We claim that momentum is conserved, o.qr h vbj e5xsru-(k- e1aq3dpsc4 98yet most moving objects eventually slow down and shr3poucj v15a9e-qsr xds bk-eq .4( 8top. Explain.

When a person jumps from a tree to the 4+t 3ygq7mxf bxq2c0lground, what happens to the momentum of the person upon striking the grox3 7mq+qb fx4g2clty0und?

When you release an inflated but untied balloon, why does it fly across the rozy29/fpi uia;w) 2odd om?f)w 92 ydz/idi ;p2uoa

It is said that in ancient times a rich man with a bag of gold :+cm :e*yzlaq /bd1 phcoins 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 sav ymdche+ 1 :zqp:a/*ble himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is ess xf* 1:6shl6enybuz*: kr o lwwo/.jt2entially in a val *ewsko* fw 2h:tnyj .u/b1:6l 6ozxrcuum?

According to Eq. 7–5, the longer the impact timiw a fa*g k6rar)5 p6i05qky1ie of an impulse, the smaller the force 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. 5a1 6wqagry r*6i0ii)fpkk5a

Cars used to be built as rigid as possible to whgtm): zn3gmis n8 k47ithstand collisions. Today, though, cars are designed to have “crumple zones”8nmn4g)imsg: 7khzt 3 that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball fu:ogqi8+uiiyz:+f 6sg rther than a ball tossed in the air by the batter?: :zugsq+8ii o +6ifgy

Is it possible for an object to goj,z2cby/3g e;vem 0 receive a larger impulse from a small force than from a larg0e gc /vejy2mo3gbz;,e force? Explain.

A light object and a heavy object have the same kinetic energx4qis 1r:s.aylzm , aum0r+ 3xy. Which has the greatr40,sxm:s1q+3ya. m rzlaxu ier momentum? Explain.

Describe a collision in which all kineqidb .x jl+aol:18d(t f.u d/atic energy is lost.

At a hydroelectric power plant, water is ic m/c /0msal1directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, sh lmc /a0c/m1siould 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 a6he:z8 f.:qk;yldrw x wall 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 ta54) yzk;zffonto 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 a4 );aztfk5 yzfny part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carryix g,fiys7b(r.ng a heavy load in your arms?

Why is the CM of a 1-m length z*yu p4,*qk .de lqk rv7cuz;w( zw6(uof pipe at its mid-point, whereas this is not true for your arm or 7q(uk 6.r zu*dqk ;zpuw4 *ze(l,cvwyleg?

Show on a diagram ho) ya- :skoit q8ktq, hs0xd:jnm:9q1pi( (hekw your CM shifts when you change from a lying position to a sitting positimkoq8y t 1q9ds-(pej:,s):h i ti0xh( kk: qanon.

If only an external force can change the tl i4xmes0ootv8,r 66e c-s+dmomentum of the center of mass of an object, how can the internal force of an 8t6o+s er,ixsv e4mldo60-ct engine accelerate a car?

A rocket following a parabolic path through the air suddenl ewpxoaa by, nn:,g7lm5lnm x,*5y-y4y explodes into many pieces. What cag y5 7o4-nn lln,:y aemaxpwx,ymb*5 ,n you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow z6x1 4,gmxj4b2m)d )sf jbco vflying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 jtpg3t(6q oy6 s. What is the skier’s changeyjt(g3pq6to 6 in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizon()endg* z :uigtal line drive straight back toward the pitcher at 52m/s If the contact time between bat and ball* nie)d z(gu:g is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a speed ofu tb,dkb px rh*0sv51* 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The 1shb uk5dprtv*0*b ,x 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 propellk,/;ptir 5(+yqwit ccing gases are expelle tc5 /+tk;p, iwqyir(cd 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 at m(6, x +bs5slv h;fewc$4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless b lr1ls0tmw9ecb+ 7e9track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What tce9 wsr9l0em+b 1lb7will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at s1mmb+ ,ux-pl $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of 100km/h bm(i;i4 co qp5 (4yqaoIf the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the fo ;qy4ao 4(oqi(pbic 5mrce of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts ay)oy9:*6rqiq)qsx*m*m:gjcv7 l vez long 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 Ignolvmv)s **:i: y) e79jqmqr *zc ygqx6oring 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 agsyq0nt8p c:p b.sk-3lpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, wt cqn38ps - 0bps:.ygkhat 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 49qhp4x rg2zc and emerges cleanly at 170m/s If the block is s2 pxgr4 4zqh9ctationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at aque4,k zfgor.)v-d 1 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 wsz.qo eo erp98 t. )o/n1ofr*nith a velocity of 115m/s To alter its courp.r.oeo*9qf) o8 zr/enot1 nsse 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 4u1sfalupa*7n r)b3m qk n5/-u 5m/s The golf club was in contact with the a1uu7b3l a ksqrm /p5nfu*-) nball 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 velocity of 8.5m/s and comes to rest inxy k4x1ox/7yh sdv:0e a time interval of 8.0 ms. (a) What is the impulse given to tyv xy xek:7odx410/hshe 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 strimn -d 6qhqfblnv+ 8o33sp/+qikes 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 :8dfk+a/u 8u- vs.1d by-rv0cvax psdcrashworthiness of new automobile models. Cars are tested by smasavkv+d-sd xcs88-var.fub d:1u/0yp hing 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. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at1lzpknlp j)w2 6l m:v0:eldm6 4m/s to the east and is stopped in 0.75 s by a hean: j1 zlkpl v6mpmlw2:d)l0e6d-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 (mad/i kyb+16 nqz e1ry+t6 0oyhkss 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a funyzqyhrnd6 i61+ b1yk/k t eo0+ction 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 without breaking the l;c.j qumy8i a/3+glilower leg bone of either leg? Ignore air resistance and assume the CM 8ic;li3lja/yqm. + guof 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 (+x direction) with a speed of collb g1k,-l+mye b746szn7 rqpxlides heal gm1rpbly -+n4sqzx,b7ek7 6 d-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-on collisivm5+x dfo8bg;4l5 ky yon with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of ogy yk 5 ;8lmfv54b+dxeach object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastic head-on collision.)tm3jr ;hp kl p4h/;lijyt;,e If one ball’s initial speed was 2m/s and the other’s was 3m/s)3emryjtpl j/p ;;4hk, iht;l in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s6 vqk:6l7r xwi.2lju f 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 collision?(Let A reprv7u2.i k qll66r:jwfxesent 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 xg08fpqa7l gte h8q a3de .6/jwith a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming /tea6 fjgqx3 808 e7dq.ahplg 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 approai. lkvpx91 x57atfx(o ches the other directly 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 appavxol9kpft7x(x. 5i1roaches 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 col49ujx6zk,a qmq/ at.q2 mmm,olision with a second ball initially at rest. The second ball moves off with /qk zu9ama62 ,mm4 xqo.,jqtmhalf 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 oi0j)hl-v s)2 4(v, qgdur eyxdown a frictionless incline as shown in Fig. 7–35, and elastically ivojqy)hsx( ru-,02eg l4vd) 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 an object of mas ( dx*y4(tqvhr( 0wtebs 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, projenvs 1h4udc -w :r:bp9xctile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the cprh w9n-1budxv :s :4pendulum 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 itselhby+9r0vhh *t fa 151km5gz jjf in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swin v+bfr1 m10khhj5az*hj5t9 ygg 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 kinetic energy h8ykd7 f34/z wpfuhu .bsgkg f76 t7n,lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosionoh.*f 48w8y ny8zfm mf5vyac2 breaks an object, initially at rest, into two pieces, one of which ha58 wfy*v.zh8com fyf4am2 y8n s 1.5 times the mass of the 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-kg SUV stopped at avr w2r 8;,)c 6eng:kozioh0cz red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police of:kzi cn c 0o),2oewvg 68rzr;hficer, 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 to a height of t qj0(7ffw3 ls1.20 m. Approximately how many rebo(fjq t7ws 30flunds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collis u)3btj a;i26rvlhh9mion of two objects is the coefficient of r l)muvahri;t 93 6h2jbestitution, 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, one with three times the ma( ar;gbn5u14 5dnceboss of the other. A depression is made in both faces of the cut,b4n du5ogranc 1(5 ;be 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 d 3srn1n jcdq ush0) /s78 6:yghy5fxqqirection at 5.5m/s collides head-on with a 10.0-kg object mosgdy:fn)sq0n 83qyr q/h5 s 61cxjh7uving 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 rz dikyz*nwsn) 04;pe j7.w 3laest decays into a second nucleus, an electron, and a neutrino. The electron ande awki*n4.z)wn;l0 3y7 j pzsd 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 mass h9jz7g(1ke sg $m_\mathrm{A}=0.400$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 betweps ,s;mfs jrh1h(xq 8z2f 3is.en two objects of equal mass, each having initial speed the two move off together with speed v/3 What was tqh zix281,hsf(s;spr jsm3 f. he angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal m fwd, c.b7zymy y;y-v5ass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward .yy 7-5d mywfzv,c b;yalong the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? 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 collis /iy-s etb;ab,m5xdq-ion with another atom at rest. After the impac xbtq -dbi,sa-5e my/;t, 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 elastq9.xq.ahw3w a ic collision with another atom at rest. After the impact, the neon atom travels away at. .qh3xqwa9aw 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-masslkcy4xrg z2*i -crx8 7 system shown in Fig. 7–38. Specify relative to ic*y42 zx8r-rckg xl7the left-hand 1.00-kg mass.    m

  The distance between a carboc,1yzy-l19 lth 5 r y lq/9c4z(dipfqsn 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 bet q 6u2v1uog7zhind 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 froutv6zq2u 1 7ogm 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 feuka9 *up0ss,irryboat. If three cars, each of maaik9 0*pussu ,ss 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidel/ f+g;kvh) g0s+thptbnh l. 2s $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of tomato paste (see Fc7gj0+svog/r9cpxf (+;p e+t q2 rq guig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that+q9(osgr 70;2g+reux/ft pqvjgp c c+ 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 q)q27 msbj5tf8xreklb7; u. pcut out of it. The center of the smaller circle is .bb u75pr ek fljmq)2 ;7q8stxa distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1hx0lgkl;6.d 2yf2i u v, and calculate the mass of one of your l.hxd2y ki gl;6l0v2u fegs.    kg

  Determine the CM of an outstretched arm usinggo9c knur i;,lt qf44( Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculayjn.e, ; -nsmqfar z9k:b3+: sx8uxjc te the position of the CM of an arm bent at a right angle. Assum rk: 8 x,q +snues.ya;x:j3bjmz-f9nce that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in *x r/axvhs4s 0kz96qga position such that his arms and legs are hanging vertically, and his trunk agssz6 09/ kxv4*qrxahnd head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth anxi8za7v6 y t6fd Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart oapln; h.f6h s.ol/m a1n 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 un2vd )4hvczm2g (z)s4dgkng;t iform 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 gzv)(mtv c g2sk)hzdd n;4g42 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.t/ /nb+i0bmz5r a o;jq00 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. 7–42rm;bob +/iqt 0n5a j/z. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–149yva:vjk:9w,is811d qhpt eq -pf sj , (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 theihff+ 1 ,sv;rdeeu1t9u(m ya6m0iefn/i f4u( air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and dirf6rfi+ma e,f/yms( ei ef;n (4u h91ui1 tvdu0ection (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizube)e jcx5 )xwn-e o7k:zl7:lontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contaco)lbejxc xk:)e 7e:w7 u 5lz-nt time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travelinn3hm(qc.uj3 pg 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 wp gutd*t )u:)i4z7e lbith the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratc7tu4izdtue ) pgb*:l )h shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by pushing ymc-1l0ro e r 98o-fksoff with his legs from an 1800-kg space caermoc0k- 9rfys8-lo1psule.
(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 apv 2g+p wb5h b08eoga5t rest in outer space. They then push each other apart. How far apart arebo a g2hvb8wpp5+5g0 e they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collisio8::iupwj n sd71cnmn 0n with a second ball (at rest) and rebounds in the opposite direction with a speed equal to sni pcd: :8n7wm1jn0u 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 witnejhrno kf;8 )t 9ap2hcfz94.f zss in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before pzk 9ht r9 a2zhfj;.)n48f focapplying the brakes.    mi/h

A golf ball rolls off the top of a flight of concretkmd)n: +2dggls:h 5 xve 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, what is the bounce height on the fourth bounce when the balv:mg5xsd+:l2n )hk gd l reaches the bottom of the stairs?

  A bullet is fired vertically inoibev 9lpx28zk ,f, 8qto a 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.2z pq9,xfikv l ,b8o8e0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood placed onhc 9g;rw)d- y*u)fpjq a horizontal surface j jwh uc*gf;)q-y9 )rpdust in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowbo*fc5 2qp 32jva:lqpk hat of mass 80 kg. Wp2 fq*aqc 2h5kpjvl :3ith the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass wo rt v0/13zuskas 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 twovg(c5f 9g:q5hq4gd 3egx *lmi fragments by an explosion. One frfeq5q h3g *l(i x:5 vgmgcgd49agment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the ujs f/*8xkyev/al:3nformula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses q:) s,pjo o0,cke -y)ka612 jzctpvz n$m_A$ = 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 r(q* pk0yex d3best decays radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the sd0p(*xebyq k 3peed 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)9x7a44uh cnch7ungu 3 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 a1i1r ,bfd2ssp 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 ismuyaw,19 h n(bwy p:oq86sl1 b to rebound from M, slide up the incline, stop, slide down the 8lmu9 :(6bys,woh1 ynap 1wqbincline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. ,x /p0og*hp .t o)bh,kdu)g rlFigure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the o/.*th)rdg0 b )kxh ,o,guplpSun) 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