We claim that momentum is conserved, ihyg+rn.7n q 2x. 1t/up/gixfyet most moving objects eventually slow down and stop. Exp u1/x.gnir nhtg.qpx+ 2y/ if7lain.

When a person jumps from a tree to the ground, what hap*t 7-t nn8creipens to the momentum of the person upon striking the ground?8-t7ncnri * et

When you release an inflated but untied40j5f0uclkua p a0ee (dy 22pv balloon, why does it fly across the rooml 2 pjuupcf0 0aeke0v d425(ay?

It is said that in ancient times a rich man with a bag of gold coins froze9 ety /pm1xum4 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 save himself had hem9/ xum e1y4tp not been so miserly?

How can a rocket change direction when (t6f4sqcuhhd6cl 1 o, it is far out in space and is essentially in a vacu6s6hctql,u ocf4hd1 (um?

According to Eq. 7–5, the longer the impact time of an impulse, the s0t auga xh3jwgzkis2 o*);fzh:f r;7 /maller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On trfw0ua3g tkx: a*o;h)jg / zzfis7h2;his 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. Tsp0uhmp2 l2t5oday, though, cars are designed to have “crumple zones” that collapse upon imp s0 2lm2tuh5ppact. What is the advantage of this new design?

Why can a batter hit a pitchhi) bddc4hl-7ed baseball further than a ball tossed in the air by the l b ihhd-cd74)batter?

Is it possible for an object to receive a larger impulse po n u0+sfq+ pqa5+5lafrom a small force than f+lasppa +u5 q 5of0+qnrom a large force? Explain.

A light object and a heavy object have the sameal)ku;v;bpc/ c)he9y kinetic energy. Which has the gr;aup; e) )hb9v/ckc yleater momentum? Explain.

Describe a collision in which all kineticpgh; ) hy:clvid7y)sm pb8,a / energy is lost.

At a hydroelectric power plant,1j1qpypb7, * nefltx 2 water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebof2tp xynlj,7b e*1pq1unds?

A squash ball hits a walujku55(jaunwt0 g1wu+ea rlk:; r :k3 l 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 heighjs2e8loq fhjsz96 (e2t h onto 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 esj2hsz26ej(f 9 q lo8conserved 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 hlz(aeh )9fkv 6eavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, wm-w q40et9bqlvk1 5d ehereas this is not truek9 ld1 0bqv-eme45t qw for your arm or leg?

Show on a diagram how your CM shifts when you cujx ynh4+ v+s /d9:ph52u acunhange from a lying position to a sitting posiu h+v:+9 unncsapj5x d 24/yhution.

If only an external force can change the momd p,kh(-siy)a entum of the center of mass of an object, how can the internal force of an e,ya-s(pi)kh dngine accelerate a car?

A rocket following a part ur, s.cyss .d55qnn9:(fkwr abolic path through the air suddenly explodes into many pieces. What can you say about the motion ofur.5( kdns fw,stn .5:9sqrcy this system of pieces?

  What is the magnitude of the momentum o ary; n v9jmxu76qo6t,f a 28-g sparrow flying with a speed of 8.4rn6 t o;u,769xqajymv m/s    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 5)g d+j czdk*ps. What is the skier’s change in velocity? dz c*)pkg5d+j    m/s

  A 0.145-kg baseball bpo.0n- 0s c *3jvnazzt9n ph3pitched at 39 m/s is hit on a horizontal line drive straight back toward bov.n03- 3 n9zzjhs0*appnt cthe pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a speo 8sg 95k3 k3 rcli3:nwpsf6ifed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was inik3:ngi 35fr3spw8s fockl9 i6tially 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 the propelling gases ae/9 .ou wa2lmbre expelled at a r.bu9a mw2leo/ ate of 1500kg/s with 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 apparent breakaway f ofi0og;v4tahczf 1oj6,0 ji2or a touchdown is tackled from behind. When he6;a2 ,iho gv4o 0fcift0j z1oj was tackled by an 85-kg cornerback running at 5.5m/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 frictionler :pb8ikp kw 5/,fehnkf7o:1mss track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto ti pe78,fk n:m/5bofwhrkk p: 1he car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/su,jp,lzi4y, bzr/1eg strikes a second boxcar at rest. The two stick together and move off with a speed of 6m/s What is the mass of the second gu,i/e,4 yjbrl,pz 1zcar?    m/s

  During a Chicago storm, winds can whip horizo3m, ncse -i 6ucxvjufgx +a:r k:3q(:vntally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assu+iu,cmfk-rg(:nxa uc3 q63v: es:vxjme 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 lfi:.)fp8.v k out,,wsd )zuo a level track. Snow begins to fall verkdf)uf. ) v.tiz u,o8psw:o,ltically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initialp-oja ;e jw-ey v)htjfv(wk 9bh8269xly moving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted? ot(b)9jjk 9h- xfa v62;pwj8wy-he ev   m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of / o(:daot 3fz uxvk g s918,1cr8rlbeywood and emerges cleanly at 170m/s If the block is stationary on a frictionless /3dl8z f8oba(g19kyes:rxuc tv,1rosurface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is tg6t-9i )ostmezz di(4r. 6px rraveling 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 kyny * d l (iyy)q 96-)cvp4abr(b5qbtmg is traveling in outer space with a velocity of 115m*iybp y 5ncv-r )9aq q4(y (lb)mbd6yt/s To alter 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 0.045q xe:hhmd*;i. kg is hit off the tee at a speed of 45m/s The golf club was x. m*qh;edhi: 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 q7fdqnvq( - .6ak(pbxnail at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 msaq-pknq6qdbx (f7 (.v . (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=0nbakd/n k ,xavt*uzp6:6q s5 8.06kg 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 o+-fri( , gybudyl3e( vf new automobile models. Cars are tested by smashing them into fixed, massive barriers l(i,3(eg ry+ubyfv -d 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 runningt w ij7 6rl25ul l.qhvg3rvspk2vl 08( at 4m/s to the east and is stopped in 0.75 s by a head-3rgpvl2l wl i6k7ur.( v jqv25tl8hs0on tackle by a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis bab9a 1scs.qw5 all (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–qc15.9ab sasw33 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 3b+v 7 +eq0boxfj+cwican a 75-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit +fi3xb j q0+wv ec+bo7area) 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 eas;( qly7 xdlb9fpuk ;7dt (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction x7(k bdq 9;pul7;dyflof 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/s has a head-onko9r l( pip*e2 collision with a 0.900- el pr*2oik9p(kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg 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 *h-/jior, q3ht2xhwv;j; nk tl3i ly3head-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 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 directionklhlh j;qt3t* 3joirx3h,n; y-2 iwv/ . ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides head-on with a 0gqsqa6yz+t7jn2h/j 3 -q-q ,iekkq (h.090-kg ball initially moving away from it at a3q sg7(qk6nj tkaq z- hhy+ie,2q-j/q 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 movingt3wjx+n - wk/ d,oy5nh with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounce -od5xhkj,nn ww3+y/ ts 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 amay6he /z1p vr)uqb 43ng+uqp3usement park ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mv)z+ 1p 6/pqne3r h34 bugayquass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a second ball in8g.jh0c i-u -sidij*-m okn;y itially at rest. Theo ;ndji ug*.ym --kjh 0cii-8s 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 frictionless incline as shown in Fig.cfd9 1z7teerk4u9qwtx6x2 g / 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the ifz6d 24e1tcuex g9qwt7xk 9r/ncline 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 ofry.c )s/t8tywg v..fkz8-k od an object of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 resultsgb3d. z:s 3w ic nd.yix+ryy70 in a maximum height h of the pendulum equal to 2.6 cm. A second wdniziy: ysc3gxr3 .y0.+db 7projectile 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 travj9ckv,4f7/ -gk dr xgf1qmp /f 7zw-exeling 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-lekxgg9f4d /fcw, p1zx / kr-7-fjq7mvong string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for th jf82b(xwv yx0b5ksvs+ kd- k*e fraction of 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, m4c nknvqv44)into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were q)n4 44vmvcknreleased 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 into the rear end of a 23zwd(5 ym jhx-900-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 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 represe jhxd( m-5z9ywnt the SUV) $\approx$    m/s

  A ball is dropped from a height of ug1d0e yi0+ au1.50 m and rebounds to a height of 1.20 m. Approximately how many r0igu 1e+0 uadyebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two o pe y1leq26)qybjects is the coefficient of1p6 lyyqe) q2e restitution, 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 in 3e4oxhwkh wuxh; otdz--8-, rto two pieces, one 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 th, 4 ohehwkr;xht- z-8ux-wd3o e 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 head-on with a (hd:n6 a) z-v dx;wz6g;sjrec10.0-kg object moving in the -x direction at 4m/s Find the final velocity of ea a6 jc6(rn;s)zhwdg ;exvd:-zch 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 nucqvqoq4 *hrct6bk ,x:5leus, an electron, and a neutri4kq *cvx6oq 5bq:rh,t no. The electron and neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of mpgd kbrz*b:* 3ass $m_\mathrm{A}=0.400$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, pt))+fs 5 6 spaqc wz8v*ea7uv5.zld 6e0nkq beach having initial speed the two move off together with speed v/3 What was the ana57bs0 ulk t 6fn.epcw)szp qd8az eq)56 *vv+gle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles ay lyd. by*9cn94o d;va-nmjt8(ey- ouxoaj5(nd meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what alydayn.yn v(t-ou c8jmo*boa-e949y ( d; jx5re 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 ebw39tl-29e pe dzgzi*u (po+ilastic collision with another atom at rest. After the impact, the neon atom tra9w idgpp2bzet +3*ize o9l(-uvels 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 with0:ygxk -rp og+y9kln) another atom at rest. After the impact, the neon atom tgk09+-n o:pgry) yxlkravels 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 F4iv ,fn7cn9on g2u7pml36cr lig. 7–38. Specify relative to the left-hand p7rug43cl, n 6nvlmn72fcio 91.00-kg mass.    m

  The distance between a carbon at9:5n:h sr1lz jc0dbu wom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of the c 5f, 0dbj8b8zo )rcgitar. How far from the frd gr0 tfbz8,jcibo8)5ont of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the 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 usec-v ;0g as)r6gmovg9 qd as a ferryboat. If sga cog)0-m ;r9gvvq6three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides 8qxgsop 3pp -6$l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of tomato paste (f2ja:e. o-s8c/xqpu 4r rwfziv n3 h:+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 tippz+cxi2u/qfras:h :wevnp.4-f3 oj8 ring it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radiuy :w, r.+eek n/q8kg1j+bknthfyy +:vs R cut out of it. The center of the smaller circl,kej r.kyb:8hve+fn t:+gny kq/+ yw1e 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 thod9 c u+vxx(i,dprs9 ,xse in Table 7–1, and calculate the massr ,ddvx x9sp,ic+x(u9 of one of your legs.    kg

  Determine the CM of an outstretched arm cb0,b 1tfh9 zui,,lxh 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 thu6(qvsl;/ cxf e CM of an arm bent at a right angle. Asslf6u qs/c; x(vume that the person 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 hanax7dmoe. 7f-j1j+n pb (wp az1ging 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 b1-z. p 1a+op j(fmbjdx7e7awn ody? Use Table 7–1.

The masses of the Earth and M j7x*s 67c2m 9 x(zfp)1yxwqgetd-h iuoon 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 86o , oo:ibp6hc s*m9snljz/ 9m0-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 diameteka; i oebjwcc9unrih/5 ).+c5r 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom.bwi ;ucc9+/ior)jc 55kha e n of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindri q8z95:psfye ucal head of mass 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 far above the bottom of the handle is the point that will follow a parabolic trajectfu9zs : py5e8qory?    d    d

  (a) Suppose that in Examp( 6-oaw 7mtcka7.4k nmrhh. v1qs(gv ole 7–14 (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 thf1 rmut847+ vyx cce+ie air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slxu7fecvy +1r8c4m+t iides 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 i7pngbhin g v-5:8ps ,and is popped straiigsbivn-p ,8 : hp75ngght up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with s8 zt3rjtc:zb0e ;d.jc u6* e2sdjum(ypeed $v_0$ 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.nn1rdj1 v q(sf;l- uj5 7–43. Relative dimensions are also shown. Should the player be worried about this being a “f-sdn n1j5 (vl1urjq; 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/svk4 djno+fi/x z36 mm45k+5ttwdr 9ph3m l) qa by pushing off with his legs from an 1800-kg spkqdm4 jl+k/n+4f z5p6ivr5 t xh3 twm m3d)9aoace 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 z r/3uzi:jte 1lfe 9p*n49e zxix-)hq 60 kg and the other 80 kg, are initially at rest in outer x4 1je9i le ) ntqp/he39*ufiz:zz-xrspace. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (at p flf4b)i2 ;:bbiw3zbrest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the second bapilz )2b:;iffbw 4b3 bll? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a cx6zx 7b8t42 drc k, *n7apsxqoourt case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90kxk xcp4zs7tb8oa*, 26x qd nr7m/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total vertiqo9.,lpui.y/vqkrv t9 de y(4cal height 4.00 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, yu l.qr4dvtoep( kq 9,./9yv iwhat is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest dir53ikx 9 jbc-vuectly 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 becomes embedv-5c u39b jkxided in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood plachx iu*x)pu2b hbse1i66a - x8ned on a horizontan1 p)uxh6* b2-8hxuias xi be6l surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit 6p evb/szu42pb -uochh* .d5zin 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 move? The boat z- hcu2ppvzsobu h4/db5*e.6will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was aw759b em1pf lr(ysj *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 isij6-as9x1q j (idqu 3v sc3(eo suddenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their ocaiv( q1ds9js-6e 3xj(i q3umasses?   

  The force on a bullet is given by the formul hd1so.iac/b: 2bo-qla 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 9 ho,a+ phjt/8 x/7sc0evtaxk$m_A$ = 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 gqc5zyei a7l qe q3v,dbzkvyb5+2+4+ alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particl7qbz q3 be 5k 5cv4y+ygediqvz+2,l+ae is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angle of;lis8mx1kgg*i. axh 5 ,o,lua8.vvru 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 a 30.0 /f tf;ij0+or s$^{\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), wha r2a w dp.(m(y//ytbgtt is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide with M again? (2gmwp (//tdrya bt.y   kg (Let A represent mass m, and B represent mass M.)

  The gravitational slin 5z0v+ fm*v +zybb f*ei1m2zfxgshot effect. Figure 7–47 shows the planet Saturn moving in tzfbvzi5f *1v*0x+mzfm 2by+ ehe negative 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