We claim that momentum is conserved, yet most movinqn.: 2fi n.1oyjkz/m5icyd 5cg objects eventually slow down and stop. Ex. . czoy2d1nnc/fyi:j k5i5m qplain.

When a person jumps from a tree to the -nw0.l4 z0kf m5jwp1uhdj u (fground, what happens to the momentum of the person upon striking the grounhwz lwk(05u fj-mdnf 1.0p4ujd?

When you release an inflated but untied balloon, why does it f;,0aj.)e pnjl po p+mnly across the room?.+;pnjlja n)opp0,e m

It is said that in ancient times a rich t 9v/,rh/5hxu/pzw h hman with a bag of gold coins froze to death while stranded on a frozen lakp zh vhu5h9 h/t/rx/w,e. 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 ac .yhyo3dlw)3 nd is essentially in w 3do.y)yhl3c a vacuum?

According to Eq. 7–5, the lo20/ wucxybo jouaz- 0)nger 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, which are intended to inflate during an automobile collision and reduce the possibilou yzoj-c)0/axwb 20u ity of fracture or death.

Cars used to be built as rigid asgq5.57cttnjsqe5 1 xa possible to withstand collisions. Today, though, cars 7 5g ta1qjx 5cne5.stqare designed to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tos 4ylq7up5iqa6h r)i7zmxs r(oehu+ //sed in the air by t /ph7mle6ay/sh4xuu 7)rqo5q+ (iizrhe batter?

Is it possible for an object to receive lg)yk/p ld )e,9kzkizick3 ( -a larger impulse from a small force than from a lk3)ke y) k9z-dz ic(i,lglk/parge force? Explain.

A light object and a heavy 4vd skky;, yju08l ya1object have the same kinetic energy. Which has the greater momentum? Explai,ylvu;0y 4 jy1a kdsk8n.

Describe a collision in which all kine t59gtrefap pi878eq 8tic energy is lost.

At a hydroelectric power pla/9 2alk9ju xxq1f4sc cnt, 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 to a dead sto9q4cxl juxa k/c1s2f9p, or so that the water rebounds?

A squash ball hits a s nexl+jkl:xx8 og fzc2jvj4m4 (t8s9vue-1: wall at a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard spt8 fus2l0p /jteel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) tlfsp0/uj2 p8 Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backm2/ kgk( q)mrlcfex*8 ward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe h kww bpd p9392 9wx2.wltoe5oat its mid-point, whereas this is not true for your arm or le92tl pxw2 wb.5wo9p3 9odwehkg?

Show on a diagram how your CM shifts when you change from a lying pon1caj, 26 jzamsition to a sitting posi12,jj a6ma nzction.

If only an external force can chanl5-0 p-wmlbb4x4;n,48xulm k o fuf hrge the momentum of the center of mass of an object, how can the internal force of an engp- n4omll85wu - lx4r 4uhxmkbb f,0f;ine accelerate a car?

A rocket following a p0n nx jic6 4 ex -fy *exfy))9zjs59ydpgw,,rdarabolic path through the air suddenly explodes into many pieces. What can you say about the motion of this system of rj zi06xf94p,de)gnnxjf5 ceyyxd ,s w)9y-*pieces?

  What is the magnitude of the momentum of a 28 abd,jgj2.irk87 xd g-b*xdc 1-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a vud73y4fy4 cu2usn c:c*y: lg65-kg skier for 20 s. What is the skie::2gudsnuly* 74ccyfv 4y cu3r’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive strl9z7 )/vrndelaight back toward the pitcher at 52m/s If the col7d v/lzer)n9ntact 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 horizontall4(ud gim2+3s i2bezhby with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was32b sd4hu miiz(2eb +g initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling 2xei-jx0ud yga2: /t fgases are expellyax2 tj0d2-u ef/i:gx ed at a rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving a vq+n:lsev4dv)g.ng9ob8:qe ks tj19 t $4.1 \; m/s$ 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 kaj.h 567 k9bycqs/ttalone on alevel frictionless track with a constant speed of 18m/s A 5350-kg lah65 . ybct9kq/ jkt7soad,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at e4x,m vc jp, sem-qc68tvovty-; 2tc*$15 \; m/s$ 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 horizontallyv6fj*ozv-.pcj 1 5ijss: 4p: 0xelzz3,eo sx u at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is bfi., 5cjlsx :p eopxu- 3z6eo*zj vz04s1jsv: rought 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 constant speed of 8.6m/s on a le(6rkrv/c 24 mzd3vwzl vel track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignorin4kv6wr2z lcz 3r/vm( dg friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially mo4ll5 q vh77ivsving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpvil qv47l7hs5 ha 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 pene bmbn6n*rsp)3trates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surfac m3br*s)p6b nne when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speed ofnz :e4l rfj.rj7sh 5yeme26x . $5.80\times10^3\mathrm{~m/s}$ 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 of 1:w n.4r0zl axu15m/s To alter its course rn 0 zxa:4u.lwby 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 ap1syl1mv/ e u4 speed of 45m/s The golf club was in col4 se/ympu1v1ntact with 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 velocity of 8.5m/s and comes to rest in a m//io3tr *dlvimjl4vt1.h q + time interval of 8.0 ms. (a) Wh3v mo vtq/.1 mt l*r+jii4l/hdat is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes a wp/57psxk kay1 )rz 9xdall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthiness of new aul,ke 01 pzqg;ftomobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg1qflpez;g, k0 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 wvy zs hq* 5fa.;jadg8a3cj-4 in 0.75 s by a head-on 8wh 3dj*z 5j;yf-vasqaa g.4ctackle by 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 ten h2 u.jn;* dkt,s-1icuh- jmfxnis ball (mass 0.060 kg) points in the +x direction and is given by the graph o jit2kdm-c.jns* f;1x,-hhuuf Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking the lowdhdm3uz((y1p er leg bone of either leg? Ignore amy (p3(uhdz1dir 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 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 9o1rezo)ci(: 8gie f weast (+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 ec8iig(:weo19 r)fz oball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/sj6kipb cv :8hgjl4 8,cqwn *-t fu+(uj has a head-on collision with a 0.900-kg puck initially at r 6* kg c:u(iq48fuhcn v+-8jjb lwtpj,est. 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 elastic headenal61u .j2 vn-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 repnjln2v eu61. aresent 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/sfq1;th/q) sxa5yu+ ob 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 thtbxsafo; /uh15yq q )+e 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 8.5mk0:xnkaorp6 t)) 6diu/s collides head-on and elastically w d r6:)u0nkpix)tao 6kith 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 ahoh(sa (x0n*g7 qr.vmmusement park ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). xag.r(0qohn7msvh( *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 cwp 4,8,c ui68iq -x ovk/aw2 kvacpnf8r9oxg -ollision with a second ball initially at rest. The s rq826xc x,wiafv-ion 9k4u,ogp-cav/w8 kp8econd ball moves off with half 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 sn s-7itx58ont lides down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only onetns t-o87x5in-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 suur z,si k *s2+m g5l0g-vfd3an 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 expeu- qn:+w5rf ppriment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A sep+qwfn p- :ru5cond 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 2x;62ww) 2(y uwhaxmxqk;2d r zq, djt3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the ve;q) ;d2k22q (wy x6xj hwzxautrw2d,mrtical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy losfhv4ge2 i57 k(( n;5tkff(hqg95jjl w: kytdvt, $(\Delta\mathrm{KE/KE})$ 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, into7jk7t hlx)9xc two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A repcht9)x k7xj7 lresent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides iniwp,y-: insz;/v x1byto the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports1yni:pvs/ zi,-xy ;wb car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from + o1/s*b adsim*aq *sda height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before loib +sq1ss**am /od*adsing 90% of its energy?   

A measure of inelasticity in a head-on q *vvf:vc0a(rv(ic+fy w0ku 4collision of two objects is the coefficient of restifvcc*:yv wqru(fv+0a 4i(0vk tution, 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 ina i - o*qt4ys;bbkns*zk 1ypap*4(g.ato two pieces, one with three times the mass of the other. Ap4bbat.yk io zp**a; s*n1(- s agq4yk 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 of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on wub 2ufmz;o-3 18 dgdycith a 10.0-kg object moving in the -x direction at 4m/s Find the final velgd8 bu-1z;fmd3uyo2cocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an 0t 98kv.(hj eei7vlnxelectron, and a neutrino. The electron and neutrino are emitted at right angles and haveve lt(.897kn v 0ixjhe momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of mass 66opedl3f;dlsh oj3l4mj)t *$m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equal mass, each onr-l ,fe7ld e8:;gbu having initial speed the two move off together with spe,n rbl-god: e le7;8ufed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass movekd1f 2j e 05ihfv0tb5xq-k gr. 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 alonkivbq 0dx 01ft.-rh55fjgke2 g the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) maoai1 9-j /0u:cojh gbckes a perfectly elastic collision with another atom at rest. After the ij0/ho:-9u j1cabo gci 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) xjms x(e-6 on45oi j+;cagxdft 6su* .makes a perfectly elastic collision with another atom at rest.c *4.o metxs5s66fixua x j+jo;n-( gd 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 p6n/m+pukonhsz1s;* 1m va i6 k 2u(t6yspy6nthe three-mass system shown in Fig. 7–38. Specify relative to th2supmaps6 k6 unmp+ 6tvyzi(1*6n1 n/s;hyoke left-hand 1.00-kg mass.    m

  The distance between a carb h9wchbkmt71b2e/ +.ch l 3zshtlz2;n on 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 cr/v61mlt b60ip gwyj4ar is 2.50 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front se /wg0y m6i4bvl1pt j6rat 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 used as a f7djbic8*( .zb-w sjnwerryboat. If three cars, each of mass 1200 kgbbj(*.zi -7 s wd8wcjn, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides x4 ao j(((il3fuxhb h5sb-*ww $l_0$,$2l_0$, 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 load7mz+kno h+xhw5o x1b 5o5 -7ptg1 jrkv 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 horizont htkozb7mj+go51p n5vkhxox 1 +r75- wal 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 rai l2zc9qai/k 8dius 2R has a circular hole of radius R cut out of it. The center of the kc / ii8l9aq2zsmaller 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 are the s 8)k4 *u+ngpgmb+wez 56vxqiyame as those in Table 7–1, and calculate the massiv4*+ +mbx6pnw)zegqu 8gky 5 of one of your legs.    kg

  Determine the CM of an outstretched arm using Table 3 w vjb:c0clgi1qj/ 6hgqt.m7l-+ rg w7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent atu(j ;ga(kht, g z2o,m;wcsha9 a right angle. Assume that the perst9 ;a (og ,g hjwk,z(hsa;cu2mon is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position suc0t(/ p3xz jvhae;crp 0h 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 this CM be outside t; (t30hrp/ vzcx0epj ahe body? Use Table 7–1.

The masses of the Earth and Moon are t;d 2o zflof0zd *1*wb$5.98\times10^{24}$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 108p0bl- ic:yo:fm(n ia.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 a uniform cylindrical head of mass 2.00 kg and ahv*a2nazzl:5 )cf oq2 diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.24 c2 h5zn* z2:af)valoq0 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?    cm

  A mallet consists of a uniform cylindrical head of mass 2.0 :2/mvy -8qyhvkyk/ c. eqop/y0 kg and a diameter 0.0800 m mounted on a uniform cylindricc q8eho yq2 :/ m/kvv/y-.yykpal handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Exampl9ns3:n z.7x.usdoo4u wu 7ughe 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 stationary21rnn7 8:dgi jfxu gf8 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 Earth) does the balloon then move?un2nj1 87gd:irfg fx8 What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is poig4fge 6 xz rgx4,/trme r4u12pped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on1rur x6i4f/ g4ete 4,xzgg2 rm the ball during the contact.    $^{\circ} $

  A rocket of mass m travelings-g b j6ba9zkv( w*-wm with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with +np 8.,,6u)iqki7rl0iwnx f o*y assdthe corner pocket shot shown in Fig. 7–43. Relati6,r8d+i . a7piu nl wqysfi,*o)n0kxsve dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) /g d11qf.mav8-eftw jacquires a speed of 2.5m/s by pushing off with his legs from an 1800-kg space capsuf8tm d/we.g q-1a 1fvjle.
(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 initially at reseau eh3o,4d( xwl6 e7ot in outer space. They then push each other apart. How far apart are they when the liola 3(,eohexd ew764ughter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ba yjr4t24q .jahll (at rest) and rebounds in the opposite direction wir42a.y jthq j4th 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 an automobnd/ ,h/; v yxzl, hm:+2wx*wu4ykzboeile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver ok ,x4w:+b wlde2zy ,hmyo;*zh//xvnuf car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the toy2.5/ t whdulhp of a flight of concrete steps 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 are2ulh5wht dy ./ perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rebrr,)j *vow8(2fp riz /:qz mhst directly above it. If the bullet has a mass of 29.0 g and a vr)mjw/f2zhqr (zobr*,i: 8p speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded inj utf8h4wv5h; a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient ofuj 8hwt h5v;4f 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 72,5/o wz rbb2)o 8buoqcxl au55 kg and the other of mass 60 kg, sit in a rowboat of mass 80 kg. Witx)ob, uqobo2a/z lrbw5 58c2 uh 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 wq (f71chysjk .as 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 int tb)aa (km2i+- pn9w :/)aktaryyasr ,o two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is thet sr rta/b,iy+m- (pa9aa)) yan2:kkw ratio of their masses?   

  The force on a bullet is given by the formula F qjly3k-evbh0v 8b.9k= 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 64 oh*uvz thbgyw,1 +i$m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively i7qzz ik3s,hoj:z+u :uh2c dd.nto an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus ifqd h3zd+ou:7u i.k2sjz:, czh 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 anmasfq6:ldyj2: y j r65 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 -. nq 8c1mof-ovaxn 6ndown 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 it i iss1rf2f (n/;bw/swps to rebound from M, slide up the incline, stop, slide down the inclifsss/b; 2r/ 1 fiw(nwpne, 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 planet Saturn movinc dnlw7xnq7kfe 3b 4ey/4y m*20hgw/kg in the negative x direction at its orbital speed (with respec dm0wy lb*fcxyhkgw /3 e7474qknne2/ t 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