We claim that momentum is conserved, yet most moving objects 0p9dmd1 t,lnp eventually slow down and sto t 9p1npmldd,0p. Explain.

When a person jumps from a tree to the ground, what happens to v/(/nb p/b+(x kzq bvvthe momentum of the person upon striking the gr +bn//z/ vvx((bvbkp qound?

When you release an inflated but untied bahi; /i 8ybkk0njh/ius) x8z2alloon, why does it fly across the roomkuh 2)b 0y8inzs;i /jx 8ih/ka?

It is said that in ancient times a rich mdx/y;f d/ k7p nd6dye/an 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 shp7ked/6/y f;xnd d/d yore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is 2p nkg0x))a5 b8rua2+ utsrsn essentially in a5n2r0gbu2 k +pa8)rsasnt )ux vacuum?

According to Eq. 7–5, the longer the impact time ci;0owra; z7b1qrw e 6of an impulse, the smaller the force can be for the same momentum change, and hence the smaller qw6r0;;acrb 7i eoz 1wthe deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Today, thoug/ea2 rd; i67ax c+tsvgx, cbn0h, cars are designed to have “crumple zones” tdvb,x2t6c/a igx+;ea0 rcns 7hat collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball ffv n4q05ccu*t urther than a ball tossed in the air by the b fnq*u4c vc0t5atter?

Is it possible for an object to receive a largern7yszcjpp7d pkghe9- u c+a64t te205 impulse from a small force than from a large force? Exgu7p k6ep ez+-54s0c2jhcdn t7t apy9plain.

A light object and a heavy object sw3a;0b0ajjt 4,zfzhhave the same kinetic energy. Which has the greater moment;a0sz, 4fjtj30 w hazbum? Explain.

Describe a collision in which all kinetic energy is los/4*mz)8loxc4sskpj (,zpx8ql m x3rst.

At a hydroelectric power pl de7y, -e da:zcv/d +yy1lxu4sa)ye9l ant, 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 d4sl +9lyxe,d /dayvceyua7:1-y e)z that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall ws 19n3ue:h gzzd3k (cat 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 bu:w j2i59lo0c6bmvg from a height 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, durin0c69bv 52mo lw:jg buig 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 whe, r;m a9h;vbgeill2t2 n carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, wh f0i1iy+/5u pygtna k+ereas this is not true for your +f0y/ainig5 tpu y1 k+arm or leg?

Show on a diagram how your CM shifts when you change from a lying position f8 5ampgeg9*e to a sitting gp e9f5a8*egmposition.

If only an external force can t.lptk*io2 kypza 8 86change the momentum of the center of mass of an object, how can the internal fo*p8yl8ko. a26pztkt irce of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly gr yzc 1n.*yrp d-vz,5explodes into many pieces. What cdr 5c,zg1np -z *rv.yyan you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed oq* x k(vp 9xp;r76clj8glh7orf $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N2hyo-1f9ap3 fa9l crc acts on a 65-kg skier for 20 s. What is the ski-a9loy9hfr p2fc1ac3 er’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive strai y*-xe6* :+ gicxazjvq 2o:atyght *yto qa *2vcj6-yi::+egxaxz back toward the 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 ak9/tr5j a0d-iuvidy( speed of 10 m/s Fig. below Calculu9j ia(y-vk/5dri0 dt ate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the x)1* wcwq*ws 9k5si ejpropelling gases are expelled at a rate o9w15q* eikjxc) ws*ws f $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback move8;(cx2xxmyr r5ll8n5l4)ij+ q gg oving at $4.1 \; m/s$ 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 alo-bnysjvw 59e4 gf 1enb- /i)vpne on alevel frictionless track with a constant spee9n1w e y4bjn-v) g5/sbep- fvid of 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 travexqb( ,g*1gtfeling at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whi knozcx izaq 2mp0w1289hr, .cp 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 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 t8ro.ckqw zcnx19mzp h0i a,22he 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 bvdkb jlxhf;lrr:26;f /0ow5a constant speed of 8.6m/s on a level track. lr;:6wv 2 r dl jhk/0oxfbf5b;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 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420k(kkkg9eq-xl2 wz0a+*4rn1rc t e l8tm/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 of0keea wtk4 qcrk1 9*ztg+lxrlk(n- 28 222 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-kg block of wood and emerges p r 6km21yl:u1aeuud( cleanly at 170m/s If the block is stationary on a frictionless surfa1e up(rd2lmuk16a: uyce when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling egvf b64w+f+(w8hh yr at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a velock d :lxm-qj(il333:npyv lxe 4ity of 115m/s To alter i v3d 3iynj4lx llq-3mp(xek:: ts course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed of 45m/s T2wbi*x497l v p5bpm wnhe golf club was in contactwl i mppv2nw 75bb9*x4 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 strikevwbnj*c +0fw:s a nail at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impu*vwjc0 f +w:bnlse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg8u:ydtg0ktz ) 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 autoouts(-uc mc3qh1gt w . 0:imy3mobile 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 m w .t iuc-oh3umtys cq(:0g13exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped ibpmb9 f 3(rat1n 0.75 s by a heaa f3b19rtmpb(d-on 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 ball (mass 0.060 kg) poi0x: .x atbo1ek9 uo;e3k dmik,nts in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use .b1kk:m e dootx, 3ake;ix09ugraphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg pe 7 wajo+xz.0lgxtq-:+n8udx frson 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 tl+do 07+.jwux axnz8fg: q-txhe 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 27 6wocmbvfg1east (+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 0.447omc6gwb2v 1f0-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 eas8 ys,uu cwsrylr tk11/8)o3 4kjqg(kct with a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object gu 3u(sk8sko1ylcr1wqy)c 4t r/,kj8 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 heafvdh cc4 z;hpr :c;7c8d-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 movi8ch c;dzrc;v p7hcf4:ng at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving 4j q* oitaeno7z**5ijkd:f8zwith 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 of each ball after the collitao *i j* qz4k:ei5jo*8fdzn 7sion?(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 ofx c1ya72krhn) 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the ina2y1) khrncx7 coming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as one approd 1f5v8x/ yc8pq6oc2pf d, uuiaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing td 1 8f uuyvc85/cpxdo,f6 ipq2o 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 col t 2sd+wfiu 3/qnf8x;hlision with a second ball initially at rest. The second ball moves off with half tfxsi/w fnt 8dqh +;3u2he 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 slide+kx775uz;qox xnl . w ;lf:yqqs down a frictionless incline as shown in Fig. 7–35, and o;qluy q:;fqx+7 5xkw lnz7x.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 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 .lnnw/z3mmf- 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 experi )ha.sjp x,i0cment, projectile 1 results in a maximum height h of the pendulum equal to 2.jxp, si)ahc 0.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kloi 2pxm2c:6h(b lqy-g pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components2moyqp:b-2l 6xi c( lh of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the frlf go,1j .-n tkgrb-5aaction 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, into two pieces, bfi 61y-: xmvmone of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, ho6iy:vx 1bmfm-w much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUVg*g4a gn,xn a6q5f5v1rbu22zg xt(qo stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skinfq4xuqraat n2x2o*5g,6 g(gzg 1v 5bd 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 represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds a+1zjx(fvrwt3b )iz+ to a height of 1.20 m. Approxivzrf(a13wit+ x b)jz+ mately how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is ttv./q+qxv7az ei xs-*he coefficient of restitution, e, defined is. xve+v-xqt7 a*q/z 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 into4m1a1jg/fj9y *sc pan two pieces, one with three times the mass of the other. A depression is made in both faces of t1aj p*4s f/jmca19ygn he cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the m 2*(.6nu u .kldgwzjz+x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find thg2 kj m*.zd.wun(u6lze 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 auzg9.xsg v, w; neutrino. The electron and neutrino are emitzsw9;. ggx ,vuted 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 mom7xin7bl g*+,ir r d47d wc cm5(agx)ass $m_\mathrm{A}=0.400$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 bet5 oaw pqxv5u.2ween two objects of equal mass, each hav.xuqw2 5o5a vping initial 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 meet at the originxu,0y2uavkf rb.fko:ql;x - -q w85by 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 baqlvow- -x,kuk.y2ax8bqur0f f5y ;b: ll 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 elasy0kfmk -f tj04tic collision with another atom at rest. After the impact, k4tj0ff y0km-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

  A neon atom (m=20u) makes a perfectly elastic collision with another atom at c;mq7 vc p7(4, gn moy4xbmj)urest. After the impact, the neon atom travelm4 ,ujqm p)xc;4v7yn gocb(m7s 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 sysfys+ v;) kkg(utem shown in Fig. 7–38. Specify relative to the le k; syk()uvf+gft-hand 1.00-kg mass.    m

  The distance between v; (8m 2qjjz/ws27 kfimtgbn:a carbon 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 os*o..0:(ucswi nvnt behind the front of the car. How far from the front of tv(ncoiwu:nt .os0*s.he 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 used as a yu +lhw*3m+cd ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine thyu*h c+3 dmlw+e CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesdo *pe6k c607gvq 0vxh $l_0$,$2l_0$, 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:jw*,yi yzz a4 cases of tomato paste (see Fig. 7–40), each of which is a cizy:zw 4 a*,jyube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2-.x 83n bxnjrgei999qfh x9f uR has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the centeqbnux 9g ni8fj.9e3xhf9x-r9r of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calcula3b5*nwsqd4g o d8c:lc te the mass of one ofnc cdq43bwgdo l*58:s your legs.    kg

  Determine the CM of an outstretched arr- q)u8 p7usblm 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 tio*3rrmp3 g5c;voj8 arm bent at a right angle. Assume t*o8tgojm; c ir3 rv5p3hat 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 legp h;6-gs29k 0r rggo;r6*-ghojrgf hc s are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Wilcf rh2 kgp-60ojro*grg;9 ;ggrh-6 shl this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon are.5/tyzvip ;l) o9kwaj: q gz0hvla;-h $5.98\times10^{24}$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 manc h80 tqcc5e6x 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 cylin3gdsfk0 ;enmb a2w6ccg:) )j 6wp:azwdrical 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 a0 bn)wdgz6f :smwc2c3pgw:)6e; kj aof 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 diamete 9 nf)aloy:hetddg;, +q:pwp2 r 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 wiepfdo t2l ny ,a)hdp:w+:9gq ;ll follow a parabolic trajectory?    d    d

  (a) Suppose that in E//dp9(y icwzb xample 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 the air and stati.cx 0ws3i7co(fo; mpy onary 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 what speed and direction37p.; fxoc0y(scomi w (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at -/efx gng2g d-strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the baegx-2ngfg /d- ll during the contact.    $^{\circ} $

  A rocket of mass m travel*s j.k6 r b-ap97z )t30xboxk9ko.boayo gm o(ing with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced w30. vou *owlcqmn1e,rith the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be wor ow0.e3mrq lu,1o*cvnried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (inckxm-vt4)ude*m 0 xj u.luding space suit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-kg space ca x4ut.0)-jmu*dxke mvpsule.
(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 ini /ogv; k:z)xf outer space. They then push each other apart.zxv o;gf:ik/) 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 (a2o w wst0l5.nce 0yi3qy2 w5obt rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the0ww.0s w3i5bq52noc2lyeyto second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a colzy f7oo f8yl-79n., tkzp3cw urt 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 theow ,7znc-t yzlf.fpy o3k8 97l locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off thev dc1+5wu. 6lwo ar x;q;kzj-s top of a flight of concrete steps 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, xv -q 6so;;5wujclzk+ dw.ra1what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40hm:dctc83tbws 2)0sd- c, kic-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in itmdc) tc-8c,cws:th0 ki23 sdb ?    m

  A 25-g bullet strikes bmtv:s4t-r9 2nhmw m4a td1m7 and becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of then7s b4rmt-mm : wv4a m1td29ht bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 x,0;xsrz.*j 3d0 e gjl3ggvtrkg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what di,dv 3eg.rr g jtg03l;0zsxx*jrection 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 wa5zu;w zrylh) .s about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragmen72*zovw3ucvo91ww w)qy j0yw ts by an explosion. One fragment acquires twice the kinetic energy of the w9)uqcvzw 2w 37yo ojw*vyw01 other. What is the ratio of their masses?   

  The force on a bullet is given by th1+ 4:bbft lrase 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 masses2umdyp rp)n+xms83pqh8 n*ag0t0 vk8 $m_A$ = 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 intok+ s hfmv 8/3y.tedtz3uw c.*7im x;nn2tbtd; an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alxefvd3 sn/bwn 3z2c+ y*u.t i8;tmmdh;tk .t7pha 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 angle of 30 h3duss3,a xo5z 2 wu7h$^{\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 slm2 z5n- o x.,gdn8uar).3 yrrczd6 kbxides down 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 lfl rm1hiff 1)/3-pcz+o ;carto rebound from M, slide up the incline, stpma o)lr ilf3 c/;zr1- 1fchf+op, slide down 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 pla:+t: us)p rnhjnet Saturn moving in the negative x direction at its orbital speed ()+rht:s n :jupwith 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