We claim that momentum is conserved, yet most moving objects eventually slc (dp4vbmx*v, ow down and stop.,m4(dcpb* vxv Explain.

When a person jumps from a tree to the ground, what happens tn0py87s l w,o)kow r-to the momentum of the pen0o k, y8olpt )rsww7-rson upon striking the ground?

When you release an inflated but u1l, 7m iygl:vlntied balloon, why does it fly across the roomill:1 v,lmg7y?

It is said that in ancient times a rich man with a bag of b-.okwpqb2)2fp hh jhf3 *a(ngold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could np j()fph w3a2-b *q.ofkbh2 hhe have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is es,i, xpq,qeyx 8sentially in a vacuy, xx,,qqiep8um?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller t y3j4kaw(s3+*iwyp:d f y/mm vhe force can be for the same momentum change, and hemj *k4isyw3 yv/dpy3 af+m(:wnce the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Todaic b 8nsnqq )7)ij;35wuais,*02bhzec i+tze y, though, cars are designed to have “crumplen2b n hzi ,e8+c70qt)scs* z) ;u b53qeaiwiji zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball furte)z3.ygc4 ivh 4 2axpgher than a ball tossed in the air by the batt.cxg) paheyv4 2 3i4gzer?

Is it possible for an object to receive a larger impulse from a sm 6rbmp skwc,.ffl:2g)all force than from a large force? Explai :cg2mrkb,p ffwl6 .s)n.

A light object and a heavy object have the same kinetic energy. Which has thp /aavak5 2wr;e greater pv a2 ra5wa/k;momentum? Explain.

Describe a collision in which all kinetic energo*jusa+b83- u-f,s el6ga ix py is lost.

At a hydroelectric power plant, water is directejq:/hfrtg/ge gz1o ,:)8rg;mi ka* mx d at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turb ,khrggigamm8 :* /g/)1 rzjeto:fxq;ine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a walvdpn* s b*zg8b 0h-r7ml 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 ontoq c,2 fr2fpplyq7 s55c a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that y sc7c5 2qlprqfp2 f,5falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavyj i/e2bnuz ;e (hz) mo(-d7r+t,lc16grzx znp load in your arms?

Why is the CM of a 1-m length+xz5p+movok 6 of pipe at its mid-point, whereas this is not true for your ooz+6x k5vm+p arm or leg?

Show on a diagram how your CM shifda-xyzdghtz+4-7.p r/ i,e ngts when you change from a lying position to a sitting positiondy7 hzigz-pa.r4g tx,edn+ / -.

If only an external fliz;l / a3*odborce can change the momentum of the center of mass of an obje l;o3az* id/blct, how can the internal force of an engine accelerate a car?

A rocket following a parabolic path ,0/rs 8 y)rj)mlsl c eq.nfv*ethrough the air suddenly explodes into many pieces. What can you say about the motion of this system of pieces?q0en),ms/l.*)8clyf e rrv js

  What is the magnitude of the momentum of 1hwlzh.hpa y9a7*x n; a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What 7j nlo06-t*hj*hvpt+u mh 3e0 bvwvy1 is the skier’s lj*6*wv07nh 1j 3mo-vh+htyp0 e utbvchange in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/kd*btr)tpj a+ 5x(bt5cadb-7d/ m* qgs is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact*r/5d7 * bb(kcaqdg+t tb5jxt)dm -ap time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package oc *6w0 dn)l1z3hep ncsut 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 wadnecz)hc s31w6l p *n0ter resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propellingm r0bu)7b xjisdt5 *a6 gases are expelled at 7d6b *us m0jab 5i)rtxa 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 aq1g1 ibxk,i51z op*uyt $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless trac 3k.0 l k+ kd8cg0wl1ohyms7qrk with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?k o7y q0cdlsk gm 1h+.wk083rl    m/s

  A 9300-kg boxcar travelingxndy .du2;*mru-yf c5 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, winds can whip horizontally at speeds of 100km/h If th3ruf+ cy86kbn7 pxs4he air strikes a person at the rate of 40kg/s per square meter and is brought cb 8xyhfknup4r6s+3 7to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed o*-0az3v crw.arp*5(zvv iuh bf .se0nf 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/mv nhescrwav0.fivapz u*5-30z*(rb .in 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 part2t e oz1h7zarc:uc) *yb4ypd*icle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 apz rbd:c24u*e hyto *)z1cy7u 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 5)q-scmcfhf3 j rh.7 apenetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how .c57m h3s qjh-fa) cfrfast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is travelikhsy,.gu2kn7 7c7 lm+jry 6th ng 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 wvzt2m 5e ;zv1g lq5z)zith a velocity of 115m/s To alt 5)1zqtezzz;5vm2 g vler its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed of 45m/s The golf )o2)m09ikmyda g 4znk clua)imn9 )0gmzd4yk2kob was in contact 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 axiovs, w1h 2:zn6+/jspo0u8 w i frkd1nd comes to rest in a time interval of 8.0 ms. (a) Whf2s osx8 v r6,01i: 1i/d zw+ophjwunkat 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 k83 43*kwvrcdfj+y bh0,/lpqw bik2f 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 nl)8vm xn-7.kb0rl+ub cdp ;thew automobile models. Cars are tested by smashing them into firnpk 8 0)dm.ullcbh7b;xv +t -xed, 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 the east and is stopped in rjz2ohpxnjse06 v;:0i/a( ht 0.75 s by a head-on tackle by a tackler running d;hjrap t 0z(vinsj:/x0h2 o6e ue 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 (madqkz9 hog24 r:wl3 j9gss 0.060 kg) points in the +x direction and is given by the graph of Fi2 3 jrhdl:wkq 9g4g9zog. 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 wi)zd ancr6 ua1o/ sl(fc6oqs3vj gp3)+ thout 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). Assume the br /6(a+pu3s f3l )coqjvocdzgrs1na6)eaking 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 coll rexrj,46zlj2ides 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,lj2xrjr ,46ez and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a c(psg 5.4mt,avr :wrjhead-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 represt.:jscag(v4p5 m rw,r ent 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 head-on colep,4rqwmmap me:nv2 4.+ hg(ulision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/e ra2ev+ :w,44 mup hp.qnmg(ms 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 cq/s .yt y qql;.g(s+t1nvfo0j ollides head-on with a 0.090-kg ball initially moving atts+; qon v0 ..qgs(/1yjq lyfway 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 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/s collidh,l-9he e dgz/es head-on and elastically with another ball initially at rest. Afterward thegdl-/he h9,z e 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 amusementv9 g3,svsv f5y1q dn7v park ride collide elastically as one approaches the other directly from the rear (Fig. 7–34) vvs3yn17v,s9v 5 qdfg. Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a seconm+es :2hupq)md ball initially at rest. The second ball moves off with half the originaesm ) m+u2ph:ql 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 shown (aci8.yf: 09e edh+eja j1blhin Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both .yji1: ea09jfeh 8e+(abclh dleave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an jr848 56d eb ;armgxckd6lh5e 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 expd+c u-bw1(ns-xo,l lbk)mo ;aeriment, projectile 1 results in a maximum height h of the pendulum equalw( omd + a-co)b;bn,x u1klls- 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 buries itself in a 3.6-kg pendulum hangin;rc*w0b2r0tadnnv s ;g 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.vert* ;ab c0r tw;2vsndn0rical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic ;bbe3x7c dvu/ 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 object, initially at reyg4(iobn ru75 l*v q(est, 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 he(u5nobr yeiqv(*l g47avier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear q, me5f;b )rzfend 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 tire qzf) ;,fbr5mes 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 frgx a6 vz* err9piht84.om a height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebouneg *ivr9xa68zr4p.h t ds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the coef 0( pn+ci sbk-(tnm.ad;vpm1u ficient of restitu(ud ; .cvpskmp+n (1nbt0 ima-tion, 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 into2k l t:ex48hlm two pieces, one with three times the mass of the other. A depression is made in both fae: t m4lx28khlces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction atg-s1xb)7tz k h 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/1bzgh- stx) k7s 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 nucleus, an electron, and a cj10*k0iyawm6vedq * neutrino. The electron0*yj1dakme v6*qwc i0 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 mas/aag18op h 8nts $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects ogkd .esqozcw45.m*:+1 qz ptof equal mass, each having initial speed p*c:z..qq5d z+4ko egtwosm 1 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 the origindnuab;r c3oiy20* p ap1c m5u- 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 Aftc pcu53u -ibyaon1amprd 0;2*er 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 a perfectly elag xtr:gz5*m)nm1) dg. j dkh,ustic collision with another atom at rest. After the impact, the neon atom travels away at ux g),gmrt5 ):dhmjzd1 .n* kga 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision with another a*ly)9)mag c kttom at rest. After the impact, t gkm)a) 9t*lcyhe 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 shown in Figp5 ikp*a5i6 ku, *nzku. 7–38. Specify relative to the u n ,a6pp uizkki5*5k*left-hand 1.00-kg mass.    m

  The distance between a carbon atlzf;h dwk f2*7sc ,i9uom ($m_{\mathrm{C}}=12\mathrm{u}$) 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 to i kc 33+w)h8;7u 5jidzdw7s6beibf tnl u61the front of the car. How far from the front of the car will the CM be when two people sit io3di;tt jb6w+dhu es 51fcn7b k6)i8 zuli37wn 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 hp3)ql,ojn2u(:sd .8wqi cbg18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM oq.lc 82:q 3d,)ugnh(ij sob pwf the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides mg-do4vls f )ab4n+4l $l_0$,$2l_0$, 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 1h)xm-5a6n w8 riwgo es5 v0hfidentical cases of tomato paste (see Fig. 7–40), eacfv )o h -we50h6x18arwmsgin5h of which 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 plate of radius 2R has a circulao;kt miq20 54:e(ckpi zsvgpkllq+ + ,iqn,d1r 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 circle, Fig. 7–41. What is the position of t ko il ( lm0esgq+2pk pq4;,51,t:ncqki+dvizhe center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportionsfd;c: k fh tzs2oas4+b3ydr s+7ym86t are the same as those in Table 7–1, and calculate the mass of osyf2skdy c6tdhf7 4 3t:mszo rb+a+8;ne of your legs.    kg

  Determine the CM of an outstretched arm using Taf7h6ggovr53q dg*xpih/-n0jble 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position oiz98njjab vkoos6 5* +9r sbg+f the CM of an arm bent at a right angle. Assume that the 69ks o*obj9 z+r5j+sbn8iv ga person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a posit7 dljzdv 51tj. i5mqc. ucd:p6ion such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below th jqudtl . mvd6.7zdj5c:1cip 5e torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth0v1zk sd *:vn oo3ebh0 and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-xrp1 d6gvdlf6 8ba3l*h.84gr roe/ml kg man stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diame * (e *d k2mzl9gvsk+v xqtz:i/o/gcv9ter 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 tv*/* 9i9 2 sotlk vgz/ :(cg+xzmevdqkhis 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.b t k 8zi )gj39i(v2cwkr8t3st00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 k8 )rzc vtswtkg8ib9t 323 (ijkg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7– f8,lf;l -lziw29), $m_{II}$=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 ma n-kkk)i wlys6o1) tk6ss M, are in the air and stationary with respect to the ground. A passenger, of mass m, then cli)6 ytklso kk)6kw-1 nimbs 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 stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is popped strai hv50 txqbb9;zght up to a heizq9tb;vxb 5h0ght of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travei:lh2lb i eyrz6tevm -mr: sk9*p7: q*ling 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 shw/)nn9-;d q+ um ghwayown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which nd whga +q w)9uy-;nm/the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (i/d lbbs, 5b my,za7rqivqj ;d0c u/pdck 82,b4ncluding space suit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-kg spac 0b/zrbbv7cy2sdd 4 ,bp; m 5l,c,qikd8qau /je 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 i.5 c0vme)m(q4r bu dgqnitially at rest in outer space. They then push each other apart. How far apart ar 4c qqdge.r5mm (vb0)ue they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a sdtqtq5 :ix;8 recond ball (at rest) and rebounds in the opposi:qdr58;q txtite direction with a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving an axr ;f() :4uzlq4 gfkp:smvc4 sutomobile 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 coefsqpls4: )4uz(xvc rff:kg4m ;ficient 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 offt30sfbbrc :,/a(smw e the top of a flight of concrete steps of total vertical height :a/f emb3t(,0wbcs rs4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions 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 int; dxf236i-jv,omq ke54xdedfo 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 ,;ee4xj3v6dqx-m ff25 kdid orise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedkl,g n+p,im 1wded 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 agki +ml,w1np,nd the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and t0(e3bhvq b4mlhe 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 m apart from e0(l4vbhm 3bqeach 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 apl0s+o/hw chd. 0k v9lbout $ 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 brok-z,h/ m(hg xc;p6dfoden apart into two fragments by an explosion. One fragment acquires twice the kinegzd/ho-xd ,;f(h6p mc tic energy of the other. What is the ratio of their masses?   

  The force on a bullet iskwb-),1(1 m(xmke kq imiir2t given by the formula 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 :mp go6b d;:2w91 -qpnfm1)b+mneh pcq8 bzal $m_A$ = 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 alpegb 8myi ;b):cha particle and a smaller nucleus. What will be the speed of this recoiling nucleus ifby)g :ibec ;m8 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 targ,f;,s eqfa6ybu s6px6et) is 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 slides dowwp 3mnk(jel g2y9a*t+ j 6/dlnn 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 i.6d zde r5dc)ns the upper limit on mass m if it is to rebound from M, slide up the incline, stop, sli5drdcz6d. e)nde 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–i zg9t68rm qx;47 shows the planet Saturn moving in the x;8gmrqiz 6t9negative 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