We claim that momentum is conserved, yet5 4og).gvv 5.aqzthdy most moving objects eventually slow down and st.hgd5vg.4qotv 5yz a) op. Explain.

When a person jumps from a tx d,a+)vn)1ztu* eb mqree to the ground, what happens to the momentum of the person up)xq+uz, bvd*1)men aton striking the ground?

When you release an inflated but untied balloon, 0eo0x8 8vmdsvwhy does it fly across the roomvs00m 8xv edo8?

It is said that in ancient tm,c/ pt-h ng9rimes 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 hg-mrp9 t/n,cto save himself had he not been so miserly?

How can a rocket change dq vuigj+6fjruixe6h71mmrg p +e+ 5. 3irection when it is far out in space and is essentially in a vacuum +mexj1m.pjg re+uf 563rviqg ih+u6 7?

According to Eq. 7–5, the longer the impact time uc4ys/ a.n478;en o,xoqqogkof an impulse, the smaller the force can be for the same momentum change, and hence the44o7s; xonegc8un,.qy ok a/q 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 t ml-)q6*, hsl/nykiveo withstand collisions. Today, though, cars are designed to have “crumple v/),6sli meqhyn- kl*zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in th23j - t o(5s2xveqgttle air by the 2-ejtx q o25gsl3vtt( batter?

Is it possible for an object to receive a larger impul: :7b+)la (- nsd rn:rei)edsxsrm ee8se from a small force than from a (mseex7iad )s+bsle :-) n rdr8 :nr:elarge force? Explain.

A light object and a heavy object have the same kinetic en;m9k2wnb6*1aunj,-e rbtlo aergy. Which has the greater momentum? Explain.l2obaw;-bannm19u j6e k* r t,

Describe a collision inddex9 ,z8sk0 s which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against tur8zk 96rslzt/- fvyqd6bine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the waterk8-6v/zld96ysf zqr t is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at ipx ks9/; tfpn/ib)n: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 onto a hard steel plnx:ogqmts +m:n .7xcr)o e2x x.q)i5gate (fixed to the Earth), from which it rebounqx7rnems: .o .g) xxxt5cqoin) m+g2:ds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavd8 o jdsqxw0kp)0+ fx4y load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, wh/grx3nryqw4 (r5 i. sqereas this is not true for your arm ow 5qyqr(/3 ir4gn.sxrr leg?

Show on a diagram how your CM shifts when you change from a lying po::lpyu)tybq o(6r* m csition to a sitting position.*mqyu (t:)oprcl y :b6

If only an external force can change the momentum of the center oohy7k/ziv (m9f mass of an object, how can the in mio/h 9v(7zkyternal force of an engine accelerate a car?

A rocket following a parabolic path through thbq 6i1u. ha4xd-jwe26vevfr 0e air suddenly explodes into many pieces. What can you say about the mvax di-6hu6e b1jr24e .0 qwvfotion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flyi:l.h 5jimi6xk5 sak3a 1j b(oing 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 theeu ngeh4)z9 -r skier’s change in venr g4 e9-ze)uhlocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive straqts.*w;lb6uf ,f myghbj -b83ight back toward the pitcher at 52m/s If thef;6gthmbl. ybf , sq-83jbu w* 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 ouvw+/3 qmgb lho8*dc5j(:xaq st horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initialw o35/x*l jq8+dbcm(: svgahqly at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases are exp1wi/ lov )zac6,oio u+elled at av/)l 6iai+o ow1 c,uzo 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 ats,5v1fn:)iwa, rsfntsr-dxt zss 9 -3 $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionle7mgc,xqq 3.ey co3.sf 1u8fe iss track with a constant speed of 1 cq3yfqo7..smgeci,38uex f 18m/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 a 5-q+tyj9 sbgxt $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of 1006((q4consyte km/h If the air strikes a person at the rate of 40kg/s per square meter and is b4t nqosc(ye(6 rought 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 constw23wqr*t, cn,rccp lqs( w 5-pant speed of 8.6m/s on a level track. Snow begins to fall vertically 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. qw l-scwc3 rppn,*ct,(2rwq5 0 min?$\approx$    m/s

  An atomic nucleus initiall, 8 mvvc/2xgray 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 / rgcma vx8,v2have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrmhr v(y- 22dilo(xzqqwlm*4-ates 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 fast does z(r(y- v4olxwmqq 2*hi2m-ldit move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speeu6qfe:ub fn +yb. p*.nd of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a velocity of 7r g3s0jy5)nz-u 9ojclw.aap 115m/s Topa3j-u5.7lyar) w9 jcosgnz 0 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 0.045 g kf69)po)5(apwwu /hry; a mnkg is hit off the tee at a speed of 45m/s The golf club was in contact with thfmu k5/a)() 6ohp ;pwr9w gyane 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 dbr9nhhz 97o4 a nail at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What ihdrbhn z 974o9s the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mas9z7 /+v:g w:jrm2cefazh *yfns 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 automob 8j8a:6 1f br.*)h jpddl gna/iq yt:hibohv08ile models. Cars are tested by smashing them into fixed, massive b1tn0odg yh vj*fai b8: qb.ih/d)pr8a8jhl 6 :arriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east w/ p4)tdd (pgqand is stopped in 0.75 s by a head-on tackle by a tackler runnin)/w(4t qd pdpgg 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 ( jkqd):/v0mh or4s-; m cmesv8mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate h8c:0es qjmrv4o;dmsv k )m/-
(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 he70rhgemff*mwv9or 4 r tz8(sz:- pi 2pight can 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 0.68rt:zo7h 4w-p 9(gi rpz2se mfr0mv*f0 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 fg k r.oq3ko4s5(bhy* kg moving east (+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 of each ball after the collision?Let A represent the 0.440-kg ball, and B rf3o q5sy(o. gr*k4bkh epresent 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-on collision widqp,3k7d d 0qcth a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will beqkpqd0,dd37 c 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 rnv384sjtqgy 8g ff6./g1g rneb1y h-yn(1 uwperfectly 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 2.00 m/s, and call that direction the positive direction.Let B represent (wv84 nh /br3g1uysqjt.gy 1regffn y-g681 nthe 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, movin(6qhho: h nloso z80*25lbvi og with a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction ol(5 hqb: 6o8*oho 2l0h vsnozif 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 0.2 cda(2+i2x giy20 kg that is moving with a speed of 8.5m/s collides head-on and +y(c 2 aixgd2ielastically with another 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,fmq ,/ r* +rkkn:gj(ddr0nv;u yf7c g park ride collide elastically as one approaches the other *0;g7rkj:y /mg+,,f nrdvc rf qn( dkudirectly 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 an elastic head-on collijri w0,6, tnmm/+*yf9zhwiw-xg;a zdsion with a second ball initially at rest. The second ball moves off with half the original spea6mwf9ix/j z w,g rd-ziwhn, t;+0*my ed 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 slidl( *p bj;u gw*l qxjkz3,p1q0xes down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off1kw lgp z0;ujbxq (**qj3x,lp 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 oxr+g0ur b-podq fl -0/bject 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 l ovf9d 2.gsz,maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pe f lzs.9dovg2,ndulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg pendulum hangl31ksci13hnfxtg+:is:0*lpic wq m7 ing on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s dis pm3i ckqnhisl1g wc1:tx3f+ *s:l70i placement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kit wt)ox- 2+fn+pe ta,nnetic 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, o32 gbs9k;f yi;y hi3kkne of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how mufs ; ykiy3kghb9;i k23ch 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 end97xz8cg e;w vybqx/8h of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates thc 7xveyq z89x;b g/hw8e 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 re6m i ua- 3istbfq4gjt+,k-s(ebounds to a height of 1.20 m. Approximately how many rebounds will the ball m4g-umeif,- bais k3j +6st( tqake before losing 90% of its energy?   

A measure of inelasticity in au vd)nb6m) qfb(4 px:g head-on collision of two objects is the coefficient of restitution, e, defi xnbu)(gf6 qdpb4)vm:ned 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 tnai0u-uj1e s1s,cujmm f 15 2himes 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 rea5 sue1mm,su-u1 ihfc2n aj10j ssembled. 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 1g6. lvwu no +d+xwz54l0.0n.d+5lguwz lwoxv6+4 -kg object moving in the -x direction 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 electrxol i /st6hfx t7b5z3:on, and a neutrino. The electron and neutrino are emitted at 3 :6f bttizxh57xo s/lright 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 masq5,;bk y+-chracp o-x.kxsx.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 p1h-bzyg0-l dzor 4whvog 12, of equal mass, each having initialgbdwl--go1ozzhv 4 1r phy2,0 speed the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and mvjy,rj)0sy8 ch ltioxh 2x8yk 57+4djeet 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 are their two speeds? direc84oh,)7tsj0 + ix rlc8yj5ykd2xvjh ytion 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 perfecth 0j2ce*hp) q jnh88t +j-oznily elastic collision with another atom at rest. After the impact, the ntj+enh * )02phh cq-jn8 o8ijzeon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision with another atom ljx v)bvzx/3o ox.)u vn3:6flat rest. After the impact, the neon atom travels away at a.oxfbloxzv v)): 3jlvn /x3u6 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 6f0 v5(msjkjz system shown in Fig. 7–38. Specify relaz0(6jj5 vsk fmtive to the left-hand 1.00-kg mass.    m

  The distance between a carbon atom rp3jt:6g( wgn($m_{\mathrm{C}}=12\mathrm{u}$) 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 1 sv/t7 hr2/avted6jr,71hmz,atku7 m050-kg car is 2.50 m behind the 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 car, and z2vrrkt6/ /t 7 a, muahs17h,ejt7m vdthree 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 ferowkvv+mm ey;ps810 +m ryboat. If three cars, each of mass 1200 kg, occupy itkmvov8pm+ 0;wsm ye1+s NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side)ty( xyte-, kys $l_0$,$2l_0$, 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 ofn :p*yl ja-f5i identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the 5lnfj :-ai*yphorizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cut ovyw8uwu(q;1) ,maw zxut of it. The center of the smaller circle is a distance 0.80R from the center C of the largwx( v)wwy;z8m ,u1ua qer 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 Tao/n7)-4y/e flt hg1xrvgsss.ble 7–1, and calculate the mass of of 7gs 4yeor-l/vsg .hs1nt/)x ne of your legs.    kg

  Determine the CM of an outstretched arm using Tsp k90zp0f:00tifj osable 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate th y6ab0by 9hwa6e position of the CM of an arm bent at a right angle. Assume that ab 0w9byhay6 6the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a q:jt-wmwwnup*+v : z+position such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculat:ww:mvz+wp+*tq- jnu e how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth ogatqed e-k2, qnjjgw-o2(98 and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apq 1jr7yv6dug kcoh-c+ +xjb1k1) th0 sart 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 ofpacb.hn;1k i 4 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 k1 cp4bn.ia;h parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass r fqhbfq9x-,0 .7 8qytxkc *af2.00 kg and a diameter 0.0800 m mounted o xtf yfb7cq0fh*qq8rkx . 9a,-n 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?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29), k e s5*dn:5bah h:uqz:v, ;6j hn,fjiz$m_{II}$=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,+:db5/ . qirh)y3gc-qy 2 cynb 2u6ienhjcjf 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 measured with respen3 qgejd6 jyr.25h+-hnb/, f: icyc2)ucibqy ct 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 7 c;ip.syt(i09cdwz8t u -xis u +jai1 strikes a bat and is popped straight up to a height of 55.6 m. If (td9c y7sptiw si c-;i.uz1i0ux+aj8the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travelk( zk/5g+y1gqal1dm eing 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. 7–43. c16)gqa ycrb)*jjklk (q r :t 4zf,)c* fwby)eRelative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall int(*rgekybqk)rt)lc*,y c z 4 1cjff)qa6j wb):o a pocket? Give details.

  A 140-kg astronaut (including spacjvbx8xjdz ..6 2 i(/ocgr1zkme suit) acquires a speed of 2.5m/s by pushing off with his legs /bj2j.zcrxdg(.o1k 86 v izmxfrom 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 of mass 60 kg and the other 80 kg, are inyb)euz88 i. nnitially at rest in outer space. They then push each other apart. How far apart are they when the lighter a8ni8b.yez)u n stronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (a2su(w*m av 6w7x *fdbnt rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mu dv(bwwxs*m *f627a nass 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 invo f-y/h4ot )hes;uld.z lving 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 554/; d.yozt fsu hlh-e)-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete stepcgf/m ayy1oyo*0 6/p0t1fak xs of total vertical 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, what is the bounce height on the fourth bounce when the ballfyp0xc/ga01oat /1m6*o y ky f reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest djbdsuq 6z-*2rirectly above it. If the bullbr2*qs z-u6 jdet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood ply)wsg j;;v4z xaced 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 drives the block a distance of 9.5 m before it comes to rest, what was the muzs ygx)vj4 ;wz;zle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowboat o)vl7y /to 1crk u5of( *cfvn4 yqyp-vltu/-u 3f mass 80 kg. With the boat initiall1-y/r cy t/uknpoolu) 3lv- *y 745tffvv uqc(y 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 (i,cubxd0f ka.10 nsx $ 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 su* z*ln.r aoocqz4 zo1)ddenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the z o1ozzoq)cra*n* . 4lratio of their masses?   

  The force on a bullet is given by the fo8 x2x+z9+ dl*mt sisvco)jsqp-u9 a .xrmula 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 massesh6 crt gim u- oqm3b23+13a+1wjpdtv f $m_A$ = 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 radioacti3zomcvmzt p9bd e +4-)vely into an alpha particle and a smaller nucleus. What will be the speed of this recoiling9me czp+ ob4 -tm3dv)z 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 n4gp5:s6 zvasangle 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 dowp1anm/roa 7 i ,b2t:knn 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 on mass m if it is to rebo40xcv*t ,v6kjzyuke8 und from M, slide up the incline, stop, slide down, c84jekzux6 kvt 0v*y the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn mov qjt p5bfo/+o/7*ne rling in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Satu 7lrojf/pob*/5n +eqtrn 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