We claim that momentum is conserved, yet mo9,m jg2s37 i8ggjx4pvmky 1zg st moving objects eventually slow down andij7jxg 2g9 g83gzm, 4pm1vkys stop. Explain.

When a person jumps from a tree to the ground,4bylbov(5(b48- qw ot-8ukzq5qz c ke what happens to the momentum of the person upon striking the grqk k(oqc-88u4q5 b(e4t z5by w obv-zlound?

When you release an inflated but untied balloon, why does it fly t,scs lon0w0rc/z3 8sacross the room?/30 slss zc0oct 8,wrn

It is said that in ancient times a rich man with a bag of gold coins froze to de yibae ..cb7s)ath wy7 i bascb.).ehile 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 and sp)n, 9s;vc(d5iae0j zm q:pmis essentially in a vacuum? 5 dvp0 c(jn:;mmas,zi9epq )s

According to Eq. 7–5, the longer the impact time of an impulse, the smaller t/8ofr tc d6dd,,9hpl6 i wh38gkbz;vthe force can be for the same momentum change, and hence the smaller the deformation of the object on c8; btzkwp,/6 r8ddf hhvo ,l6t3dig9 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, thoug5)p 3 2;zg,qofofznw pxnouc *7lt1m. h, cars are designed to have “crumple zones” that collapse upon impact. Whz3,n7qc;zn t5u mox.* 2opwl1g of)fpat is the advantage of this new design?

Why can a batter hit a0i(vz.n;ip*h+ox ole 9s bw /4 pipt:a pitched baseball further than a ball tossed in the air by t :/9z(voi x;.wpaeo pplh*i 4nis+bt0he batter?

Is it possible for an object to receive a larger impulse from a small fo l fgaq6y;sxmed7l1** rce than from a large force? Expl leq7md*6l ;gxfas1y*ain.

A light object and a heavy object have the same kinetic energy. Whic00ih1qmp lmq-fov ;7ip0orxm vr9n58 h has the greater momentum? Exh 0 q p1ofomn lvxr8i7r0q9;0v-pmm5i plain.

Describe a collision in w;zjiym,(kmpq bv::kjmjt8ghm (4 50zhich all kinetic energy is lost.

At a hydroelectric powerd; mkk)8ww)rz plant, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought 8k rz)dmww ;)kto a dead stop, or so that the water rebounds?

A squash ball hits a frzxz l21pwsy;3 f 0d:wall 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 from a heigga07ostewrd e i-a( k8 k4p 5/y0gn4suht h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that fal/y 8d4ski -o7atgr5(ew gnea04sp 0kuls and sticks to the steel plate.

Why do you tend to lean backward when cav f*:aaun2ki 7im334ma9xaq* lf5ma prrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, wheusqy(5( kg 52:bfapynreas this is not true f:sy 5(yqapu( bknf25gor your arm or leg?

Show on a diagram how your CM shifts when you change from a lying position to ( ih-iwq4+d6ebqb g8 ia sitting position.+ew-d(qb4 8 qi6b hiig

If only an external fordg:tt7o7dsp jq i):aeunxk :d, y4,f4ce can change the momentum of the center of mass of an object, how can the inte7t:7e)k4sqddyif j:tu 4 :,onxdg,a prnal force of an engine accelerate a car?

A rocket following a parabolic path through the amj06ju u/kj8:q:vgj kir suddenly explodes into many pieces. What can you say about the motion of this system of pi/:ujk v0ujk gj6q8: jmeces?

  What is the magnitude of the momentum of a 28-g sparrowkfl7evt +rp4- flying with a speed of 8.4ev7ltp4k-+ fr m/s    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. 0yej x9h+*)6ay 2c sl6aeeyfiWhat is the skier’s change in velocity+c xea6*e)h ja96fi0syle 2yy?    m/s

  A 0.145-kg baseball pitch 1b rod7c3cli6ed at 39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time between bat oc1bdc6 i73r land 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 horizontallyxt (m5n asbheqe2jl5pm 7/;7p with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assbe25q(5j77/tns lpm emh ap;x uming 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 velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling i4 0eqcyani0pk*6.w w gases are expelled atan k6ci.*wye0p0qw i 4 a rate 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 apparent breakaway for a touchdown is *rj7meb ,w2pwy1x -a u(wx2 twtackled 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 immediately after,e ma-(ujrx wbtwx7wwp*2y12 the tackle?    m/s

  A 12,600-kg railroad car travels alone on ;*5k c(2zwahzrov0 w1ezfb -qalevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s nqhczao;(w2z1bz ve*kf rw05-ew speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a se s/ebn4 3syu5qcond boxcar at rest. The two stick tob3senu4q/s5 ygether and move 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 60r inua;-cbt sfw;*qat speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter b ;srfcq0niw u at-*;6and 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 of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a cons y3 2ibo1nzasn o;400nw;aqxdtant speed of 8.6m/s on a level track. Snow begins to fall ven;syzqono0 a1 3bawdi02nx; 4rtically 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 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an al mu6qw 092jukfpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has 9k06umfujw 2qa 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 bloc.a knb2rx67ws zg re 0bq(0j;lk of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bul( 0keg2lbr6nwr b.zs7 qax;j0let emerges?    m/s

  A 975-kg two-stage rocket is tr8ggk74 8cwl 7cd6jw1,d kcjldaveling 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 spaco5z5 yxa726pcvrjvniyo7 8bz*( d8ji e with a velocity of 115m/s To alo z75by8y j c2z6nv*id ij7p5ox r(va8ter 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 hin a rjp1y/6.y1nt se:ut off the tee at a speed of 45m/s The golf club was in contact wityay1p/1ne: rsj .tnu6h 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 nailezqzhz9hqrs 4 ao:+l+; g zer. :;o*es at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) Wh4*ehzgeq zrez hra+9;ozlss;.qo:: + at 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. hv6(udrbkhe;q6l 9gut h3u *206kg 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 charl z;:g/in0hgklw qj7-ge 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 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car byk-w zg :lli0gh7q/;jn the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is r6lx* mtblq *p0ldaj (,unning at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by aq6 jlt*,0llm*ba (pd x 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 kgv437n(e wazur d0i v1d) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use grri 73dvw0( dz u4e1nvaaphical 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 ge;ker g4u1i 2jump 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). Aseeui k4g2 1g;rsume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of 0o yla cn 6nhmq-q:cyfc1d4,2 cv-a2f collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will bnqcfdac: ql-c2, ah c4o16m0vf n-2yye the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east 6s8)gkdsgg8k jbdq b3nzw.:dr.4; gswith a speed of 3m/s has a head-on collision with a 0.900-kg puck ibs 8grd4 8g3s:dggjkbs .)w qd .k6zn;nitially 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 elaste8gq. 6dz4 bf3km so.dic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite d mfgod683d.e s q.k4zbirection. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, movin1z:-j+*pp hgz.7qkdu obt atx5f ,et*g 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 di:tz .f ok*teqha-5 7xpdtb1pg ,u+z*jrection 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 m4gcpn0xq:e9 yohgk 03*jxv (goving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softba eo4g:x3n9k 0yv g 0ph*jgx(cqll 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 z2bqzjdh.ur+6 n. t k+park ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 k.jhr2d+ k.zq 6ztnbu+g 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 eq.u-jy00muo9t xm 1df lastic head-on collision with a second ball initially at rest. The second ball moves off with h mxod9uj0utmq1 .0 y-falf the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides do9uxso+lp7hph/zj 3 5awn a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizonto /j al7z9hpx5sh3up+ally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general casemn/ xpcdzx j,/*v0;in of an object of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a max;q6zl3 .h) kumye/x ggimum height h of the pendulum equal to 2.6 cm. A second projectile ce g uxy)/;zgk.h3mlq6auses 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 bunjkqhz ifw;1 0 1v(i;xries itself in a 3.6-kg pendulum hanging on a 2.8-m-loi0;kx1z(fi1 hw jqvn;ng string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy loskpgriwalg8f41+v8 t (el az9-t, $(\Delta\mathrm{KE/KE})$ 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 piecek-xp:g)56g bpv3e jo0wvm tc.s, one of which has 1.5 times the mass of the . weg)p-t5k3 b0gp xc 6:jvvmoother. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV d.4p7 r*x t:uqm.gqjy 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 thupdx.y*r 7 mqjq4.:gt e sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height of cf-lj6z) 4t l-y1iucn 1.20 m. Approximately how many rebounds will the ball make befor)yzl j-ci16 c4nfl-tue losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the czt nt z+fv 5fjby)3abl.jj:sv 6 z7d7(y;ub:v oefficient of sz6 uzf z:7 vt 3b.nvj)+v7a(l5 ftj; :bbjyydrestitution, 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 pr gx)6fj v9a,/vnncw* ieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio og*n,a vrxcfjn9w 6v /)f 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 collides head-on with a /a ; zk+pxv,if10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each masskz /a+ip, v;xf 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 e-53a6 xqr nebinto a second nucleus, an electron, and a neutrino. The electro5b en6q -xa3ren and neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of maszcg) q mo-40n;bh)0fn0 vicql 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 objects o.tir0dg;gyr kebt ; )0f equal mass, each having initial speed the two move off together with speed v/3 What was the angle beteb00grg;y)t;.ir dktween their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at ricqosk4 .z,h qjfmw a)hx03 ,2yght 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 direction of ball A and what are their two speeds? directionsz0f2 ,3q,hjhk)w qa4 .ocxy m 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 elastic collisionl,p7hmy5g2 jw with another atom at rest. After the impact, the neon atom travels away at agl52 7j whm,py 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 at0k8*6ek b zwhaom at rest. Afb 0haw 8kke*6zter 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 thr9ny r6qr ojcc)k7u1yvosvby( li58 12ee-mass system shown in Fig. 7–38. Specify relativ9scbo1 )(c7k8yuyl2 r15yqv rjvi no6 e to the left-hand 1.00-kg mass.    m

  The distance between a carbon ato hqr:thm*d u hj2*.p 4;:ia6gdvqf g9g/4csgpm ($m_{\mathrm{C}}=12\mathrm{u}$) 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. :sp 7/f5jllv2qx owfy9lvfg3 , nqi56How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each pervn w37qsp ol: xfq9vfj/f 52 gy6i5ll,son has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a a+4dykmf3j*rm +,amg .o(u ni98ezfiferryboat. If thk*y+o83mnz94 (ae ,r du+iif m.mjf agree cars, 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 i.glx7w pfe.u ;lur6/qqmm i*i, ) /kk$l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of tomato paste (see Fig. 7k 2lzdr+ z( ;d yjn7fm;g;xhs2–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, s n 7dmk hzgj rs;;22;xfyl(zd+o that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius i.vdjx *+h9c6 lnecy29 s6s )gbz vd+q2R has a circular hole of radius R cut out of it. T9 6gs+s6lzn.*di9v )c2hqvye+ cb dj xhe 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 subtraction.]   R

  Assume that your proportions yz,vo 7+y2igwf8fh: oi2lj1 63 f yrspare the same as those in Table 7–1, and calculate the mass ijo1f6ory 82vl+w7hyf, zy3f2g s p: iof one of your legs.    kg

  Determine the CM of an outstretched arm using Tabmj53lm+ 0bp;ptghpq5 le 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate thbp l24o e yyh1cjdsvob1m229*e position of the CM of an arm bent at a right angle. As9 s ob2vbypldhmoyj 114*ec22sume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a posit+-.q)kxtr pspqmn o 0+ion such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far p- pqmxtq.nk) s +0+orbelow the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Ear4yb-7md8 s lhtvph63k th 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 frictionlessb0a wkdhjq/v6nhm 0g9// kof7 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 om,5du w-0 l7pet g+scef 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 mall uw s+c,mtg le7p-0d5eet 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 cylindricalz c-vhiq1m,t1tc2g38h) kdvl 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 shm dc1 hit-h8v,ctq2z3)1l kgvown 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 zr2w xas :kk;tlr)6 a.Example 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 mco(e9v( uc wm)o7bn)jass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respectonc )7ej o9(m)uwbv( c to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat 4 ;.bj vc,n x+dz5hbriand is popped straight up to a hec vrij5 .x4 db+b;h,nzight of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with spee/ + 5,0cbow2jny mh4nr7hhf5 yl n,2ae t-wdkad $v_0$ 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 cornerv ho663hlk1vux)m3 ya pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being) 6vo36a k 1lxum3vyhh a “scratch 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 1kr5.bjz f 7edby pushing off with his legs fromf5zd k71eb.j r 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 ko/i.m(hc r a,y4 u*w 4fmk0*rbk6q hbzg, are initially at rest in outer space. They then push each other apart. How far apart are they whu w(rm/k6h4zfbmc i*yo4 q*ahb k0. r,en the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a seg8b+8tdmf sih(, mw*q ctd +j3cond ball (at rest) and mgjibt(qdsw8 8 + 3h, cf*dtm+rebounds 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 q :1gx wr (5fmre;7gin5 7ndhwcase 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 cfr win57d g5r:hmex (7qw n1;gar B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of cont f ,1yg43bxracrete steps of total vertical height 4. at, 3rg4ybx1f00 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 the stairs?

  A bullet is fired vertically into a 1.40- +f67 5tlmzfq6vjl 5awkg block of wood at rest directly above it. If the bulletl w6t a5ql+f7 6fj5zvm has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikesx-t4wad2wsw s9aaoaqrr4 y;:m; e5n-im-y9 k and 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 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? a54w ;y:mas;aoqredwsm-- 4waix- 9trk2yn9    m/s

  Two people, one of mass 75 kg and the other of2nqa6eu ur:8 h mass 60 kg, sit in a rowboat of mau 6eqru a2:hn8ss 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass washp5vspk7 3eb 8yv:0q z 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 b(i ndj( msms 3j tbk4o906+bgtwo fragments by an explosion. One g6 4skjmm+9dnb tbj0 3s(b(oifragment 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-hq** bj55 os / jbx:rhla2z9gy( $1.8 \times10^{ 5}$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 massesn+jtu6 ok 8tmm /qyl: .cm6hf6b i:,gr $m_A$ = 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 decfq k)gs -m:vz-ays radioactively into an alpha particle and a smaller nucleus.vz-m f k-q:)gs What will 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 fired at an arylb;v yt7 9 q3y kpf29yns.:ungle 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=2.2gvm 81 rlj2u+ p;bi4fxkg slides down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the uppw;;g +u gnjmooi2; j)ier limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline;wn j;og)j2go;imi+ u, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the a ;uojdqg 4qc 0v7y5(aplanet Saturn moving in the negative x direction at its orbital speed ;quq(g7aoyc04 v5j da (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