We claim that momentum is conserved, yet most moy9ku+4b0 l1uh 2yz zqpving objects eventually slow down and stop. Explain.p9l+k y4hb1yu q0zz u2

When a person jumps from a tree to the ground, what happens to the9jz hcr69jhm + momentum of the person h hc96jzj9+rm upon striking the ground?

When you release an inflated but unp-feprpmstj/ c*q6 +ayy h;m.z1q d 568xz: mntied balloon, why does it fly across the roommyp+ nrh j:z- ; p.q16dpmca*st mz8 5f6x/eyq?

It is said that in ancient times a rich man with a bag of0*8 zeduct oh* gold coins froze to death while stranded on a frozen lake. 0*zte u8o*hdc 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 submnna e, 8 p,8zt2k5epace and is essentially e z2p bu8m,tank5ne8 ,in a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, thex rao2sh9a-t 7 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 inflaao7hst xa -29rte during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand colli)y4vrmvsm.3k4 l3vm uxcm;v /sions. Today, though, cars are designed to have “crumple zones” tha) xc/ rm s4 ;vm33l.4vmyuvmkvt collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further thanuuoh56kn9p+9) p-d ioa+j nhk-k vzb, a ball tossed in the air by the batk nk+b -uh+oip,59 n6od9uha -p jk)vzter?

Is it possible for an ob10 (/i;da :qqioz6 kcbys7j1ub wxa2xject to receive a larger impulse from a small force than from a large q(xq ii abc1d;kuw6 y2:bzj0xs 17a/oforce? Explain.

A light object and a heavy objeu qsjt*x ;55rzu)qv1e ct have the same kinetic energy. Which has the greater momentum? Ex 5j1u;5qvs*)xzqret uplain.

Describe a collision in which all kinetic energy is l6 rwr,67yxt cx bmp0c.ost.

At a hydroelectric power plant, water is directed at high speed -o495l t c3b3lgopjnt against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed pl g-5cb9 3jol4t o3ntso that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall agfiotqh78wct9u62 ymk;6 7l5c:ph but 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 fr(y bt.w bd2j6ir jjmcfgc .5jnr,1l3 ,om a height h onto a hard steel plate (fixed to the Earth), from which it reb ri,j1jnj b wcbg,23lr.y.j(ct m5fd 6ounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load fmq jyx.s;b- e g sg2n ,,o)kb:h. *h9znszn2oin your arms?

Why is the CM of a 1-m leng /a/pw8wbczn. th of pipe at its mid-point, whereas this is not true for z/w 8w.bp /canyour arm or leg?

Show on a diagram how your CM w) zrc4msg.6 oshifts when you change from a lying position to a sitting position. .wg6zrmco s4)

If only an external force can cah.8eukj l81tn3j4 ,rur2uq thange the momentum of the center of mass of an object, how can the internal force ofrhjr,u8l.ak u1n8tqet 2u43j an engine accelerate a car?

A rocket following a parabolic path throb(ob zejtk8* ;ugh the air suddenly explodes into many pieces. What can you say about the moz8e ;j (ob*bkttion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flyine9-b b. 4ng wi;+bnru 4:yierhg with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg zzx5p 3mc p o3ay(/ .86onfxncskier for 20 s. What is the skier’s change in velocity?35c.yx p o(/z 6no83pznxcmfa    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal lin5c )g jhv/rwg5e drive straight back toward the pit) hc/rw55gvjg cher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throwujl 4+jt+39c*5 kepxmemmgb5s a 6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistepb kj5e+ 4*mlcmjm 39ux5 g+tance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases are z0t. .ijc8gtnm nm+ w.expelled at a zwgtnjti0m.+..8nm c 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 at0d v+hufcv*i2 $4.1 \; m/s$ 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 trf h4xuug,l4rzbp 402n v7s 0fiavels alone on alevel frictionless track with a constant speed of 18ixf v2 z 4uu bplf74nsg04h,0rm/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 travelam z i2 )o(f1ypub1sflrx8 ;-zing at $15 \; m/s$ 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, win5 aus)l32liewi- gf 6zds can whip horizontally at 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 fo il e)6-5a3 gufli2zswrce 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 wscv 56bk,j)x5cq0w:uv4 ia cconstant speed of 8.6m/s on a level track. Snow begins to fall vertically and5qvxk :u iscvw05,abc )cw 4j6 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 my(xj/v jc/y k(oving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does jvyyx(k/j /(c the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-anihmzd24 u9- kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface2nu 9dma4i-hz when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is travexg8o/*f 0ggv xbmy 4g;ling 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 spacx - c:q.7s/j-t4 ghu(u4pyd3woxrea tdkzt-(e with a velocity of 115m/s To alter its course by 35.0 t 3-7(r-upotds4td/uqxhax-(zc kw4 j e .g:y $^{\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 te4g q xx;f*u4/,+ dinu pxxkly-e at a speed of 45m/s The golf club was in contanu4pk;gyldx+-q uxi x f,*x/ 4ct 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 reo-yjif vu6;2mst in a time interval of 8.0 myfiv;6oj u-2ms. (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 and speed v=25m/s strikes a d9x+ .5gep;9ey -lj prx wt*p*n okmzo7wk8g)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 thel: ,+p l zgozr0mafx36 crashworthiness of new automobile models. Cars are tested by smashirxpmzfl+603a l,zo :g ng them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car 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 theo/r yyzrd+dy /f9 x-sz m8gq57 east and is stopped in 0.75 s by a head7/ d-8y5+qgzx o rz9y/dsmr yf-on tackle 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 tennis ball (mass 0xqkg d6b+b7l ,.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a functib +xgd6lq,k 7bon 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 juwxg5 ypg m*/qn 7gm;(mmp 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, 5nm7;wyg / gm pq(*mgxin 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 speed of c 9v:ce(xzs2p4b (dktjollides head-on with a 0.220-kg ball at rest. If the collz(sjkxdvb2 9t(:ce4 pision 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 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 of2 j51nbpm1i y.bh:ocj 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision,o y :j.m2 nbb1c1hipj5 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 undev t6s y 82i)+fmibgz oaz.7li6rgo a perfectly elastic head-on collision. If onva )28+ifm6 7blitis6z.z ogy e ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m 0u7x8 auhxh8mir6vzi++i5ji /s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg 6x0j7ai 8zm8u hiiuvx+i r5+hball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 q a6xeyd 2w5l3kg that is moving with a speed of 8.5m/s collides head-on and elastically with an d5a eyql623wxother 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 amusemea6x)xb .owahx 94(cq5e4i c wynt park ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A 9ie4 wochq(wbx y)6acax4.x5has 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 seuah ighbrz - p -ieuj2:ygt*(+ 4g/gu*cond ball initially at rest. The second ball moves off with half the original speeagh(uu y pbr-*g -+i*:2 4ethgjuzg/ id 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 downmpp95ya.xz ;dt 05 kdu a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom ty50d.5 dkpm u p;9xazthat is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an obja (5f)ed8 rr.mc;za tkect 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 experimenmk- j 4x n)aenz:2v,zet, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectilevex:)njzm e 4nz-2ka , 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 pendulusnzf+0h(- wo:n au vw4m hanging 4wazuonvwh -:s0+f n(on a 2.8-m-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 energy los1bt gu qxemfo,9)1)*d vg1t npt, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially 8xok,bi+z1 m d*h p,dpat 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 each piece acquire? (Let A represent the heavier particle, an pbmhip*,d d,z+x8o 1kd B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stoph xvx /4wmwfmov 5ewp1(/g+/eped 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 c/eve/ o+/x 45(w 1wmgwhxpfmv oefficient 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) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rfm h0qb3(x+ :fau 4bzkyyfm:1ebounds to a height of 1.20 m. Approximately how many reboun1u xyh z3m:mbk04q: yff(fab +ds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of/rd96 mzr .;ms o29usclhuum2xos 84q two objects is the coefficient of restitution, e,u9d8mrm9q l./6 22hcuusmso ;rxs 4oz 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, onl) (,c a iuh 4nzayik,p)/cr+o3hjia/e with three times the mass of the other. A depression is made in both faces of the cut, so that a firecrackel,4ihji )+o npr)aa/(h uc y/ci3az,kr 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/(lv-zlx9 kp7 7wkedp/5y z oj collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the finaledl/z/lkx97z (p o-j5k v7wpy 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 9 cx fb rm/b-n(lh5;yasrunw- e 3a86psecond nucleus, an electron, and a neutrino. The electron and neutrino are emittu58f- w/nrs r;xhy l(cpaben 93m-a6bed 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 mass4k oh ur82nhy7 $m_\mathrm{A}=0.400$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 ob5q2dt: hzy+ y s9 6lffvz4*lkyjects of equal mass, each having initial speed y26zyqff+ yk dlz*:9vs 5tl 4h the 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 they b,+7c mj)5qm 2svpql origin of an xy coordinate system. Ball A is moving upward along thm27 by,s lcvq+p5)qjm e y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? 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 aot70y:x f : ra:ni3byq perfectly elastic collision with another atom at rest. After the impact, the neon ry:y 3bfxt0:q a7:ionatom 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 coll *1*:tuj.mszwdf.l df ision with another atom at rest. A.: z*fl.tjd d*1ufwm sfter the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system show.tyxgps-(c l4ty rb:wx ne;2/j ;(jcvn in Fig. 7–38. Specify relative to the left-hand 1.00-kgb;(jpcyng/es xrvct. : -jwt4l 2(x;y mass.    m

  The distance betweenp0t kv42)1h7h dv rtta a carbon 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 1050-1omymk kl2;o(lj t4a ax*j2z3g+d h5k kg car is 2.50 m behind the front of the car. How far from the front of+21jo;5a4z2hxg kk*jl(3aolmy dk t m the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each 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 ferrf (q(jmqya:h -bqc2sqi) g5) xp0e.ozyboat. If three cars, each of massep(s2ao0mxzb gyqqqh.5j) ):(f-qi c 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*cl d2.o+9 arg /hrwof.n;qa 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 load of identical cases of to/gqlr(k v5d37,g8ng3bxy urtmato paste (see Fig. 7–40), each of wh,v8nxlykr3/drg 5b7(3ut q ggich is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular p5t;kub;o)e jb8bd xs9 q+ w;xplate of radius 2R has a circular hole of radius R cut out of it. The center of the smaller circlej9kpdebt )8+qbb5uxxw s;; ;o 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 same as those in Table 7–1, and calculatf b*njjo l)fe-ah02e8 e the mass of one ofel0j2)8jenof -a h*bf your legs.    kg

  Determine the CM of an outstretched arm using Table 7 gn+ wqktf8 k30//fjaf–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 gj*r f8d*xdcqr*1,w s at a right angle. Assume that the person is 15*j1dgcsxrr* ,w d*qf85 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such tbat6 3mv o3wu*hat his arms and legs are hanging vertically, and his trunw 3 tmv6a*obu3k and head are horizontal, 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 and Moon af, 1tgtfixvx m(.0( um1r ,oiqre $5.98\times10^{24}$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 frictionless ic tf*f(yte.u, h ax;9jxe.
(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 cylindric n uo0tnt)k3u4:4mh qh1 5rmdcal head of mass 2.00 kg and a diameter 0.0800 m mounted4 5 0rm3dtkhu1qum : n4t)conh 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(r0z jo3ck o2s nbii().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 io si k0()o3n2z jrc(bin 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 Example 7–1k+fe4v it,i2d 4 (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 stati.m /kbt gcu-u 5y3q(fkonary with respect to the ground. A passenger, of mass m, then climbs o(bkf5- q gmy./3tckuu ut 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 stops?

  An 0.145-kg baseball pitched horizont l:ghcpj5 -fy;ally 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 during the pgf5cj;lyh - :contact.    $^{\circ} $

  A rocket of mass m traveling w)x:d :+ hjqgjgith 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 shein.zz 4r-a- utf(akix5w 61efw1d4qown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this bein wzkq (e f-15fxur4e4iwa-zn ad1.it 6g a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (i3ggx+d00 aql including space suit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800+qdg0i g 03axl-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 ah7 ymghjv,.8/m qklv2nd the other 80 kg, are initially at rest in outer space. They then puymvhl 2vh.qjk ,7g 8m/sh each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (atg-ypmvv( oy5x( k2f7i8jy7p e rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the secvj( ygpiy yp8(5e7mofxv 7k- 2ond ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case i l-wmdg6d6j)u nvolving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while 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-mph66ldg mw) ud-j (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight ov4 9qd 06prnq7 u qnwayc1/dg(f concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal pap/v1rndq64nuw09(7qqc d yagrt 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 into0mg,ifx ;gav: a 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet b:fa , gmxgi0v;ecomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood placed *o r :hyt8jg8mon 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 oh8j:gt *omy r8f 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of masc;yw0 vq60aj es 75 kg and the other of mass 60 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 me0vja6q ; 0wyc 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 was aboutqqqd i7iot**, $ 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 ard5o,ww 4h2 yqpart into two fragments by an explosion. One fragment acquires twi,qdo2hr4 ww5 yce the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F =+e,,wugd0pih 1 +zdlh zctpc5+ cy0g ) 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 massesqqp/w yvxkb3z(d-n 91 $m_A$ = 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 into an alpha particle and-m j.c:opqeu/ a smaller nucleus. What will be tpcem/ :.- jquohe speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angle of 30 zk1cki 05(;la fk-tpx $^{\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 slide 4. qe svahissh56g tt5)f/w)d v2qd-ns down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on8.kqm qo ch:h..e,2uf1rn fmj mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, f 8h.mc.,.jfm1q2e:o uk nqr hand 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 jx p( 3zrdf,/ai4pp8t moving in the negative x direction at its orbitappt4fzp /(3xr 8jid ,al 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