We claim that momentum is conserved, yet most moving objects eventually 3xcchh(j/b-wslow down and stop. Explain.xhj b/- 3hc(cw

When a person jumps from a tree to the ground, what )*j-vrdxu 7p xh2 zog3happens to the momentum of the person upon striking the * pr32 juo-vhx7dx) gzground?

When you release an inflated but untied balloon, 4.nytu+8wuc qpgetk -da m7 (*why does it fly across the room?mw.yq c7 gt( t8euk*n4+pd ua-

It is said that in ancient tim7:ii;yf +g bfpes a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Bef giybf7p i+;:cause the ice was frictionless, he could not push himself to shore. 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 uuf(psu w,),jd 8)diuspace and is essentially in a vacu )d,u jf)iw,s udp8(uuum?

According to Eq. 7–5, the longer the impact time of an impulse, the small 4nibtzenkhnhy,802 ;er the force can be for the same momentum change, and hence the smaller the deformatiot b n0h,eh;k8 2z4nynin 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 collisionst+ )cffj fo;/nus8fw1. Today, though, cars are designed to hav fo/jfwnf+s1fct 8u ;)e “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in the air byn-wt cg cm2p.5. om3jl ttpjg n-o3 cl 2m.5c.mwhe batter?

Is it possible for an object to receive a larger impu(jd f t7 )1v8bwk.c)zreke*pmlse from a small force than from a 7ev)kp j8w.c(d1r* bf)ke m ztlarge force? Explain.

A light object and a heavy object have the same kinetic ener0x,cgh cs )og-gy. Which has the greater momen-,csgho)cxg 0 tum? Explain.

Describe a collision bjwtslxke n,r(q0q2)w8i :q(in which all kinetic energy is lost.

At a hydroelectric power plant, water is directed hey f,phwj6;00h4 a:zj 7j iwvat high speed against turbine blades on an axle that turns an electric generator. For maxieyj6:h 40;ah0zviwjj,hfw p 7mum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall ad*egoeq-zb2 wjic km(n2+,dgz+c g)/t a 45 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixed to 0l (atjh.ixr2 qia+q9 the Earth), from which it rebounds at very .20(i ahq qxj9+lart inearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean bac: xf9ghn6u gh*kward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pip hwc93j3t7 njye at its mid-point, whereas this is not true for your arm o3j7cjhw n9 ty3r leg?

Show on a diagram how your CM shifts when you ch)7k)m hevluy:uw6r: eange from a lying position to a sitting poek 7mw:h6l yu:) ruev)sition.

If only an external force can cha18mfrrfhzsgbn,n6n s*jw8sv w7) ;8pp6*xhwnge the momentum of the center of mass of an object, how can the internal force of ann*8 ;8gz fs6n1wb78hr, fxwvsnp rmspwhj6)* engine accelerate a car?

A rocket following a parabolic path through the air suddxdd3b: xy+ g f(d3e9oaenly explodes into many pieces. What can you say about3eda(:f+9bo y xd3xd g the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow fhzp e6uoi; yh x*( o(4d,lvyca)rl0*l lying with a speed of 8.4 y oc;h)u46l,xvz(adyleo(* rp0h* lim/s    $kg\;m/s$

  A constant friction force of 25 N acts on m 87 k4;qmhkpa5o9wnm a 65-kg skier for 20 s. What is the skier’s change in velocitmm hpwm5 q879ak n4o;ky?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line d6rvqd +5e5ysirive straight back toward6ivrds55+ yqe 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 pa-bf8ay/57i6d hemhsh*e3eh yckage out horizontally 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 the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The vel-y 8f5i 3ad m/7he*ehhhb6 seyocity of the boat is    m/s

  Calculate the force exert4b ;za7ijczz ; 4lydc.ed on a rocket, given that the propelling gases are expelled at a rate of 1500kg/b;c. ; lj44z7iz zcydas with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an apparent bre9mysr o/z(z y(akaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual speed immediately after the ta9r(so(zym/ zyckle?    m/s

  A 12,600-kg railroad car ;la47b/ uv9n belh)fj :z ij1ptravels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the c jp9 1vbe) 7fj:banlh4l ;z/iuar’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a umemlkvb0 *,b(pi (2w second boxcar at rest. The two stick together and move off with a speed of 6mv0e( ub, pki*2mlwb(m /s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speeds of u9.yvyl(u i y/100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, /u( yy 9yvlui.estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car c12(w*3uhqwpxtiab .vxr2t. doasts along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of th.quvraw2 wt3b*dhx( 2t px 1.ie car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially)n,6lv, n8eguc dcu6x moving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particlel6g n,8cv,6x cne u)du have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood dl7z +r qq(x1tand emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the b7xlqt rd(1z+q ullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a spee8 3jhf33g omgad 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 vep6zj3dqu6 r p5w y-z7clocity of 115m j3w 6r5dc67qyzupzp-/s To alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed of 45m/s The golz.0:wc pjavl1gnsb; 5edg 1 k5f club wasvpd0 1blj :1z g;5. ckwansge5 in contact 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 strikes a nail at a velocity of 8.5m/s and comes to rest i/*easoqh ws 62ckz7n;n a time interval of 8.0 ms. (a) What is the impulse given to the n* 6w7a/ kqsnohzs2 c;eail?    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 striiy4r hc2*bl.osp+ b :wkes 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 dy7e/2xvd.7di7 c+lni m9pxjmodels. 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 impaxc7 vj + i.9ddlni/yd77x 2epmct 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 s by a heurk*j6ajb4,ome v: 7 zad-on tacvk,6:z*e 4rj o aujmb7kle 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 act)x pmwyk3(u h(.h0ih6hxhz -ving on a tennis ball (mass 0.060 kg) points in the +x direction and is given by the graph .3x)huxh-06p (i kmyh(v hzwh of Fig. 7–33 as a function 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 w qbbcmz+5;fcml6d7 0nithout breaking the lower leg bone of either leg? Ignore air resbq l+0dfbc6m 5zcn7m;istance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x directionfqv q:s.;c 1ts6dpuw4,1u w /fec+t ni) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, tvpe,6qu1f s f :tqdwn 1/cs+i.cuw;4what 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-0v efs8t 8qv8z5ch cz-wtw:t4on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collisv4wzq8ts: fht80c58 zwecv - tion, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly k6aif5gsda k9)zw 71w elastic head-on collision. If one ball’s initial speed 6z17skaa5w9d k figw)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 3.00 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/s collides head-on with t 4/+jwftjb6 qa 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 represent the 0.060-kg tennis ball, and let B represent the 0.090-kg /46wq bj+ jfttball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg tj zk2ff02 fl 8w0zl.vxhat is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterwardjf x lf8220kzwz0. lvf the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an 1cp uusd6 -fi-amusement park ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences indfcu- 6upsi-1 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 el zkjg .9e ib9fgii* cua*1(ip ,g*-jjmastic head-on collision with a second ball initially at rest. The second ball moves off with half the orei .aif mg(b*1* kgizi ,cp9j*gj-9ujiginal 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 zlqg-ck;i2 q3muy .d 7qt2i6 gshown in Fig. 7–35, and elasticall 27idcqk- z23t q;lu.ymqg ig6y 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 ,2s+qle)j1 8sc2qaw so7ljhoof 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 experim)9 xihm/iof i-(7ktsta lf4v6ent, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swinfatsio/mf67v x(-hl 9 i4it)kg twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg pendulumvm4eujhos s6)1kb.t 0g tia; 2 hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine thi 04o.;t kshsg2vutbja)6em1 e vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the -;fpd;y,-fj. pymlmq fraction 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, oqv a,wi 56lsow*6puln1xq;:kne of which has 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 l 6n ,l k qvwu*qsapxli;w:65o1ighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the l (gysa7o . 2zqhqlm 1u8v2fo7rear 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, lgv ol1u7 m yzhsa7.(qo2q82 fknowing 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 ren-x lol8f+ 8ivdm t,,ubounds to a height of 1.20 m. Approximately how many rebounds will the ball make beix o,n 8+lm, tv-lfu8dfore losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects isftoe(2.4fmd61fueub2a84eqi; v p yy the coefficient of restitu( pemo 42teiq.8d f2y6 vuaeuf;b1f y4tion, 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 mass of;pr63 :l0hzh 1cwuy7qw )yove the other. A depression is made in both 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 blocly ;cy01w7pewz r 3q6hovh: )uk travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x 94lf q2 dhtv0kdirection at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass if: h 94 0lkfvtd2q
(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 ele x vpdp0qh0pnt0s7kh5r8+ y u+ctron, and a neutrino. The electron and neutrino are emitted at right angle+d00tph+ 8vn0 qp5suk ryxh 7ps 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 massuia 4mbl0cr 8) $m_\mathrm{A}=0.400$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 c;ztmzl3+ 3 gj9awg sf (;v2vuyollision between two objects of equal mass, each having initialv(+; 3fyj9m;u3wa2g zztgslv speed the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mg3gxt sl,u9gcb(0 dxfq,w 31n9pw5t lass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumedt ,uxq3t(9cl,3gpn0gsx1w g dl 5f bw9 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 collision f/t cj d;u:/yv*: kzdgwith another atom at rest. After the impact, thezt /g vc*:dd;uk y:f/j 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 md,6ilch u:*mb0wk nutd: 2mqt 21qhbf/( -jwa perfectly elastic collision with another atom at rest. After the impa/ (hb-2tw* mlqcfhub n du 1iq mtm0d:2jw,6k:ct, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown inygoksjb w5 4e gyayo:s-94- t; Fig. 7–38. Specify relative to the leb9oyss o:4 -yeywj4-a5kg ;gtft-hand 1.00-kg mass.    m

  The distance between a carbo 2b;h9hc4 xmnjn 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 4kjd:g bg(e6k( 4z2ap2o-hrv8 mukhs 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? A a2 2(md:r ukhgsopjzk8-6gkbevh(44ssume 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 ferrym14k(n+u m ;m m ml+.fmmegi)hboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, n m m14++mgmi.(mmek);lufhm determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidez/hwiy9mv0x7,zwc r , i-h*fms $l_0$,$2l_0$, 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 ad- -,n0hdy0:bxkj 9 qmqx3gd- 3 ldvkFig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that thehkd0d-3dl - x3qd, :a x 9nbv0gkyjmq- 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 o/ ry dmsb v lw/le1:)2/qqojr-f radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of r/e1w-l qqyjr//vbsl:)od2 mthe 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 those5n0 w8 neh5wq2drt8e6x14o 6zvdvt0o+juwf j in Table 7–1, and calculate the +rovf 5o4e8 h6tewtn vnu 2jqj056d0x8wwz1 d mass of one of your legs.    kg

  Determine the CM of an outstret4qgbe9cve apkeqg3+f+m4iyl 8) a -( kched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm ben31 ,m 4bvi8rbv :wjgdtt at a right angle. Assume that the person is 155 cm tai,b:t4b 8mdvrw gj13vll. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs ar9 aff 0v6+3xdzs m vm21,wpy jue.y9gve hanging vertically, and his trunk and head are horizontal, calayvf9uefswjm vd +zyv6mp 9 g,0x123.culate 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 ar-tiw(+wfd6v 3) miblnu t:-pnd 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 on friy4s4kjzhq40 0 vs- zshar z(4ictionless 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 cyi0pfsj /gq/kf8f *pih0; c+va9e bcl1 lindrical 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 bottomqh vifes0*f+1gi/lfbjppk a80;cc /9 of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform 1 *51m1tit cp,xe vbcjcylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handlec1*btp m1i 1,cxt5vj e of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29)p+z(pc w, ; d3ukgumf), $m_{II}$=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 gondolag5s +j-8+ ehry xht p1n5fww*1pltsu8, of mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down5hg 5l8t y+ es8srf-w+1pxhp 1 j*tuwn a rope with speed measured 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 p2-toz lfk.j g5itched horizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact tim g5f-kzjtl2. oe is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with spw4uo */)f kgw*u2eahgeed $v_0$ 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 px/brr tyq9 +ly 5,r9y)-m bidnevh1 c3ocket shot shown in Fig. 7–43. Relative dimensions are y ve)trq+51lcyi9, b3 ybn/ 9mdh-rxralso shown. Should the player be worried about this being 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 of 2.vgm wzukl.54) o +:qdsc zlne z,bn:295m/s by pushing off with his legs from an 1800-kg space cap+:eu:2sg9wq 5odzbzlm.)z ln cnkv,4 sule.
(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 9 ;bd9zvgx2uq initially at rest in outer space. They then push each other apart. How far apart are they when the lightergd vu9qxz b92; astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elakjs(nl 1seo.)r7yr e3wdvopaw0 m -5-stic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to onea3m5koow1.wy (70-lvn jd-erersp )s-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 8,ux0; e)l xrbumxtpk l 356zswitness 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.)xz; mll pxer,6 bku 5t0x38us 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 applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete stk ykbgnjp-4r1wu 0l*g6 j 2xv7eps 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 bal-6bjynj gkl 7p1g2kxuw0 *r v4l reaches the bottom of the stairs?

  A bullet is fired vemjb7l sn 3s+r+bb5u79hrrvr .rtically into a 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0hs3br 9ujn7l svb+rrr 7 +.5mb 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+ e d3w7pmz9jyov;2gh7t; ubm 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 bloc7pdt7v;o e mwj h;m+23gzby 9uk 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 krr/su1dkf3 3xg, 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 direction will the boat move? Tf/1sku3 xr3rd he boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass y8or*-6* du : nrd kafcwpcj48was 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 fragments 1 dx2a9q tjz+qby an explosion. One fragment acquires twice the kinetic energy of the other. What is the1 qx+ j9qadt2z ratio of their masses?   

  The force on a bullet is given by the formula F = 580dw5az gh12,8cb(ijtp -( $1.8 \times10^{ 5}$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 massesow7g m.+roa/t $m_A$ = 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 radinzw s f-v)/+tbwmkq6e2z z:x5oactively into an alpha particle and a smaller nucleus. What tn mwz/6: +-bz2e skv5qwfz)x will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired (2aqf1z rco5kb:ht; eat 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 a 30./b34 ;qsrdb al0 $^{\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 ts m dv/ 9jhvtgn)g:9l-o rebound from M, slide up the incline, stop, slide down the incline, and collide wi/l vsmj)-ndt:vh g99 gth M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. F;c,msr e+r ycug ;hdrb;)3 zo.igure 7–47 shows the planet Saturn moving in the negative x direction at its ory ;3ru.c,ogch r+ ) rzedb;;smbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s