We claim that momentum is conserved, yet most moving objects eventuall qkss,k3fl/j7y slow down fk 7lks/qj3,s and stop. Explain.

When a person jumps from a tree to the ground, what happens to the momentum/6vec it4nv. ny-v 57y39lbvo-m nl gp of the person upon sb. n-vlv/nn4 tm3-g9ci7pe yyl 5ovv6 triking the ground?

When you release an inflated but untied ballo ,s +obuw nsxqd**hhpfu8.) +xon, why does it fly across the room?)*s ,.+o hf *sbqxpuw8+nhuxd

It is said that in ancient times a rich man with a bag of gol(v bn)an9w7 -bz1yi tu*f1 mrcd coins froze to deathyna-t i1n)m vzr 1wc b(9u*fb7 while stranded on a frozen lake. 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 changel)p kcch2boc f. zl)+* direction when it is far out in space and is essentially inf2b)k. poc) lcch +zl* a vacuum?

According to Eq. 7–5, the longer the impact time o. )sng5wj5mt), h ue/ 7*awu sxmltz+if an impulse, the smaller the force can be for the sam+njw) 5tu )/m *hztlx5s s,gu.wm iae7e 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 inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisiony +cr3ep8e;lv,rl0hz)q*1zkbumc) vs. Today, though, p c8),3zc;v ) +rlu*v0elyhezmbq1rk cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitc l1d dtkr165 ;fxseq( k6f,.aq4jqqndhed baseball further than a ball tossed in the air by the bats1 qddt4 (6f1d5le.;krqqx,jqan6fkter?

Is it possible for an object to receive a larger impulse fc0 oi:en3ml1 jrom a small force than from a large force? Expl1:ecn3j0mil o ain.

A light object and a heavy object have the same kga le9omvk 22cp5 :9srinetic energy. Which has the greater momentum? Explain5kr9 m2cp og2 sa:ve9l.

Describe a collision in whx,ek.q1 2ioawph 6*lg/k, 5) gzvozsoich all kinetic energy is lost.

At a hydroelectric power plant, wary,0ey09l)j xn ster. ter is directed at high speed against turbine blades on an axle thatersj)ln.exy ,9ry00 t turns an electric generator. For 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 wall uoqbt+00 hvvpb00r*v5j8d9+f tuqqjat 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 ontivqgwnlh+9,r s zc;-/ o a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is thes,c in hqr9v;gz -/l+w 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 in you eajcy339rtfl 3)0ifh r arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereae +ej wk27k3tas this is not true for your a72wk a+j3 eektrm or leg?

Show on a diagram how your CM shifts wo)vr c 2pl/wp7hen you change from a lying position to a sitting positionplop crvw/)7 2.

If only an external force can change th8 hr m1b1)kh b)mc6bhhd ),rcce momentum of the center of mass of an object, how can the internal fcm1d rr)bk8b),hbch h1c)6mh orce of an engine accelerate a car?

A rocket following a parabolic path throughv /gm6moa56 vj,zk: nl the air suddenly explodes into many pieces. What can you say about the motion of this s m5n/l v,:j g6mo6avkzystem of pieces?

  What is the magnitude of the momnrg qov+l /u t2tds42.entum of 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 is toe w3n ;u*2h x5evtr)ehe skier’s change in velocity?xuvr* ;32)entheow 5e    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line d-z x7u5eq* ojp+/d .ry p:bmkcrive straight back toward the pitcher at 52mz x.pkpj:cbey om/-q d 5*u+7r/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 throws a 6.40-kg package out horizonmx mc96z4:bhs-ml+n r,)qpf utally 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 resistanc4bsunzm pq-x) 6fm+ h:,mclr9 e. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gaseblp;jm c 4*sc o.jc,(oz.ik*es are expell jl4 z .,*c bckopm(c;jo.*sieed at a 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 er1j: bts5n8 eat $4.1 \; m/s$ 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 8-0 rguor,nnn travels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. Wha rrg ,o0nu8nn-t will be the car’s new speed?    m/s

  A 9300-kg boxcar travelinev4:nmvet og-z)y4 6g e-zd;z qw9 )skg 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 whihvm*zf t*0 l ,2ffpe)qedrdlmh-3i w i7d49 s2p horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square ft s- * 2)mdpl4e2dr 0l,q3mhifw 9dvihf z*7emeter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of 8.6m/s on a pl:ye.yo7g-l 6o gks(level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what76l(oyog-sg.lp y e:k is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 4q5oo .f1we7.bkytb/ ya+ sol)20m/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,ly7b)by5aefswok qo/.t. o +1 what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg blqsy1v9ql/iv6q zq3 q 0ock of wood and emerges cleanly at 170s qy9 qq6v0viq31zq/lm/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling 1/3dq eqjb)b vym(ef/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 sp )zc4ftkp9r ir, ;cds+ace with a velocity of 115m/s To alter iicrz tk),dr9fc+ 4 ;spts 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 ;we4) hgaajob )(jd l,is hit off the tee at a speed of 45m/s The golf club w)e,ajg 4 l(hb;ja o)dwas 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:jr i 8jfs+eum8xx2w. comes to rest in a time interval of 8.0 ms. (a) What is the irewmxx2u f:j8j .8 si+mpulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass2gpp.ni.m j gu:ht0 7r78l cqz m=0.06kg and speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthiness of new automobilvyp-c42*y jhjf 4dm w:e models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average f:wy4h*v2 -pcyd4m jfj orce 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 tgcy5f/)v /.pcrw *es stopped in 0.75 s by a head-on tackle by a tackler c s/r5.* fy/ecgv) pwtrunning due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points in7nhs9q;m q0 c+lpaqg46fzv : x the +x direction and is given by the grapm4 f0s9+hvxp;q:qgn c zl6aq7h of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-9kv 3hpz-/62uacl)w42b a vojo 5yvaw kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from 5692kzujc42b wvho lwy/ a-v3o)v paathe 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) wppkj y6u 2a4mr .(y,u8xtxb +pith a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg bt y2bx6+j4(u k mxp,.ypu8arpall. $v'_A$    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 3mibx;d x296ue lzdu*2ek) ;mzs/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each obkbeimuu z* x6s) e2ddlz ;x9;2ject after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastic head-on collisie6)a /:r;m a8e wwcmmxon. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their e mw/mra68 ;maxew)c:speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collidexm 3p.t7kq yu2s 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 l yt 3ukmp2qx.7et 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 collides i3p(ng-a, zplks,w //ub s8onhead-on and elastically with another ball initially at rest. Afterward the incomin w,,lo/n3p bp8ss ig(n/-kzuag 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 elastically as oneoauvu(3fhyn xi+8 ;u7 c 0,akk approaches the other directl k,8(fiyau7+hvau o; n3xukc0y 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 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 anhlw0ce d39v6a elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original speed l wh06d3vcea9of 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 inbco61 w4hpbz4ep;iu; cline as shown in Fig. 7–35, and elastically strikes another czu;1;pcbh p 46eo4wib ube 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 leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an oxy/aii hi au h-q;6)z4bject 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 maf 1m1 upot(drv7 de ae uz:ozoix)i6y 8t.-q+8ximum height h of the pendulum equal to 2.6 cm. A second projecft-xydoeo:apze8q1m ru u i7oz )8dv 16(+.ti tile 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 axlhx aj ,(87gm 3.6-kg pendulum hanging on a 2.8-m-long string, which makeh 7m,gjxxl 8(as 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 kayc/a04) svlof kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into two pieces, ones+ ka ht/gk:zqhx+bpw-c34 ya2vx4+ r of whazvxw pbqy+ + a2s:3hxc4/tk- h+gk4rich 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, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides ijg qmn, tn2+a3ge14 1 13hmo+i rfzkainto the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stoppoi,nigmkje+arn13tg1h+a 1 3mz2 4fqing. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to t;t:-.vs2 v rxmdh*l)tc t;yba height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of itsth b ct)vl;y ttx*v;.2sdmr: - energy?   

A measure of inelasticity in a head-on col4 t0prlkj 1iid742umplision of two objects is the coefficient of restitution, e, defijp4i idlp7mt 4r210u kned 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, oie73wnhh 9u:xwo zlx) takggb)54 (4vne with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. T 73x5wwa(it n9bgux4ego hh v)4)lk z:he 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 directjfpc 9cjfrk.rm ,(37 ;a jh3:4lwtxrjion at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find .,39amrtk3w;jhlj:x f p4rj jcfr(c7 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, aaz03:y7iw*n mduj s +mnd a neutrino. zdj0:m3 7+awynsiu*mThe electron and neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of masci+ 7pyt ll*,qq 8y*hzs $m_\mathrm{A}=0.400$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 be )iziwkic-: u;esy.3 jtween two objects of equal mass, each having initial speed the two move off togetci-k:.yj3 ;iweziu) s her with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal c8 10)7 xqiwbwrds av:k19vld4rg6wg mass 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 modwr8) rvbw di6w9sgkq711l:c 4g0 xav ving 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 a perfectly elastic collisi8/g*xmgmnx2q9vq k5q(wq o/ son with another atom at rest. After the impact, the neon 8*q m(295 q qko qxvgxs/wn/gmatom 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 perfectlo/(b whg a1p4uy elastic collision with another atom at rest. After the impact, the neon atom tr4p1u(o/b ghaw avels 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 tg(-l.k4u pd+a .dcxs zhe three-mass system shown in Fig. 7–38. Specify relative 4s-gl+.dp kc d(.z xauto the left-hand 1.00-kg mass.    m

  The distance between a carb jhnq;zp9*) q9g2yw*7 vff lbgon 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 thd mnm5:0-vpz :4vsne p.) wjyae front of the car. How far from the front of the car will the CM be when two people sit in twammnjs n)v:e 4v0:d p5 pz.y-he 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 lg-j npr,, tls37mv .emass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW cornt3pg l.r,nls emv-j,7ers, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidefjxb64vu.5h qvpx+. ss $l_0$,$2l_0$, 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 hxdq(h n4tzc,7 gw x+g/as a load of identical cases of tomato paste (see Fig. 7–40), each xqxn/7zgg t ,(w h4cd+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 hasym7b9or.p -1 kdj.ou 1ght2z m a circular hole of radius R cut out of it. The center of thj1 oz1.2yg bm9.o -rp d7hukmte smaller circle 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 Tableb plr xbqav2o:g) **ar/8xpix:y;p7 t 7–1, and calculate the mass of one of your legs pbao/lyr) v xqti8*apbx;2 7x::grp*.    kg

  Determine the CM of an outstretc 0g b3giy.qi5whed 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 right 40ey - g4hsxbe2yli0 nangle. Assume that the perse2yxl4e g-04hs yn0bion is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are p6r.+ f9suvopjg 5o w6hanging vertically, and his trunk and head are horizontal, calculate vgswp5op9.f u+ r66ojhow 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 andyu:(2 s pzz(im 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 fr g(, 9)s gx,m52kx4tmzdrmyk rictionless 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.kxw18 gj.9c zn00 kg and a diameter 0.0800 m mounted on a uniform cylindrical w1gkcn8 j.zx9 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 m puhe:w19ihr29s:t*x io g7haass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how f:opaigx9hwu 1:*hhrti9 27e sar above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–1qg* (3h o oudb*v9nq xp782unu4 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and stationary wit6eld;+ jyalc u +u4w h:)rpt2th respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. Wu: pw2lucl 4ha6r; jd)+etty +ith 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 8x jm(wb*qo f/ strikes a bat and is popped straight up to a height of 55.6 m. If the contact/8f m(j *boxqw time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling withf feayg5c*8tbs4xja(1 :jvf , 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 poc t.row)k2g t8yket shot shown in Fig. 7–43. Relativt2oy kg)r 8tw.e dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquirescggx9c5b4 n l p7:fdmdgi;*+s a speed of 2.5m/s by pushing off with c g*;7cl4p:dsbf 9ggmxnd5i +his legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one t7 7lhz 176 r4k6,pkwcozt rtdof mass 60 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut has m tr6z,77rwp ctkol4kt6 z1 7hdoved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second hl8st1 hgav(;os )se5ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is th;l1o hs5 )e(vhtsgas 8e 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 w,xj ox+doz2)r bow (6ltu4m1an 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 w o1 jb rw2oxl+),zu(wt64om xdas 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 verk07x oz; xehx,tical height 4.00 m. The ball hits four times on the way down, each;xk x07zxe,o h 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 blocx 0+03yvzw bz4*6+y mecg bqyzk 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 wily0m +ygqb*ev3zy w +6zbz0 4xcl the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a. aoz3fp 0o-ea 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of k fo. -3za0peoainetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg a73q p*72.shrhfy0 qrr d1gskand 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 m apart from each other, now exchange seats. How far and in what direction will the boat mov17g7 *psq qkrfa.0 r3hsrd2yh e? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass ae vf5qv3q* vaui5ow5d6mo7q6lr5 9iwas about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into .ndaf-y* n- ez,o0(rsw:ksq y two fragments by an explosion. One fragment acyfsa*n.,knezs:(-0yod- r qwquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the fo 8w 70zbk( kxcr;r1ptxrmula 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 ewo5g0 jcw96su vm2/p$m_A$ = 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 radio ,v)tx7 r2wqcyactively into an alpha particle and a smallerc, 7rv )wtqx2y nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an ang at;yh9o(am t)le 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 jvc*g (xc:wah oi4r5 ,j. nta: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 onfe1y fg /)* wv-bunz5u mass m if it is to rebound from M, slide up the inclizw g)u*yn-5f/fve1u bne, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figur-28 pfqmis;;nlbk e6fe 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sqmfk;f- 6i8e;p2 lnb 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