We claim that momentum is consdv 8 ox8:+cguperved, yet most moving objects eventually slow down and stop. Expla8+vgo:d8 p cxuin.

When a person jumps from a tree to the ground, what happens to twmj 3u 20gqh)che momentum of the person upon strimu3j g0wc)qh2king the ground?

When you release an inflated 02 xrxc fnbl*q yd1,5fbut untied balloon, why does it fly across the room?nb5 10 fq cydf2l*r,xx

It is said that in ancienty f9wka qx 77wa)hg87m times 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 done to savwa78m 9axg7)qkhwf 7 ye himself had he not been so miserly?

How can a rocket chan 8dod 0w0jd et:tfxie1/t )7kuge direction when it is far out in space and is essentially ieutdjtfe t 0w)id1x70dk/: o 8n a vacuum?

According to Eq. 7–5, the longer the impact time of an 35;wrs 3 dcwtgif n,v2impulse, the smaller the force can be for the same momentum change, and hence the s,sf2n i3g5;vr wdwct3 maller 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 possibao as2a8 /dd-fs22q1dz zgga, le to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon 8zq d 2 2d2,fgaada s-gas/zo1impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball qyltz* 3ms )t7utf41wfurther than a ball tossed in the air by the batter?yuz 3t*wl tsmqtf4 7)1

Is it possible for an object to receive a larger - ln(m9a+jssm 0 eq8w7tsavz:c)uc)eimpulse from a small force than from a laruwa8e a7v- c9n(ezljs:)ss +c) qm0m tge force? Explain.

A light object and a heavf y aq7b3t:,se33gbn by object have the same kinetic energy. Which has the greater momentum? Expl7abeg,bqntf bs 3 3y:3ain.

Describe a collision in which al x,tvfj(8 bman5-s-nll kinetic energy is lost.

At a hydroelectric power plant,d+u b2est u69bj;0( p /s0xjv+grias u water is directed at high speed against turbine blades on an axle that turns an electric generator. Fu 2+ sbgsxj/ apvu+( 69btr;dsuj00ieor maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wh0:qqvnt2,6;hs v v bmall at a 45 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h ontm )n jxyp;b 05kptls94du5e( co 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 falls and dj mupb55e) pxynl4sc t90k(;sticks to the steel plate.

Why do you tend to lel .pxzy2x61 ehan backward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, wm ygkxidk56 ;b;6 rhpail2p68hereas this is not true for your arm axd6kyg2;k bp;p ir mlh6856i or leg?

Show on a diagram how your CMc40s angccy*yg;d p(e,1gm 0 :wc(gcl shifts when you change from a lying position to a sitting positlgpnc *;0gw yyg c:(c(,ec c1sg d0ma4ion.

If only an external force ca1pd 9 c*/zhxxjn change the momentum of the center of mass of an object, how can the internal force of an enc /1*xd9phj xzgine accelerate a car?

A rocket following a parabotg ,mh1 q480zwwz8cx+9-(ny bpthl zclic path through the air suddenly explodes into many pi-b,y8m c+(1tz 0phqtln z 4wh x8czw9geces. What can you say about the motion of this system of pieces?

  What is the magnitude of the momentukbptl : vunf (kw*f:23m of a 28-g sparrow flying with a speed of 8.4 m/s :p( 3tv*wu lfkfbnk :2   $kg\;m/s$

  A constant friction force of 25 N acts on 7;ybj1wsdsy 4 pp ;s)ea 65-kg skier for 20 s. What is the skier’s change in velociyppsesy;7 1j w4;)dsb ty?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line driv v +lv+em 8sqzp)6er)ke straight back toward the pitcher at 52m/s If the contact time between bat lee6 r)k qpmv+s)z+8v and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontallypi/s6 bi,v/c o with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assumivbp/si6,i o/cng it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that thwu5le,da vv9wf, ab 2bz50q0we propelling gases are expelled at a rate of 1500kg/s withae ,9,w5 wbul2 db0avfw0qzv 5 a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an ap/ c wvs1olcd*ies7x. *parent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in tdo7s* e1c.sx/i c*lwvhe same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car traln* va6ia ex5+ z(d(dzvels alone on alevel frictionless track with a constant speed of 18midza(ve*z (65xa+n dl/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 15m/s strikes a second boxcar at rest. w0kc/7u4 gkgm The two stick together and move off with a speed of 6m/s What is the mass of the se mwuk 7g/0ckg4cond car?    m/s

  During a Chicago storm, winds can whip horizontally at s)ek0 rx0+odn qdd ky97peeds of 100km/h If the air strikes a person at the rate of 40kg/s per squyexd 70kq)ndk0dr 9o+ are 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 constanti gr4lb **x v-5qj9vgp speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at arv5b4gx j-l*qgi*9vp rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in the a)o3bl(x kz za.bu ):p8)gbrbdirection 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 the alphap(bbbbx)z:k8 . oar )z g3aul) particle have when it is emitted?    m/s

  A 23-g bullet traveling 2vlz 7;m tw21c p+-6 hs)pdkf 0nnpjl4u30m/s penetrates 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 fmv470k+p-uh)2p jwf;ls1pt ndl zcn6ast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket*1mv 9gox+50rn6w iwnrr tf:z is traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 0w.x ;kty:miv tu0.xq kg is traveling in outer space with a velocity of 115m/s To alter vkmqx: .i 0u.t;yt0xwits 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 speeh7v(;aqbu- r ud of 45m/s The golf club b;u7rqu(ha v- 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 and comes to sz;rcl5ox0n, rest in a time interval of 8.0 ms.znc0s5r; x,lo (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 1qm1sx6aduq.zb p )y2 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 charddpns.qi2 g2am;ln; 1ua/9 v9c a y*bfge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the t2. /gpil;u2nm*n1dc a9d 9b yfvs;qa aime 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 0.75 s by akarfijf.j7g2 6tc:n - head-on tackle by a tackler running due west. Calcul6 tcf7jfk-ai:rn 2.jgate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg)1wvzh-*b 83wyhyhz6a -,tuj e points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical m hyw1-36*,w zzuybvt-ahj he8 ethods 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 n 6xfgt u-rz4)a 75-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the u-xtr fgzn)46person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of collides ghsfeax.g.0)h( ,wdj head-on with a 0.220-kg be.., jwaghhg0x)d(sf all 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 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/5go+qtol,t;hi 7 a r.rs 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 repre5 ;.got+qr7 hiaolt r,sent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of58 w,+mz65gmejli fh gezy08 j equal mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 26hywgj8jlmg8i 5,z 5 zem0f+ e.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/ k-syw(7n.meb 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, ww-.km7 eysb( nhat 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 collibb99v3k- k97j;mryi4wx 0rspln xt(pdes head-on and elastically with anot99w (bm-3s4jt xkb9 rpri;vknp 0xly 7her 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 amusement park ride collide elas-1l/7 jdx mz1mra jzo8tically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is mor1a 8lo/j j1z z-xdmm7ving 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 secom 8n.fm1;5/harlh ic wnd ball in/ra f mw8i5 n1hhlcm;.itially at rest. The second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a fricvso8re1 7ofagr;v 7v tnc+b2* tionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half ittbevo7 o rav2rg+ sc8 v17;*nfs 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 object.jpth 9iehl4 - 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 maxij)-4dg2e e1zbq)vewi dq0j8omum height h of the pej0dvo4 -ezw i2ed)qb8 qg1)j endulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg penduluskleuml2a(4(0n8 jst- or:r k m hanging on a 2.8-m-long string, wh4r a82-sut (n:mojsk(l kle0rich 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 enr/49se xnd jh lq:-t2uergy 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 rest, into two pieces, onp :j 66w9ubs; 7mnizyme of which has 1.5 times the mass of the other. If 7500 J were released in ths mp:7u6 wjmyzni9b;6e explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stop 2n/oesy(y ny7vfnl/5qw95g pi ;xc6xped 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, 6nyn/x9qly/i x2(c w 7 5sp;yevf5gno 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 rebounds to a heigh5kwk vc6,dal42/pgyo jyv-4 wt of 1.20 m. Approximatelw4dw/, yvk5y6lvk cao-24pj gy how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two obgti*/p7+dt r fcp*1lna 66+yj)z;n ett y1wy bjects is the coefficient of r6dctg*yw jzb7+)t6 elt1p /1fpy+*a ; i yrnntestitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the mass lw: i h*bzzx9bl6t)n4lb5x2s of the other. A depression is made in both faces of the cut, so that a llhzx5 wbz:xt4s l9bb*2 n) i6firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides huom7c a2x/ v7)fi he9read-on with a 10.0-kg object moving in the -x di2h veuor7c9mi7a) x/f rection 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 nucleus, an electron, and .b5 yd/8oegl fz:v9pga neutrino. The electron and neutrin p:vy8/lb 5 .9gzgdfeoo 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 mas5nlwu6g:p uxko k ;o((s $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equal mass, eaczp /i1 e8qq /;qnmec6:)wnmfh h having initial speedq w :np1/)ni 6zmfm8eqe/;qhc the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mai31.cvbfc pd3 lhg aml .l6h0 l2serhnx:3-r; ss move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–3 2rhmlg-1ebr3i.lfl6x.cdlhv n:aph;s 3 0c37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic col56y07m*:p sehwafv;ed j o7z flision with another atom at rest. After the impact, the neon atom traayd6o5e7h f sm:fv e;*wzj0p7vels 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 collision with another atom a-9 kiau/ )nsop/4 zewct rest. After the impact, the neon atom travels away at a 55.6ukwa/ n)o49cpizs/-e $^{\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 s qq1o,8l*sisri.(rnw0f znl; ev3 6kFig. 7–38. Specify relative to 1z,fniwrqri(lq o*skle8 .;ss03vn 6 the left-hand 1.00-kg mass.    m

  The distance between a car(gvd isut610 vbon 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 they7/3q )l(t1o7itvruxlg b4zk front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the ck1l(t4/u r gz7lqob73vtyxi ) ar, 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 ferrybo.jxzfphf( l9jss /t z89k 5dhli 7bv4 )t*q;quat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of tqsz87 j hu) kx4* ltdlt fj bp5;v(zishqf9.9/he loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides km cbo7-9nb 6hs )qfz;f6q-jx$l_0$,$2l_0$, 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 9mp 3)8bmxd3+y jxotsof tomato paste (see Fig. 7–40), each 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 mxod9t3p m xb3 j8y)s+it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radiu 4kg0)qjtzcg24 7y6e2aer c pfs 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the yc) 4f etpgjq2a r z0k2gec764center 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 yh+zcci/tyllyr c5x9ve(2a3 k6d4 3g calculate the mass of one of your legs. (/2ci34c yyz he+ r3xyvd9lt 6klcga 5   kg

  Determine the CM of an outstretched djrn)4c pc8rq.n*v,8e z s zi/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 of the CM of an arm bent at a righp lz keu.52p4c-n5klmt angle. Assume that the person isp-k 4p nllz5 uc.kme52 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in l6k5)gdg zayh: k+2-3. h4fin tajwhu a position such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Ta)-u gkhh6 j+hlf43a n2tzyak.g i:5dw ble 7–1.

The masses of the Earth an+h me;5:3lk1t8afu pjewntd8d 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 frictionlesd)vuy :n gc63vhh-,er s 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 lz*r 5tx: nwi9diameter 0.09 nxt*rlzw5i: 800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head ofr4- gw b7/vdd,f pag1z mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of maz7fv4-a /gp1 bwgdr ,dss 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7 ue47gmy1n4-k-usw,dh m za)8m3exh.k/ecb d–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, ocvzum0x 3 re dd 1;1cpn1:,przf mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed 1xvn 13mpzr:1p ;educ crzd,0measured 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 strb1*;wbtf rtbebz 0 -*saight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball durib0r* ez - s1*bbtbftw;ng the contact.    $^{\circ} $

  A rocket of mass m travel uwneu9vc5 g0*em*ac, ing with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown in Fig. 7–4h;-q r,c h8:0izzealz 3. Relative dimensions are also shown. Should the player be 0:cer;z-i8 ,a lzhqzh worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s bb 2 +a.nwjvr h:c1gza2y pushing off with his legs from an 1800-kg 1. na2hz:a b+cwjv2rg 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 initially bl9pb)pni0rv5 3p1t dat rest in outer space. They then push each other apart. How far apart are they wh trnpbl35p0d 1ibp9v)en the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (at(,4tzqry alss.-0b1a ny- qj k rest) and rebounds in the opposite direction with a s1sqt.n-jr baq-z l0skay (,4ypeed 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 awy:n4j ky25,in *3rv rt bc3jtn automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The :y*jr4j vn5yc3t r,n3kit2bw 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 flight of concrete steps of total wkrz- ;hd)k tt(ao 3-lvertical height 4.00 m. The ball hits four timt(ot3h lk;)ad kw- rz-es 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 into a 1.40-kg block oflp6) (j ofa*a7 w(itra 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 beco6 praw(aai )jfol 7t*(mes embedded in it?    m

  A 25-g bullet strikes and becomes embedded b5tia4cp , eob9 (c:kiin a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drivesobcab (ci9:5 tk e4pi, 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 thgu:z :l*a8z4j bo, gtse other of mass 60 kg, sit in a rowboat of mass 80 kg. uzo*tzg4j ,a:l b8sg :With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was about.ja6 :2 p-qrs(qrk rtv8oc wp, $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments by an explosion. he9tb ts:pjn,oy sb(jv .o7ph(4,c(s One fragment acq9ttp,h onyvopces7sb,h (:s jj(4b( .uires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bulleymtw4h- p:gk1p2y nj1)yp4 m rt is 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 as6.;y0i11czdyc(lc dgt tn w.e: )fp$m_A$ = 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 de )h5gigqg q-2pcays radioactively into an alpha particle and a smaller nucleus. Whhpgq-q 5gi)g2 at will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay ft4;sgi(2m : zgixgc 9 .1qhhmtarget) 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 down nz 4 ewcc3ue5.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 ibm8 w+f1rfwzk;wnc au.n -::ds the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide wifa:fn8b mwnc-:u ;r 1 kw.+zwdth M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational sli 6el 9rvp85f vde0.zpangshot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (wit0e f r.5eza96d8pv lpvh 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