We claim that momentum is conserved, yet most mo)s: ztw3eupe5ving objects eventually slow down and stop. Ep euz w5s)3et:xplain.

When a person jumps from a tree to the ground, what happens to the momentum of te /e hm82npql;he person upon8qn/ 2lee;p mh striking the ground?

When you release an inflated but(i6* kgz7znnti 0h0tb untied balloon, why does it fly across the room 0 ( *7g6thktnzbni0zi?

It is said that in ancient times a rich malg-fum 0r v51 /jvffr 8s3+egjn 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 dmr03vrf1- 5 8l+e/fuj fsjggvone to save himself had he not been so miserly?

How can a rocket change directirb,y1di7 kpw ,on when it is far out in space and is essentially in,1diy,7 rpwkb a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, g--hump:mest72+c1gl . 2rbew4 bvna the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which therbl1n+ gm-e tm42ab ges:-w pv7c .u2h 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,.,uf7npi 5547t z,bt elr ihe-ozd*pk though, cars are te e 7ntpl.b dzr5ph5k, -*f,u4 7ioizdesigned to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hitq/+, 9j i kfleol,/o,ditx w+n a pitched baseball further than a ball tossed in the air by the batterlw xo,9 kl/f+ io dneq/j,i,+t?

Is it possible for an object to receive a larger impullkrl*q e,(g7 -nr6rcfse from a small force thanl ,lqgrencr*r-kf7 ( 6 from a large force? Explain.

A light object and a heavy object have the s3ddcst3+) x+)arhfw d.;gb tj ame kinetic energy. Which has the greateah)db+ r x3tcw+j.fd;s )gd3 tr momentum? Explain.

Describe a collision in which al; 0zv 7g9fwa3ip t+e+oo/mac8 .xfy ual kinetic energy is lost.

At a hydroelectric pow ,,1p* igtuvm,ff hmd6er plant, 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 b, m*h, mgfp6d,t1vu ife designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a w )ykc 4r0t 5.qhindum6qc3uy2all at 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 ste4xo*k7ktn*cqc j 8*znel 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 partqcxo*k74*z nc*tjk 8n s 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 leanlg3n-rd8yr;5 fq kp+m backward when carrying a heavy load in your arms?

Why is the CM of a 1k1lbge.kf *l 52m 5ggm5t.ybo-m length of pipe at its mid-point, whereas this is not true 1t5gl5f 2bo* k b .ml5emkgyg.for your arm or leg?

Show on a diagram how your CM shifts when you change from a lying position togqe:s09 y+t q j8fx6do a sij 09eq86dq xyfos tg:+tting position.

If only an external force can change the momentum of 6p j-e5h ji kzju1if b8k88z6uthe center of mass of an object, how can the internal jjij5z1ihz8 kpfu8-6b6u 8 ekforce of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly e8zp5gu. qcd9 xxplodes into many pieces. What can you say about the motion of th.d85xzu p gcq9is system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow ffm:2/x4z5 2v bbpxcfi lying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier fo pi3r z1f; s*th.u3uckqoh s ja+2c+;zf4jvy/r 20 s. What is the skier’s change in velocitfpsf z/r*ks4a jyuo+c qu+h32z.htc 1; vji;3y?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line driove4jfn z */yb7+ghe*ve straight back toward the pitcher at 52m/s If the contact time bz/he* neg74 voy* fj+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 horizot eokitl2m:x-49dd1mr/:lj t ntally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of t-2 ixm4lldmke jot 9td: r/1: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 puzj1k1z57 ak3zb 0 jpiropelling gases are expelled5z 1bjz zapiu 03kk17j at a rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving xy 2zc+s.i;2vhmzs v-1b s. fqat $4.1 \; m/s$ 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 on0sh r;e9yw ,xnu0jmj 0 alevel frictionless track with a constant speed of mx j00w;esunr09jy,h18m/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 travelis, :8 (4hc)klwa i/qq:iqg- .algighwng 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 whip horizontally at speeds o9h ew6k0bn 3dfq/omx1t-ib 5hf 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 per tm/5hqe1if93x6dkbo-0hbw nson. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of 8.6m/s l .jlf elfvqq sf 6w9) ts)cl)w68q/i1on a level track. Snow be qsqllwt f1i)c/f)v6.)sl 6f 9wlej8qgins 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 420m/s emits an alpha particl0j r v7r+sdmwpjdu2v m-6g9n*e in the direction of its velocity, and the0rp7*6jdw 9gvns mvdm+j2u- r 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 pex+dyepkk) la)4tgi 9ywq +f2e(r5 q+ rnetrates 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 f4rlqq+)e(iae 2+y ydpr)xk + g ftw5k9ast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speed of w8:oqbfsg74 t $5.80\times10^3\mathrm{~m/s}$ 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 wy+ 0e p /5/ctyycnwp2rith a velocity of 115m/s To alter its course bw/t c +y5yrc2ppy0/ eny 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:;znd+m: oyg2mk 1qm,isd zy( of 45m/s The golf club was in contact with yy1,dzm+ksd mmo (2 inz:qg;: the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocitywmi0+ 5xlq7g c of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to thg l0im5qcx7+w e nail?    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 st(bb kxbo8so-36a c0bb4 f1)tcyqksm)kpg+2z rikes 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 automobile m8dz- f l 8xeniv1u( b b6em1sovu.6cf,odels. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mphu6o 6fsb8zx.1 e1d i,lu ebv(mc8fn-v). 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 and is stopped in 0.75 eyfe/jpv1fkyn;gjn/k( ,+2l s by a head-on tackle by a tackler running due west. Calkef nfy 2v/y,e(;gjp1 kn+/ ljculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points in the +x vqf1 n sf;7zf-direction and is given by the graph of Fig. 7–33 as a functi7 nfs-f vzq;1fon of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump withouy7l m:fus( 9zpi .1yh1nrhem5t breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the br e1yf51ys:n7 m9iz h pr.(lmuheaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x 1a tow,*uc1zb8p h8yudirection) 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 bcz1t8o1yhu,* wu8ba pall 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/:h(uii yg,iu dpge 024 oek0y-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and y0:2yohp d 0eg,kugi(i/4ui e 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 ma/ s,rdefqwo u8b ,,0agss undergo a perfectly 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 the ball moving at 3.00e/ so b ,a,0dwqg,u8fr 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 2.5md:b 0v)am n/ld/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 aremdd)0/ al b:nv the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s collides headv1 vlfumu4f1g txy)3p6 3te8e-on and elastically with another ball initially at rest. Afterward the incominl1m)y3u4xgfv6f1 3 pet8 vtueg 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 elastical+pt),a ( btm9attya 9bsvxv3)ly as one approaches the other dib,399 tvt(ya +sv)pmbx) a attrectly 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 headm2b*q 5xinzhhb (lj7:-on collision with a second ball initially at rest. The second ball moves off with ha*(qjbihnh2bz7 5m lx: lf the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as show3aj t gxulmg 8p,,ft:3n 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 off t gp muxflta3,, :jg3t8he 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 of .hi6r:-6 cr:og j fuxmmass 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 yubwd-ys66uz:7 lb 8e results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twiy7 8z:u s 6buledy6w-bce 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.xl,i mirs eqih )0.w596-kg pendulum hanging on.x ih0,9il )wiqmser5 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.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kf6+ uukw-ro2 yinetic 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, initiallyrzin) l u + rp3c1 jtgavo0.vo9:9ny5lxo9)tc at rest, into two pieces, one of which has 1.5 times the mass of the otherx.zj5og 9ur9rn) c1nlvp0 otao v 9yc+:)3l it. 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 cwi :spos,6cec )5ort* ollides into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coeffic5p)e6:cooscw, is*rtient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height of 1.20 m. Apt3 u51ay;v*bh et/2*xf hc cluproximately how many rebounds will the ball make before losing 90% of itsy*b1vx tuauf lh2*/5tc3eh;c energy?   

A measure of inelasticity in a head-on collision of two objects 6iq: w/v5 jm10h oldpl)e3xmme.y0ypis the coefficient of restitut e/dllw p1)eomqih00pm3jyy6m5 :.vxion, 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 infkupk 5ze;k;v8* q n5kgb*3izto two pieces, one with three times the mass of the other. A depression is made in both 5;nfzq5 v3g;eiu kk* k pb8kz*faces of the 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 +x direction at 5.5m/s collides head-on with kxj(ks g/.0qhqn.x l5 a 10.. q.hn(s /kk5lqgxx j00-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 f9hfl-c, dbib3oj /(g; 9cog belectron, and a neutrino,dbgg-c9fh i3(oblj fc/o; 9b . The electron and neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of m*tu9ne ae.odws+,stc(ws v7 )*(/zg tk/cx imass $m_\mathrm{A}=0.400$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 collu( x 0qc*x6qpkse xn7-ision between two objects of equal mass, each having-uxqc e k60xn7qx* s(p 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 ordglk5+e7-m(pv x bhwj c+1cw*igin 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. 7–3wgkbm-ep1+ +w hj5ccd*l(x v77). 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 9ra - mt7hwg-7qu+sogv .fmx5a perfectly elastic collision with another atom at resvhsg9 5fq tmor-+wx7. 7-gum at. After the impact, 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 e;i1,+wph kfqq jp h,/llastic collision with another atom at rest. After the impact, the neon atom travels away ahlw1 qj qfpip ,h,+k;/t 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 shoz 9lv beot*,q7wn in Fig. 7–38. Specify relative to the left-hand 1b9ote7v q,lz *.00-kg mass.    m

  The distance between *a rqmy b)i(:amy:xr: 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 1050k6 cla4f6-k dxg-ep9r-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 three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kgfxd l6 9ga-kke cr4-6p.    m

  A square uniform raft, 18 m by 18 m, ofa4o7tcp omq2: mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the lopotq7o:4 2a mcaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidex9pm zh qm2bcm4+ *,lds $l_0$,$2l_0$, 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 identqm6n*g 8l3j 1mrk(q0/ej un ihical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in tkn3qj/g qulni m*e6(1jmhr08 he horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cuc,xxgpifqol3*xtd +4+ 9 ljsp + -qzk0t out of it. The center of thljc+4x-kg+l3qoq+pix9z, pxsd ft 0* e smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportionssm)nm09u; 9c + ct zu +ji8oanf.,ptqhh h1zr3 are the same as those in Table 7–1, and calculate the ma it9zq3nmasuz 0fh 8+r; 9mhcn h 1+otjpu,c).ss of one of your legs.    kg

  Determine the CM of an outstretched 06h5y n k1qtnwarm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent at a right ang ajd5 c+f8unm3le. Assume that the personf njuda3m5+8c is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position suck v,wr s/:km9oh that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will twms /:r9,kovkhis CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon are )eriazz. ed fpz,8,;w $5.98\times10^{24}$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 8 ;bwx dt7:oto+0-kg man stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a unifo:dby52w97,sbox9b sxck y s.bl /qpm(rm cylindrical 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 thebk7dms29yyp:o/sxblb .,w 9s( c qb5x 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 /x(yj )ablg-ntr);aq 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, hy/jl) x ab)nq;gtr(a-ow 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 (F5 /q+okp/8t7g czv-nyxsgl b,l7a -jlig. 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 macunc5; zejg;- zc;i;h cu l/yc 5c93awss 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 measuzcc ; c5zl-i j;ahyc5nuc3c;eg9w /u;red with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat andemw2tyg/*mag a*x .k6 xkb4s. is popped straight up to a height of 55.6 m. If the xm42kax*s k..tw6gbg*y/a e m contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m tra7jih h7i o z w)p qh/78tw/kd5tiy,s4mzc2 9blveling 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 ptvqd h5p)09y/mqoiei w0oq /.ocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this betmeqioow 0/5qd / 90hv)yq.iping a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed ofzp pm. wnk3y19fy47ukm vhk3- 2.5m/s by pushing off with his legs from an 1800-kg spacekp yfu.zyk7wnvp m1 33 h9-k4m 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,./ xpq /-3a-/kex6thmayt dm; zl.j xr are initially at rest in outer space. They thenk6 zj mh-xxaq- e..3//md p/yl;rxatt push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision wi4 mgd:cp (vgjvfp8i4; th a second ball (at rest) and rebounds in t4p i4:vgmv; j8 fp(dcghe opposite direction with 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 aha7h:-c)v 9fyi rn1r cn 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. rf7c) :ry -h a1icn9hvShow 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 verphy4mp2a, f* +;z9)on e eohjttical 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. I4f hhjt;+ep menp9a *2)yooz,f all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at res mu10xyt 2awew jofd,s. 8z9y/t 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 itz ,jus 82mfxy0y9. da1t wewo/?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg bkp)pohz3 /v wgzz,21j lock of wood placed on a horizopzv ,jzp2z/wg)oh 1k 3ntal 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 ohc4 )q aw14 prr+r i85f2kjnquf mass 60 kg, sit in a rowboat of mass 80 kg. With the boat iwpkq2q5r1+)r fu n4h4 8cirja nitially 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 abouug cpvd r61v:mcn8*aq-t4j9gt $ 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 suddenlym (pkbse7 6hm5+uweni4t7om; broken apart into two fragments by an explosion. One fragmentnsp6;w (m7 7b 5t4hioeu emkm+ acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet isz *4 3jg:5+v, yxrtrqvv8htwe given 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 massesyczf7 p7z b:dpj-ep.. $m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha particle and adq 9q o5nmhz bsv+o:66 smaller nucleus. What will be the speed of this recoiling nucleus if the sqmz:9 bq6 h65v+noodspeed 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 angle 8,s;j)w *qxtm-qbebj 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 do5 gv21hqld .lhwn 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 mpo/x6 i n9wrlz21z5ks if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide with M again?xkno9l/15 r iw2z6ps z    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–n gyym1ng ;w9-47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of -ng; mgynw19y 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