We claim that momentum is conserved, yet most moving objects eventually slow dovp ,l9rcladmfqy( 2u41tcz/b20edm ( wn and stam 9lz c(r,(l4bpe10 2/ cft2dyduvmqop. Explain.

When a person jumps from a tree to the52mfzd f3+b1r0xp leash,.qx ground, what happens to the momentum of the person upon striking thembx5 . qsa0dx3zh, +ef21rfl p ground?

When you release an inflated but untied balloon, why does it ,96sz .tgtdqh fly across the roomhq 9dtgst.,z6 ?

It is said that in ancient e htyc01og.is 1.0bnttimes a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have don .t0 yte11bshiocg .0ne to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and /fc:(z;k )ckra7tc i6afb 1si is essentially kiatbcf6:z /rk 7c()ifsac;1 in a vacuum?

According to Eq. 7–5, the longer t* qxnksn;dfkm3f*n0oa3h3 c :9bu/ jc he 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 k/*q39c anu;*3m:cfxo n3jfs k h bd0nthis 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, thougm 57k:d2lv/pot; dhtgh, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage okg:vd2to l;5pdm7/ thf this new design?

Why can a batter hit a pitched baseball further than a ball tossed h3owtmt lpj d,,2 7us7in the air by the ba p7ud oml27t3ht,j,swtter?

Is it possible for an object to receive a larger impulse from a small fom/ aa-(zmowf4rce than from a large force? Expla/ mmza-(wof4ain.

A light object and a heavy object have the samey/1:x e3jgmza-t 0jfd kinetic energy. Which has the greate0:m f/ a1djgyz-xjte 3r momentum? Explain.

Describe a collision in which all kinetic energy is wcou of u6:ez)m12 s.ybu;(tyoscy+ 9lost.

At a hydroelectric power plant, water is direc;hui79tb u3wcoffk1+z m/v9gw2h e.q ted 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 hf39f9tew;c7 wo+ /b kmuviq2 zhg.1udead stop, or so that the water rebounds?

A squash ball hits a wi4v;1b lc*zwcu ;mxs9 all 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 steel pls /tcpn o.ir69ate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momeirn/s.96topc ntum 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 backward when carrying a heavy load i hbiv0b i ,yvi--yzy5)n your arms?

Why is the CM of a 1-m lengthd7klni*mpm. t-tg 8 u7 of pipe at its mid-point, whereas this is not true for yil 7k 7mtm t8-gnup.d*our arm or leg?

Show on a diagram how your CM shifts -g0i ;gt1zn*qmd r3opwhen you change from a lying position to a o;0zggpdrt*- 3i1qm nsitting position.

If only an external force can change the momentum of the center of mass of an84knq+v mby8n object, howmv8k84bn+n qy can the internal force of an engine accelerate a car?

A rocket following a parabolic path through the - ;qid6luxwl/ ot; qc:air suddenly explodes into many pieces. What can you say aboutw uti-ld ;cq :6oqx/;l the motion of this system of pieces?

  What is the magnitude of y( 9.si c5yp(y agure 2yr8:pgthe momentum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N ac ny(6wf:o-a0 2safjew ts on a 65-kg skier for 20 s. What is the skier’s changf:ya0e(aw6j onf- 2 wse in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/(h ,9pk2j7c 7yj *us yii+lhols is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time beojy 2 (ui7cl9,lkp7s*j yhhi+tween 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 packalh0 1eu* tyuvw2747g xmal0 jlzm7w9zge out horizontally with a speed of 10 y0 llut7mewx4z19 gw*0z7ah27 lm juvm/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket :y9gm)3aockbv z8s/b, given that the propelling gases are expelled at a byv9)a:b ok3msczg/8rate 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 4eajyrxo/do02y a j/y947gkc at $4.1 \; m/s$ 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 carpo6vx.tob x6j0h q9amx /(n; g travels alone on alevel frictionless track with a constant spe6j;9ooh.b xqgxmn6pv0a/ x (ted of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at ub 7jrp52xow o3/msf;p *f.k d$15 \; m/s$ 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 whil5ulmn dtx2 u*ou:vv9;1 q+ xnp horizontally at speeds of 100km/h If the air strikes a person at txn n d 1:ou2t9muvl+ 5*qxul;vhe 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 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 spee qm:ss+f h/j5ad of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is q/5ah ms:jf+s the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s (d /twd /k uy9k;dnm)lhujb8gr 1r48memits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle81m luyru/trh8d nwdm;/k 4gd9b k(j) has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg bl9 6he ri) gl7.3bbmllgock of wood and emerges clea rlbim9l 3blhgeg)6 7.nly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket r4:9;ya n o6scl4p xowis 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 -n .0d9-gc-r *d9my)i cvk bh7zjvybewith a velocity of 115m/s To alter its course byr)zvy*yh.7 9k-jd- bndcegcm i-9 v0 b 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed o)o7 r:(9ulxoz7 ckjt4 fqen (cf 45m/s The golf club was in contact with thek)( j4(o o:c7c7xtqulzref n9 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 velocitaq85ys( f(cpmiqt0 5 /qwixj gk2);cr y of 8.5m/s and comes to rest in a time inter qy05i/) acc5q(qrgi sjpfk2xtw;m8 (val of 8.0 ms. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg .uh m;n/on,;w y gpty:and speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthiness of new automobile e sud;ofa 7rjxy*c+f6q:: ,enmodels. 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 ex *resy :;6ej n7fdxua,qcf: o+erted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in 0.7/tf hak):yfgin , 0p7q2p2pb u5 s by a head-on tackle by a tackler running due west. Ca gnft7pfk2,uqi:)hpy/0b2 p a lculate
(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 orhw e6sq oe6-wzpz8- 233np nun a tennis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical6e6p3 zop2nu rw 3h e8zwsn--q 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 75mqwcy iy 21;(w-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Ay2m;iqyww 1 (cssume 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 directio33 x8hd nqm+qmandn+p,aw q, .n) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ballwqam,.n3 3+nd p adn +,qhqm8x. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving ea)6t )8rsioksqro z j1,,s9foxst 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 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 pi 9kosorsj sfxz 8),r6) ,qot1uck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of0j (alo60. afitfk9sn equal mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and t.fijka( 906a0osftnl he 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 collid 2pmk d25f;(jlwxmyy 4es head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0kfyxml5 42(jd2mw p;y .090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m : focs*r*) bi+qj/.uuyr7xp mj*nld7 /s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a si/*u j:l.co*d+yr 7fr7upsj nx b)*qmpeed 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 cot6 8bo5.xg pc q bwhk96h+sd5xllide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A hb k8qts 5 6xhd+po .g596whxbcas a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a second b*ekhahx 2mv;8c 8sb(d all initially at rest. The second ball hhsbmac8*;ev(x8k d 2moves 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 slides down a frictionless incline as u*773qxbqn ue 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 c*qbu xqu77 n3em high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an v7vcg)(d) bewgf b,r: 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 mawe s(o7b8q6 pfximum height h of the pendulum equal to 2.6 cm. A second projecties (ow6bp8 f7qle causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg pendulh uxt v-s0fd:b5r ,;tjum hanging on a 2.8-0 ;vb:ut x-f5shr,djtm-long 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 enerd/j:*e* hr axrgy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, ird 9)4(f pzrk: xyvzmkg,+5 kbnitially at rest, into 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 ep+kk fzr)vm dy9xrkg(z 45:b, ach 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-kgh)jvgn,ont8 + 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 cotg ,j)hvn8+ nar, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a hc4*+f /sawkrfu1f1a. j9svnueight of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing s.f /s+c4vujk*ru11aa wff 9n90% of its energy?   

A measure of inelasticity in a head-on collision of two ozdlx:- dp d2q(3sz 0nrbjects is the coefficient of 2ds x0 ql3(z pnz-rd:drestitution, 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 g*;ojv6m 7is*ddg;p p times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in iiovpgmjd*; 6*pg sd; 7t 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 moviaww(3 , lus(dtng in the +x direction at 5.5m/s collides head-on with a 10.0( (3lwtdau,ws -kg object moving in the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second xakm: k;otv38rrbue;(e 0 hfk.:e ry/ nucleus, an electron, and a neutrino.h8; /rfyeb . aexeu3r;k 0m t:vkrk(o: The electron 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 mass 9mpl(r-9 e xqqie2* tyzfn+j6$m_\mathrm{A}=0.400$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 inelas grdl( iat3;omx5 -.artic collision between two objects of equal mass, each having initial speed the twoaotg-.m5a ril(r3dx ; move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move 2xs q)j, o5k.zqxuny2at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final directi2kqz., o nxq 5js2uyx)on 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 witnq ./ahf*:nd q/q8g xkh another atom at rest. After the impact, k.xnh *qa/ d: q8/qnfgthe neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collos j w;*vvx. p0hb+r2xision with another atom at rest. After the impact, the neon atom tv*+ x wvp2sh0b .x;rojravels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. Specif+th. rq9cprr0n ndv ,;y relative to the left-hand 1.00-kg mqrdvc9 ; rrpn,.h0t+nass.    m

  The distance between a carbow.mw/ v6oov 2in atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of the car. How f a;6s nqxegfn+vnt9;6ar 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 frontn na;s6+nxtgqv6ef; 9 ? 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 ferryboathtgj8(ydoyfc x;c8l6 (f5 h6d . If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded (y y8dh;6tx8fl o65jfgdch(c ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides ria ;x.cm1yh*yg8 2o o$l_0$,$2l_0$, 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 6hpgc du8g34wload of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length lu 6 c3p4gdwh8g. 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 )txu; 3 n(2;c n+rcnof4. ld1wqvqdcn of radius 2R has a circular hole of radius R cut out of it. The center of the smaller circle t(.ncd cu13 )l;rvxnc2d;n+w 4 f noqqis 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 same as those in Table 7–1, andwsmtu no 4*,k+ calculate the mass of one of youkosm+t,uw n *4r legs.    kg

  Determine the CM of an ou y9fc,a5sjuog6 3*0 ou b+ gay9p,fewltstretched 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 position .ib wvh 30qrw7t81aho27czhhof the CM of an arm bent at a right angle. Assume that the person ivq3 ocwr.hwh2b8 1 hh it07az7s 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs ja(6,o y uo,87sf9juh xibvqm0,;whxo d7b+oare hanging vertically, and his trunk and head are 6, oouo ;, smodqywj,ba7 +j8 x70hbvi9xu(fhhorizontal, calculate 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 f8),ggpd4 (sqhw6wiland 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 friclv yf(ce664 prtionless 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 ddedk 8pi/jrbx,4o*1 kg and a diameter 0.0800 m mounp4dj 8oexb*kd1d i,/rted 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 follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.2l aa71o8ro +sx vkuil2:bqn.p 7s g5w5.tozg00 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 ofk5 5 zllqs2iu1oagon:r 7tgax. 7ws+o82 .bvp the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 n2/-kt 6llx;t,u(fz 19l b-cvcxco bs(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 stationary with 8r0 c xmhfq29yrespect 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? What happens if the passenger h2 09m8yfqrcxstops?

  An 0.145-kg baseball pitched hot3e1qqzt ,h8ch w7drz.4mes v /lk30lrizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball durinh e4 hwzk.t8z3telc/sq3 q 7v,md10 lrg the contact.    $^{\circ} $

  A rocket of mass m traveling with spc/h 3nlb ff-c mbf3d:2tc.x6jfp2kn 8 eed $v_0$ 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 showhmdb 5.+ft e+an in Fig. 7–43. Relative dimensions are also shown. Should the player be worrie efdt5ba.mh+ +d 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) acquires a speed umm-nz2z/ /rh 9mn: wvof 2.5m/s by pushing off w:z9mr nvm-/2w/ hmnz uith his legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are inig.97 dxpxfv4:j y ei;q1j7 kuzpb-t* rtially at rest in outer space. They then push eachq: bv1tyg ujz74r -kp xj*;p dei7x.f9 other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a heah goi1 +dgmca 2j)*z.wd-on elastic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is t1oi dgm hz.2)a j*gcw+he mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expero4cr e70a) o :flf .j ede6uhp+3joz1kt witness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B o f3j0 pdc+4kooel1 oazfu7)e:.h 6 ejrf mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a ff2frw )y tq/4x m 8kbg)xjk56rlight 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 st4xrm qjgbkw/t52yxk6 8fr f)) ep 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/x7 l:7 cv3:txmt+y,wgs xpd a wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high willpcx:7swv/ yttga+xl3 :mxd , 7 the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wo ndwca.60 s3uhod 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, whn3d0u 6c. awshat was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in 0uspdtt2-n /t a rowboat of mass 80 kg. With the boat initially at rest, the two people,n0tu-t p 2s/td 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 e m z911c01wx pqznny8was 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 brophs )i2 h++uudken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their masses?uh ih2+ps) +du   

  The force on a bullet is given by the fo kutryvab5s3 9;* zfb6oo)q3drmula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses 88hd yccv5a*7d4k+izmt24y hs mc,ne $m_A$ = 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 in 4mbf*da3:0bm lyhn 4xto an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if ba bh mfyx03mn4l:*d4 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 abou ,pp;ub 2+lf mrl*2t 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 slidesz7n y )uczbh(+r+be2b 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), whp m+my 3gzs;1q,v)44gqiratj xb ,1bhat is the upper limit on mass m if it is to rebound from M,qbt ag;4i3 m1mx ,jsy41gv+ qph)bz,r slide up the 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 shows the plq2i p-1mxo 6dcanet Saturn moving in the nixp6cm-q2 d1 oegative 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