We claim that momentum is conserved, yet most moving objects eventually slow t+p*hksxi s-2down *ih-x+st k2s pand stop. Explain.

When a person jumps from a tree to the ground, what happ4q4entgq.2wz ggmr9,ens to the momentum of the person upon striking gq q 9gr.,4w emgn42tzthe ground?

When you release an inflated but untied balloon, why does it*lv,su11 1bc mp j,+gpok v7ew fly across the room? 71gpk1u,*w cjv ospl,1e+bmv

It is said that in ancient times a rich man with a bag of gold coins xim8 7mhz.lqf +cp71v froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been .fv7qzmhx+ 8 ci 7m1plso miserly?

How can a rocket change direction when it is far out in space ayu2 ce8. ghyv 1;xs t4lm(pbn-nd is essentially in a ucs2x4.l-y t;(hevg1mpy 8n bvacuum?

According to Eq. 7–5, the longer+rd u7w6s xtf5+ bxlr(kq(r c9 the impact time of an impulse, the smaller the foxrs9b+qu rktcf(d 56x(7 +r wlrce can be for the same 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 possibto2+jfse2-rh ,: .hj7nn ay 4 zxc8oxble to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this ne hx,jcaf rb8s thjezx-+22 o.4:yonn 7w design?

Why can a batter hit a pitched basb,mntd hb97s g) is/y6,m l2npeball further than a ball tossed in the air by the batterymd,sg)67bl tn/pbs hn9 2,im?

Is it possible for an object to receive a:;0xbow aq 0ta larger impulse from a small force than from a large forceqa0 ow tx;ab:0? Explain.

A light object and a heavy object have the same kinetic chq e5 o2po1e/ j2 ibs1tmjq1)energy. Which has the greater mo1oh 52t ope/ )mj1bsqij ec12qmentum? Explain.

Describe a collision in whiqiraalw k1+-n iol/89v k d6-sm( hq.gch all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed agaiz u3/+ewg mi1tj*r)q9 g-1ydk h cwr)fnst turbine blades on an axle that turns an e cgr)rdhiz/3-qme t*j+ yfw1wg9) k1ulectric 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 at abzha mr.-3r4bm o2 br3 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 h6p,uh ni/r8lmeight 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 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 puim8,p6n/u hrltty that falls and sticks to the steel plate.

Why do you tend to lean backward when carr8g6nin- 1u6(fmidwl *kx b4qlying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, wherea5 gvxa9s-m(tm s this is not true for y agmt-v9(sxm 5our arm or leg?

Show on a diagram how your CM shifts when you change from -(x .p7imc8qorwq4ht-8y7 g* gn ev yra lying position to a sitting posi nt8 - y7ep.qr7hi8xoyrqmv *g-g w4(ction.

If only an external force can change the momentum of the cenfuzw1-j.. qe fter of mass of an object, how ew-..j1f fqzu can the internal force of an engine accelerate a car?

A rocket following a parabolic path through thers/ 3b3ck hb:velqp4 - air suddenly explodes into many pieces. What can you say about the motion of this system of k- :ls4b/hvqep33rbc pieces?

  What is the magnitude of the momentum of a 28-g sparrow fxa ndl,* o.0 gj*sxg3olying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 ckpm+* heu3t( 4c-g7r yh;bxpN acts on a 65-kg skier for 20 s. What is the skier’s chanb+e 3 g h4cuyh*-kptr7 xcm;(pge in velocity?    m/s

  A 0.145-kg baseball 4 0c d 3)yz4;pqm (fgkeob9vqzpitched at 39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time bpv4yqg9 )czfzb3;4oq0kde(metween 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 threw2c. 83ro2 gp3etdo mows a 6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at resoe33tdp 22 ro.w ce8gmt. 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 eqk6 8c*xuo ce7n4 rfg,xpelled at a rate qn6cc7r*f84 exoku,g 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 at471(dqkvg z.h(vk k 73npupoa $4.1 \; m/s$ 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 pl. 8znko zmj/ 6l4 rd;ac,a/fon alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will berma pja6z4 n c/zld8k;f /.l,o the car’s new speed?    m/s

  A 9300-kg boxcar traveling fj: y/j7bc6fy 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, winchcn/vs):nd.yy/j:h - pvvx( ds can whip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to restx(ychc:vhyn.) vs/v:d/-np j, 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 cari:log 3e8v7eh(pcj 8 8dt5c ll coasts along with a constant 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 tte lle5jp( l hgo8id7: 838ccvhe speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420mk(lavyk)x bxd. *8v m6/s emits an alpha particle in the direction of its velocity, andkya md k)v86 v(lxb*x. 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?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0* 0)az -sixhla t7myt)-kg block of wood and emerges cleanly at 170m/s If the -*sl y0tt 7zm)haxi)ablock 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 tluyn.t v-qq- i.t4:b/ju (driraveling 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 mas sl8vy)4aho,ns 3180 kg is traveling in outer space with a velocity of 115mvo8ynah)s 4l,/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 0.045 kg is hit off ,f v :9odl,grmthe tee at a speed of 45m/s The golf club was in contact with the ballld mrf, ,:v9go 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 at96:z (d gwt(pe hr0ldt a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nrw9dp(0 d zg6:h(etl tail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes a wall at a 45 xc 8amw:jq: vds:kv86xz edd -. 4) xek(/ojqw$^{\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 crashworthinesug y,5mo;(jqv +7 sgtos of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. tqvj5o;su7 +om(g,gy$\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in bjkc 723j vln8*/tbu. xkwao 20.75 s by a head-on tackle by a tackler run o*nw. bxu2bj/vt 3lja27k8ckning 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 ( oed6w xvlh 6ezd229g6mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a functionwod9dzvh6g x262ee l 6 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 awo7plbj(n; emt*/4 iv (p5si75-kg person jump without breaking the lower leg bone of eithe ppo binti7(wev4s j(m/a5* ;lr 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 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 (+mgi 1 b/ bfpm i(33a.egsui+*tx direction) with a speed of collides he+uiib 3 m3pi1 ae./bgmfgts (*ad-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 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-* /lcmh42gznho* i r6don collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, andhr/ioh*d4g6n2z m cl* 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 perfectio p07bnrc duxj) a.;9ly 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 positjr7 )d 0cn9 bpuxiao;.ive 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 2.5ytowgf c)3 k); t7rkt/m/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 sp7 /)kyk)g ;wt of3trcteed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s collide)0pzx-e: (yjunlnb,-;3rn*y ;mb8blki q ylns head-on and elastically with another,:bn0e zn-;nb b ()lymlk qnx8j; rupl*-y y3i 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 amuseme51+ial57txu zn,ji dqnt park ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg15+xqin5 uajz,7dtl i, 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 heatl cj +-bqpzta*it 9baaj4042d-on collision with a second ball initially at rest. The second ball moves off with half the original speed of icp qj 4b2atb49zj al+ta-0*tthe 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 d((r /i5nkuunzqt3 dcnb4yrx9 v11 y7shown 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 cmryyc4 93(zu1u5d nqnkx/b(i7nr1td v off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object os s/wc;9u/ u+vfslru, f 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 maximuy 5jm op01vmodn:o -5cm height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swino m05dj5 yp-:c1mvonog 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 t x:xx a qgiff,stq,837n*k)o3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.verticalfn,x,sk:t8tgqxf) ia73oxq * $\approx$    m horizontal =    m

(a) Derive a formula for the fracti2b( fs/q,++lbrhzn-m 0ab xt p e*pj;lon 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, ihw rfhj2/a oqkc*9p5)*gn5v znto two pieces, one of which has 1.5 times the mass of the ofz hakqwpv9/ 2 jr)g*c55nh*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 into the rear end of a 2300-h3-,zq .8x;iqipdwcaya;9z dkg 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 speiqhz8 xad, ;yqaz93-d;w c.pied?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a heigee hhx)wl)3w )0wccb:ht of 1.20 m. Approximately how many reboun we0)hhc)e3 :xwl)c wbds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on col7hzylxg/ibh s922 d n:lision of two objects is the coefficient of restituti/2l hhdzy2ns7xb g9 :ion, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, o5ls-gf flh3b1a p :5dvne 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 wi : afgh-f5v 5pl3sdb1lth the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on wit- tkza q myu+l-:tcuaob0t+,)h a 10.0-kg object moviubz q:0u-lt + )y-+ctakomat ,ng 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 electron, and a m1jews3e fpq,hv901p7 zgi0 yneutrino. The electron and neutrino are emitted at right0yp e 1mqzh vfe0,3wg 7i19spj 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 mi +6bw cvb 8hkq1w.g6pass $m_\mathrm{A}=0.400$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, e(gskj9s :pq-vb:bx ( drlk45lach having initial speed the two move off together with speed v/3 What was thev-k 9ds b(:jkq( rgslpl54 b:x angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at trm; 2psjs,t 6ihe 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 axisst jp, ;rism62 (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 collision with another atom at r..slkqs18 )*w ;ybvb-jl)u iqwk2 srrest. After the impact, the neon atom travels away at)8lk)2 -qsjvylus*1i .qk;w srbr w.b 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 colliyo02c t3zw8as sion with another atom at rest. After the imwtocs2308 yz apact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7evm9u sm;i e67–38. Specify relative to the left-hand 1.00-kg mass.e s;6mu7m9eiv    m

  The distance between a carb*vfhnt )g j.dno( q./son 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 the front of thnp*o *x0v /a c,o4, mlb.mfgiye 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 npmocg/ yl.bam ,fi,x0 vo4 **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, iy(la 1 weoufy/ vljn8 i6,o:4qs used as a ferryboat. If three cars, each of mass 1200 kg,ofy:qe6llj o(ua1i yw 8/4n,v occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides mp+ 4vfghfyt 7tkhlc4(4mn;j 5a- hn+ikd +u-$l_0$,$2l_0$, 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 tomatow,b,x xt*71 zjtw4w zo paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the loawwj t x7,,b1w zt4z*oxd without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius Rhbwi g. lnz8h6ww/p4 py0pa,, cut out of it. The center of the smaller circle is a dista8n,p4 i.wl wwzh ahp6,yb0/gp nce 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 tholddjddr0 *;z(6duy :rse in Table 7–1, and calculate the mass of onld6rjr(u dd y;dd0:z *e of your legs.    kg

  Determine the CM of an outstretch qj(j5/c,bd +:v vjbcoed 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 a7 k el;u(9w0te a5rvdytin3 u7 right angle. Assume that the person is 155 cm tu;v9tniw ye5e3u7(kl d7t0arall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and l 6( 9nilzi5gaiegs are hanging vertically, and his trunk and head are horizontal, calculate how i(i zg65lan9ifar 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 an y/k:r*rvk( 0knrm9k xd 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 stan0q76q ibf1a abd 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 cylindrical6z *ha1zyah4 x+pf u7t 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 uhyz+ af4azxh167p* t. 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 mass 2.00 kg and a diameter 0a+mxzm8-h 4kvv5f+ b q.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 +avq8-zxf+vhmkmb 45 point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 79srh to4no ) 73 lkm2gmx fmi8ir3,g2q–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 ainl )oacf 67pusb5;f8lr and stationary with 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. With pa6 8sbu5flflcn7;o) what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched h.7s7(zccrf qcorizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the co.77 zfcsrccq(ntact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travx8c )xr(:rg 14rj vmm7)j(w imqo0wrmeling 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 v -26 (f+octyepyknh8shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cuetpkch(yof - 2y+n v86e ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space sn .u;0gks k;q:cgj8d uuit) acquires a speed of 2.5m/s by pushing off with his legs from an 1g0kc: q ;gsku8jn d.;u800-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 initially at rest in64yi.4n zxffbr g3wjkq n 6dp.c0q6y2 outer space. They then push each other apart. How far apart are they when the light.y4n4f6d6g p byjw f3r6 nk.0cqqix2 zer astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision wi qu (p7nmxy1)v d7qytenah-e cy*(gp;h d/7f*th a second ball (at rest) and rebounds in the opposite direction wimy*1vc- n pyeq* 77dd(/a( q yufg7p;hh)n extth a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving an autom6uygm -t+ex8:d b4(xelpj -j robile 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 wa:+rg 6e-dt- 4jljx bye8x up(ms 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 verticalb8lto2nv 37.qdnk 3jlau:,g o 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 ba :ugk2vob,73q 3 8olntlnd.jounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at* sdx 7+pwuhn(xiy2 *k rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bulle*ys*pxd +2uhin7 (w kxt becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a uk/of ,xz,s49g15uy+e t ylgtqun)e; 1.35-kg block of wood placed on a horizonta)t/ nyu+g4zu1 gyq eefxluk9st ;5 ,,ol 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 maszgoef-lp 6;mh.(,lcx9b jrs. s 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 rl,. 69zmjbo.e-(g lh;fp xs ceach 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 .sr4fd .i *3mgdz(ctj 0:v ispabout $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments by an expnoke+u )7pc y9losion. One fragment acquires twice the kinet k79yo+n ecu)pic energy of the other. What is the ratio of their masses?   

  The force on a bullet is giv-k* g8p e75/axynhnlwp) s3n hen by the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of massestiyp(ec9 - )qv $m_A$ = 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 rjnc 58+a6e6qod c dmu7/m(g,btso/kyest decays radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling6abdujk68tcgm /m/e s5o(nc+dy7o ,q 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 tar(o yqu1ynfv*52dn ci9get) is fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down rqzmlmdq* ++/ riif; ,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. e4eq)niy,0gq 7–46), what is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the in4iy)0,ge neq qcline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–4 pt cg/(a-+v+sk2 koejbpi8w77 shows the planet Saturn moving in the negative x di /i +t 7jkkpap8o-bc+w(sv2egrection 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