We claim that momentum is conu/mj xqo5w)fa atj*12nax-z (served, yet most moving objects eventually slow down and stouq2zjn xmaa)1 *xt jwa5( /f-op. Explain.

When a person jumps from a tree to the ground, what happep- ue6jf:eq- kns to the momentum of the person upon : jk-peq-fue6striking the ground?

When you release an inf)ua x.- ftjqiudber,7c6i 8n)lated but untied balloon, why does it fly across the roomj xb )ftq-a6,nc.u7ei)8 ird u?

It is said that in ancient times a rich man with a bag of goh / katnse6-q(ld coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himsen/-(skahe6 tq lf to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction ws.jpto+5pgg w *ym: +7qu tb7ihen it is far out in space and is essentially in a o*tt up p +77iyqbg:5gw +.msjvacuum?

According to Eq. 7–5, the longer the impact time oli, r54quyk x c35 jb*dw9)xaysmoj3*f 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 intended4 xiyoqx9y w l j3d35s) ukj,5**mcbra 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 collisiv w9al6oee0ds imcw;zw0) :yf* l1 aq6ons. Today, though, cars are designed to have “crumlz)oa660w;iws*0ec 9 1mly vedw : fqaple 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 tossed in the air bys/sl45d:js5t ( zpzaw thstas4w/d ( j:ls z5p5ze batter?

Is it possible for an object to rece p8ndf:;f 9fghive a larger impulse from a small force than from a large f dp9fnh :gf;8force? Explain.

A light object and a heavy object have the sam25z bfr*bhu yf*57 qtoe kinetic energy. Which has the greater momentum? Exphr2 *fbbq7u 5tz5f*oy lain.

Describe a collision in whicswuvi; 6,sa d,h all kinetic energy is lost.

At a hydroelectric power plant, water isv,bc(pe9qr6l obv(b , directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be desib,b 6 vp,(c orl(qebv9gned so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at2 -d3qyn*ptbwrs)6 ktpts 2)p 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 height h onto a hard steel plate (fix d ;s*7fskhovjw7 vyp 9sgny(vk3q66; ed 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 (d 9p7jgosfqyvss;v kk;(*3y 6hnw76v b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavysta7oiu 59h5* st9(ogh9fq kln ,xi1 d load in your arms?

Why is the CM of a 1-1: nopm/vmj e2m length of pipe at its mid-point, whereas this is not true for yourn j:eo/2pvm1 m arm or leg?

Show on a diagram how your CM shifts when you chang(. y-b1jn17gcla+.w )g4 xvrssvdscue from a lying position to a sitting position(a7x . ssvs)ncc1b -4lrvdgy+g.uw1 j.

If only an external force can chaucr0-q, tse x*nge the momentum of the center of mass of an object, how can the internal force of an engine accelerecuq-0 ,*sxr tate a car?

A rocket following a parabolie5.n 2bqm 4xco9cls+ph8 tnt 7c path through the air suddenly explodes into many pieces. What can you say about the motion of th9qlctebh5t2 4ps .7+n no cmx8is system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed o ru wth.s lc65l ,jaiy3xcf486f 8.4uj 6atccs5ir 3l.l846hw,y x f m/s    $kg\;m/s$

  A constant friction force of 25 N ac+e+u ztz1:vlu 7l r3q5 +poqrats on a 65-kg skier for 20 s. What is the skier’s change io+qrzu3u rapq l7 l:e1z5+v+tn velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive straightrudo;l:8z.sae 6z 0ubs1pv y 0 back toward the pitcher at 52m/s If the contact time between u68or; usybp1es0l0 :dazv.z 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 horizontally with a spe 0ibwhy.iynef : o c0s+t(u;w4p7 b;wmed 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 water resistance. The velocity of the boat iuhcwwpy7 w4;+ bo(s0 .bfn0i ym te:;is    m/s

  Calculate the force exerted on a rocket, given tbriszxx z +ur n:y6.-,hat the propelling gases are expelled at a rate of 1500kg/s with as:x z-xyi r uzn6+rb,. 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 toucpwp0ehrr+go,qu,(*v2km + y uhdown is tackled from behind. When he was mru qr*kv+e hy, op 0w,p+g2u(tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictionless track with a nkmy0dhxy4ro c 3kjkdf;u ( 1309ku b0constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onbr30ud3ynjx;m1 0 uk4o hkck0y(fk9dto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar at rest. The twou)h/i,n vb0g dc,3gtky6m9yg8+pp 4 ojax,f o stick together and move off with a speed of 6m/s What is the mass of the secondtfvphpgyub+a m k,,84xd63,ngi oj/y)co g09 car?    m/s

  During a Chicago storm, winds can whip horizontally at(ww1v,e) bvv7e2h cj0f2 bj3 u a48ylitpt v)r speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum forcevtvbvb 2e c v3w)40 rw)eh2ai,yu7tjj8 1f(lp 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 a4r x+w )weruxmf..j5 3y 2qerw uk9b)along with a constant speed of 8.6m/s on a level track. Snow m+bx q5 w9. .u4yxu2w3fjw)aerrk)e rbegins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in t1gk2tics .zo /he direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and /1t.zs 2ockgithe 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 penxziezo;r fn kw- gh5(8 /58m l3vfqggcaoz99,etrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is sq8 ki5zh vc( lfo;ax/59wzzgg-3g,e8m9frno tationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocke(zi9n k,a1p s5p gzr.st 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 witiv7taat7f5b7c8 v za *h a velocity of 115m/s fa z5av8ic7b77*ttav To alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg rktupma dtcr6erc xl.br)i1;w) 6l)3d + r85mis hit off the tee at a speed of 45m/s The golf club was in contact with the ball fort8 kcdebl;r l1i. 3 6 amr)5rutwp6)cr+mrd) x $3.5\times10^{-3}$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 av;lwb id oy36-t a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the v;bwi lo d3y-6nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg a kxjyv ;69m2e86h iiywnd 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 chargefdh.k(5- dfw qa(im*n 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 oif*q d 5dh.man-(w(fk n 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 stoppev6f u w)kz- un7xsprua8z+mh/*9qf.g d in 0.75 s by a head-on tackle by a tackler run puh rfz/ aq8f9km+ n 6.vugx*w7s)u-zning 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) points in thlgfxrsfe;g zr+6*7*ug x 30rqe +x directxlfgs;xr0*3 z 7erg+*qf rgu6ion and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without brea9/mp+9j bczwic b3u)rking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a)cwjz rbi+m/ ub9p39c 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 east (+x direction) with a sp::ic 3a)adfkm eed of collides head-on with a 0.220-kg ball at rest. If the collision is 3facima:k:d ) perfectly elastic, what will be 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, -i,zacc ) -dej g-i)g(m)fbjomoving east with a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be th -c)j gc-(idemoazj)b if)g- ,e 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 headxt*03fmvlc i +-on collision. If one ball’s initial speed was 2mxclv0i*+fmt3 /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 direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides he j :;he 90lbyd78sk7bpd vv+dtql2* daad-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg j e2:7l*v0ly9sq 8b; dh+davkb7dt dp ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg twx8,fs 2d*oft hat is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with ad8x2 s*ff,ow t 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 as9j 62 ilvbt 1r cz*l5ahx;0vod one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger m 91 ;d z56lactv*i0hvx2rlojb ass. 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 7 gm uoyet:ltrz0;7:z makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of the first ball.m0e7z:o t: ;rzul7tyg
(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 downih8 2 /n :*yz2n0jqy9in wsnzp 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 fnjq2 /:nwz2 hsp0* ini89nyzyloor, 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 m2yu kr*u(z n,hass 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 height h 03wc oiiq t.m0of the pen.i ct 0wqi3om0dulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s burivr/ d6;nam vx8es itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, whicd 6vvnxm/8ra;h 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 folz jfth+kd6u oh,d .)kp51)gur the fraction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an objecuhq+x1y,g *9m,pm3qbdc: iz k t, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were 3m+dh1gx b:imq,kqu 9pc,*y zreleased 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 cos b05iniaa: 9 g5s;fyyllides into 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 sports car, and B represent the SUV) fi0y5n ai bsg5a9;:sy$\approx$    m/s

  A ball is dropped from q 3dtvpekj1the , t)8y tin:-4a height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its energy? k4v td3:npqt,h8t1t-)ee y ij  

A measure of inelasticity in a head-on collision of two objects is the coeffg xdj9oo, 4s*nicient on ,ogdx9*jso4f restitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the mass o rzid8+yr71vl f 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. T rl+v7dzyi81 rhe 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 5.5mium49 ( uhvk kx32:dag/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mk kg u:4a3 hxidu9m2(vass 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 into4d8 zl/wbc6pjsk6 l94e8c jz w a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have mockcpde/4 jw8sj46zb8w9l lz 6menta 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 masg:s z74g mekc8s $m_\mathrm{A}=0.400$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 betw(u rauyw (49s8sd9edx( ijl1m/* utjseen two objects of equal mass, each having initial speed t(u9*(d (xli1syuawj4 jr9dusmte8s / he two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the 4xt7hpqh7 s,bq s8 pz0;dsot.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. 77;78.shb,0hqtd st s q opxz4p–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with anothernjc2h e4yitd301e y ;h atom at rest. After the impact, the neon atom travels;hd12hjic ne 3yy et40 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 5ck gvf 4s8cd/elastic collision with another atom at resc8d5vf 4s cgk/t. 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-tg hqm o-skqe);3zf+ ,mass system shown in Fig. 7–38. Specify relative to e;zhf oq +qgtkm,3-s)the left-hand 1.00-kg mass.    m

  The distance between a carbupb 0.1zg wd/9lr*ujlon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m beh je+ 3u7bkl1+rg0:i +d1l -zuvxyqw ifind the front of the car. 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 front of the car, and three people sit in the back seat 3.90 m from the front?rq +gi: yuubivd3+z7lw+ 0-1e1j kfx l Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass3k,wsy.2u wti8zy; 3 yti8yiy 6800 kg, is used as a ferryboat. If three cy8tsyiy;wiiyk 8wztu3,23y .ars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides h4ruaj )19vu9wb7mjx$l_0$,$2l_0$, 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 haos;1xzlx *g, 4llok;y dv +,sas a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. z g sk+ ,;xdyloxl1v4o;,as l*Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has 2v v e ox.m*kmy7 (1buiv8gov,a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circleb gv 7.kx,u vm*e1oyiom(v28v, 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 same as those in Table 7–1, and calculatr(i eq ++4vo6zyemh9eeen 0l)e the mass of o9 e4lv(+yh)eqr+ne6izee 0m one of your legs.    kg

  Determine the CM of an7ttn9jhg 1 zzvcq .e-0 outstretched 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 the positizmq:0qx;b9 ynx53jje on of the CM of an arm bent at a right angle. Assume that the person e0: yq mx9nzqjb53;jx is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hanging vert(//asem oyr9 u9xx1g zdyv,u.ically, and his trunk and head are horizontal, calcdey.9zrv gau ,xu/x1(y o/9smulate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth .qg ). 0cmp6zxy bd;t/xv y*vfand 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 9 pk n3zdkf2z*n6ci 1h11o -bz -bmj tmde58hn10.0 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 1s6 sw 7yj)jkua 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 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 followk) ssj7yw1u6j a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a d tdzzx ( wk242s12ka jzow82noiameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–t8ko nk2oz 1z j2a4dszw(22xw42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29),y2 rkfy/ cvtgk68 1 kz4ts-ktd821w rf $m_{II}$=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, d q,, r27v:fzh nmycp8of mass 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 respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? Whan:,dcv 7f28z rhq m,ypt happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a ba qru;v,gciscuo: 9jkt7- g b ,7fobi09t and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the averagtgcik:j7v 7u0,,ifrq g9u b;s cobo-9e force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travelivx*. y4j ec4qgng 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 the corner pocket shot shown in Fig. r(ard s) wwfr0 +6c9/rrg xl9p7–43. Relative 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 detaswg/p()60+9r rx rrfl ac dwr9ils.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5ab) txij6h0/j*g 5rnnoti*x 07bj. yfm/s by pushing off with his l)jtaijyh b*trob.n 56f* g0x xni70j/egs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 e m;ypsws m/c2uo/)9cf)y9xm7jy qf(kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are thecyyq 2j()sf m9w;c/u/m 7sy9 e) ofpxmy when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (at rest)dyrvl4ewa . (2lh;bz;)ux5x f and rebounds in the opposite direction with a speed equal to one-fourth its original spee4xl y;r5)he ( zw.2f xba;ludvd. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as (znq mzj8:5jgan expert witness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he8z jn zj:qgm5( 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 -.vpeji0 wpgh 5e5 f (a.mj*xlthe top 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 a-mhp50(jg5lv xw .jp. i*eef of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wn8*v:q:m ka9ojazfy 8 ood at rest directly above it. If the bullet has a mass of 29.0 g andj 8afz8:ma o k:v9yq*n a 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 embeddegd/t m q)puow)imaz(s9.k26 wd 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 s)) m imwo2kuqw6(tgp z 9a./sdpeed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 6)d0:prx;ll ug0 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat ; d :0pgxlr)lumove? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abor cu,9v z0 cz64ey,fvb7-g te bld5rjng(u.*tut $ 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 ( 8,(m bavrqtjbroken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the othr8(b( aqvjm,t er. What is the ratio of their masses?   

  The force on a bullet is given by the formula F =ls;klows6/* h .78fye ,ii6o gqookh1 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 )8nk2n s /d56 p4+wzhfvplufm $m_A$ = 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 intojn/ - bqoi;i)m an alpha particle and a smaller nuclionqimj; )b/-eus. 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) it4q2( g e kou0g4w-k-ba(raois fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slqi.uoxv5h .1g7ib v6 hides 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. 7–46hs)/z)+g enpa ), what is the upper limit on mass m if it is to rebound from M, slide up nzeh)g +)p/sathe incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 y jr*17w44w-qq;tk smcv2l z vshows the planet Saturn moving inzjsqy72m4 *wc qw;tvkvr4-1 l the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s