4zxe8fybzd q +1keh 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 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 fli+zxg.k;zhrvu/um / , ight of concrete steps of total vertical height 4.00 m. The ball hits four times on the w/;.xzhzu i, k+gu/rv may down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a.21t6mlbed1 4mhy g7jw wjov8 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s8 owv4m.6 gm2 1hej7wy1bdjlt 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 placum a-pg z/2rb*5 xi5 yf9 /oxjyqxl9n9i;vdq7ed on a horizontal surf; u9y/jqida5*qn i m9xv x g2-r59zyo/bxflp7ace just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rov 9yr.s5g4hmfu(;uv coj3i; pwboat 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 ap9s3 ;5mohyi.(4g vu v ufcpr;jart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass wafcr2 b / j69uddwx4,ts yr.p2ms about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments by an expq37i o -.ggjtplosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of g-i.tjgqp 3o7their masses?   

  The force on a bullet is given by the formula F = 580-( d9 nm av+,nae+lhmi3bh6;n4 o$1.8 \times10^{ 5}$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 lp4wao5d y3qo0w)ibgf .52d40 jm kzc $m_A$ = 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 decaysye hij26wteg rn 3g*ba(yw yy9)+qu7( radioactively into an alpha particle and a smaller nucleus. What wily(n*u7t j)rge+gwi2y 9 a(eh3qyby6wl be the speed 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 fir(dzvgsf8 ab vz1u-v 1)ed 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 dow,apl s 74x8sqvt.x x0h+w(edon 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 mass8w /g6qb/9e vz(u vwnn m if it is to rebound from M, slide up the incline, stop, slide dovvq/gzn/b( wenu689 wwn the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingbfj:n dms,sbe+4f ;tr;7+t jyshot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with res nt: 7;;b+frf,se +mj4dt sbjypect 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