We claim that momentum is cozvtd:hu99 5avnserved, yet most moving objects eventually slow down and stv z9v9th5 dau:op. Explain.

When a person jumps from a thd 41ou ca43 3x,mbmtuhcg9; wree to the ground, what happens to the momentum of the person upon striking tgmt43;w4xhdcou,9 hmc3b1 au he ground?

When you release an inflxu m05ntd qig 6tez70 /bsa/,dated but untied balloon, why does it fly across the room?nq,gi6/meztd xdtsua /07b50

It is said that in ancient times a rich man with a bag of gold coins frx7 epddld8 b.afu.6xm).dri +r6*neloze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have drpdx6 ax fe8udbml) rei n*..l+ 76.ddone to save himself had he not been so miserly?

How can a rocket change direction when i4/r 6eh fbgk,zqh o ox66no t 337rp-m4savq*mt is far out in space and is essentially z6x7h4/brkmnfg6mv-3*pq ho36o,qtra s eo 4 in a vacuum?

According to Eq. 7–5, the longer the imptbx4a,en9pm7od:k 8 d6x j ztalo8us7m5. ja8act time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the defo, m .t4pox 5z8nlaaa dxeu77bj68j mtd:k9so8rmation 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 withstandkyvh27en : gk4 collisions. Today, though, cars are designed to ha4y n7g h2k:vekve “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pa5ty zvlxx0-+ itched baseball further than a ball tossed in the air by t 5ylxv axt0+z-he batter?

Is it possible for an object t0h4dwcco,v h) o receive a larger impulse from a small force than from a large 4vd)w0cchh,o force? Explain.

A light object and a heavy object have .qpi0r-3bbhy /ym 9cntg2 dhjmruh2g9/r6 - gthe same kinetic energy. Which has the greater h0gyj/ q-2 i9 .ht6d g-m29bhrurbmp/r3 cy ngmomentum? Explain.

Describe a collision in which all kinetic eb ,i( wo,a3kgknergy is lost.

At a hydroelectric power plant, water fl5d/d 5 :sp4zvxwjltx )z* a e*ate(8is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum poxalte:z/f*s*5(x) l5 dv8ewd a4p jtz wer 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 ai+ ,v;c+5 dqpbzx:xs xt 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 fro9f i msnzc491e3 o0hadm a height h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of 9a f ze1s i3940ndchomputty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy loaoudk:j 0)fkd nx (n-lr g2z1k;3fvcn,d in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, wherbpc5+fmw f .kz h0(( w7lki4omeas this is not true for youk0+ mw( b4hm.c(z7ikwp lff5or arm or leg?

Show on a diagram how your CM shifts 7yj j u+/7oglg70wqmtk l+ n7pwhen you change from a lying position to a sitting position. +p nkm7glj7qou l+tw7 07gj/y

If only an external force can change the mjl wl(h nf84j 0mz;y1ds3k 5thomentum of the center of mass of an object18t ;4nw lhjkzfs 3ld(j0 y5mh, how can the internal force of an engine accelerate a car?

A rocket following a parabawg;0)yj+ct t7/n rwuolic path through the air suddenly explodes into many pieces. What can you say about the motion of this system 7untwyc at0)+jw g;/rof pieces?

  What is the magnitude of the momentum8n v8a -h/7 khnmiljd3 of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 1 ch,)x.ieovxm 0:fh a25 N acts on a 65-kg skier for 20 s. What is the skier’s change in veloce fi xv1ox:mh0),h.a city?    m/s

  A 0.145-kg baseball pitched at ud(x ocz)ekvq-) g c7(39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time between bat7)-c(qov gxc( )zde ku and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a speed o4nu;apq*sn:kj26p fq f 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The f:2pajnqqkp4 6u* ; snmass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases are expowj 2p9.zgy4yh 23uyt elled at a rate o.j22gpyztouy34y h9w f $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movin.cz2xo8j lr f4,nh. :5vmfuo og at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone onpp5ja+ qfc0o7zvb+0 ;c7 efkn alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. Whab0c opznk + fce+fj5vq70a;p7 t will be the car’s new speed?    m/s

  A 9300-kg boxcar travel 1 il.m3+1a+yqsun,v:. yrh4 uispjlt ing 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 of 100km/h;yej,h 9jfz87 xrczr80 5mb ry If the air strikes a person at the rate of 40kg5rx7yfr;myb0zjj zhc 898r, e /s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to 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 8uo3gs 7e0s:ay .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 3s7uye0:oas gthe car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving atown9h9/p (udq 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,d(q/h p9un ow9 what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a q:cz pa3)a )gx7;u:mx jp 7jkz2.0-kg block of wood and emerges cleanly q :upzaga)j7x 7c3)j:mx k;pzat 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling a/0 c( v;yw5s2i hajhsk e0wzy7t 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 injeknl.3qm lu63f7 d*k outer space with a velocity of 115m/s To alter its course e36f nl kkj*d .ml3qu7by 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 0.5g3cp y;vkviq /vy3i, 045 kg is hit off the tee at a speed of 45m/s The golf club was in /qiy, v v;kvc ypg533icontact 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 8.5)ivvy3bsbp5(i6pq 341k qhram/s and comes to rest in a time intervalq k(65 sbvy4b3)iv qraiph1 3p of 8.0 ms. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of masi p vyi4)/c,fwq. v 5hxlc8j9rs m=0.06kg and speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthinmw 28nulw r f+2)nke;aess of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to reskw+awremn2u)f 2 ;8 lnt. (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 runninw8l:c6a;bi olw 9y du91 a.snxg at 4m/s to the east and is stopped in 0.75 s by a head-on tack98ldy cnws.uxo ;la w1a96:bile 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 ba4rfj 8n9 6a9ejg9yox kll (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. U48yj 6rfgnae9xj9 o9kse 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 d2taikx7azc . 8 wl.:bthe lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distawltz d7ikx. .ab:8c 2ance 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 (oreb/wf 0250q7xdii8/i xwm8 i sn.lx+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B re q/02dx7sim efn8/ .brl0ii5 iwxxo8 wpresent 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 collision wj4mi h/e0gg.tf.c3rh ith a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'3f t4.0rgg miche./jh $_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastim)( e*o a-seme6m3zvo c head-on collision. If one ball’s initial speed was 2m/s *e 3-a( eez6)vmommo sand 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/sfg9.6-29.rakcpd2c h u gbyuq collides head-on with a 0.09.29-y6p2 q ca9k h.rgfcu gbdu0-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 ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.osii w kk1fj5wtt qpo+hwmvk1j8) 6r:j5a332 5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speedo5 k 5s33kwp 6r+iww12qtim jh v:oj1 kf)8tja 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 ambsri x 72u87qrusement 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 in passenger mass. If car A approrixs qr 8ub277aches 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 collision with a second ball inh: cn 7oz99b7pc-d buiitially at rest. The second ball moves off with half the original79: pchnbz -o9c ubid7 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-lv4b4/ akkj g incline as shown 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 the floor, where does each cube land? [Hint: Both leave the incline moving horizon4kgj a kl-/v4btally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object ofy3ecop qy.9t3kl3x 0io a7+th mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, project; fr7zo) u9;fy9oer* uvxd6wgile 1 results in a maximum height h of the y g9*;wr7zveurdo9)u6fx f ;o pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg pendulum hangin 5dm6 d7w8r7 5 9pfqeal1lrimtg on a 2.8-m-long string, which makes the pendulum swing upwardiedrl6a m9 fp7t15 rdlw57 qm8 in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for t3qz5:ts,/ ) xff;qherj mjm:bhe 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, 2vmai6czy2ot 4 va a6 ne*)md*( gip0jone mnt2i eaa d 0ji6yg*oc4pvz*mv2(6a) 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 lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV:xfbpek9 i*9a+bl x 7donj-m5 stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates temb p7k9fa 5b: lx+j9nox*i- dhe 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 2zsaf sm*f (lm+ )cd1hand rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its enecmmhdf 21lfss(*) a z+rgy?   

A measure of inelasticity in a head-on collision967jkcpxgu20mb6 bmapom h,( of two objects is the coefficient of restitut6mp90um bp 2,hckx 6gmb7a( joion, 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 piecesgapm.uc )6lc2 iqro36 , one with three times the mass of the other. A depressip) cg6roq3ulcm 26a.ion 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 block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the + oup4df ;(po)+t 3mdvmx direction 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;p( 4dftvoom3d m+pu) 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 nucleuhdyvbmg;mqq.( : q34ns at rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and .hgdny m;qq4(:3qbm v 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 mas/xv) 98laoa6zs 7 iwkms $m_\mathrm{A}=0.400$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 coll idn3x6vi74sqd bv 29cision between two objects of equal mass, each having initial speed the two move off together with speedv32q vdbi n7sci 9x4d6 v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of eman j1qc 9sprs y:f*1v,7cs o7qual mass 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 79,*sc1joqfprn 7mayvs cs:1the 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 collision with another atom at resyqzq,q r9si1;( h0 a gpkf*s-x,*xj+mqulm 6ct. zlr0 *p;y,q*aj h6qk1-u9c,xsqifmmsx(gq + 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 elastic cbgdy+cvsr ;5.ollision with another atom at rest. After the impact, the neon atom travels away at a 5g.bs v5; dy+rc5.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. Specify rel6xbex89ukr6 yative to9 be6y68 xxkur the left-hand 1.00-kg mass.    m

  The distance between a czn:a -rp.a+g sarbon 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 ic r0m,5f5b5yg xfky4gs 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 k yggm,455ff0 bcx ry5car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a ferryboat. Ifq b-v;b:yz */zgz+3yu1 kppli three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded k*u g by;p yzlv3p-/:bi z+qz1ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side :byfexb )t4a3h4k / 6 wfwgzafrx)1y s35*aess $l_0$,$2l_0$, 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 ha:2 0vuqhocsd6vq t4g5s a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator 5cqqso46g: hv uv2dt0 can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a i 9mgw0x3y q;t 2hv8e*rg6s sscircular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [8se6sqm2y i;03 g*9vwg trxhsHint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–/dsuixka *pmz 1*pl7ktc83 2 h1, and calculate the mass of one of yourtdp2skm * 8k puz3la1ch/* x7i legs.    kg

  Determine the CM of an outstretched arm df gjr (,/ )0z*mnolazusing Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the posionyzqqf;qvz84 ; g-is0l)8ai tion of the CM of an arm bent at a right angle. Assume that the person is -;;)nvqf za08ilqgqzo4s 8y i155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a pwi12) 8z7kbozsajs)s b4 je)l osition such that his arms and legs are hanging vertically, and his trunk and heasl sj iza) b7kz8 o)e42jwsb1)d 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 Eav) fkbvw -zw+0rth and 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 stan0 0ol2tc3qjeld 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 uuj hi:(jt( qg.c. k,wtniform 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 showj, .iqktc(t.gh (:uwj n 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?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a ngany0 )ertg(u.sh:1 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, intu gh:en.g 1sry )(atn0o 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 s7xnix,bq: o9)tu3vo 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and stationary wit4w2u htm me.fz),lhr x:zr7h+ h 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 direction ( r rmm:u)w +l he2f7t,hzh.xz4relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is popptlf(22/0htb2nhpw(h 1 k dp /ev xpx-v5(zepied straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average fort0 wxh/hkp5e i( zf/2h2vn2vpl-e b(p1tdxp(ce on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with s+jg/barwt d625hjk* xpeed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown in Filtigc x-nd 6bq0* bq7/g. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will - bibnq6gqx0t7d*/lcalso fall into a pocket? Give details.

  A 140-kg astronaut (including spa,mk 5d;8thwyrojlq g3zb 2 (b4ce suit) acquires a speed of 2.5m/s by pushing off with his legs lgj;rzw8omb t 3 2(b4hykq, d5from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and .8 i7ir:oi85ji.n e:0j b nh8jtvhbpnthe other 80 kg, are initially at rest in outer space. They then push each nv 0nh i t:o j5pr:ij7eijh.bn ib88.8other 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 with a second ball (a7b:xyk e) 2jghbth 75qt rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. W7 hq2gk5 ytj7h:)bexbhat is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness ib* 4 -yr1k whep48xqetn a court case involving an automobile accident. The accident involvedk4qhte1 *-yrpw 48 bxe 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 applying the brakes.    mi/h

A golf ball rolls off the top of a f688u xhw*njg0m ldi.z light of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a differ 8z*.0gmindj8xl u wh6ent step 1.0 m lower. If 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 verticaedy1o0h 8gorz)c 1o1g: s4g1utg1 dpolly into a 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high wiyogs0g4dceo )o1r1h81 g:p gtu1 1ozdll 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 oub zp /844ltx 1o.mqn :rkeoh4n a horizontal surfacteoh4pbu4qn ro k18:l.xzm /4 e just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowboat0 sg+n wtfykx v0w71skrl8a-2 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? The7k- 0ws 10y+8f tswlxr2vkgan boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass wa(g/pmz5n d z5z(5yg7u hvo-eus 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,y tja 4pfhd0+ by an explosion. One fragment acquires twice the kinetic energy of the other. Whay dt4a hp,j0f+t is the ratio of their masses?   

  The force on a bullet is given by the formula v )qq7t (fq)vjF = 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 massesir01k4q rgpy - $m_A$ = 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 anczq g/ku*uaw* 0gm8; nd a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha 0nw*qza8ugug; mk/*cparticle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angle of 30 *)5mgq t oy3h 4j4gkjbsuas,xo, g/w1$^{\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 donewi t50.kd x6wn 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), wjjza w+s8kid)8 4bcf/hat is the upper limit on mass m if it is to rebound from M, slic88j jakzb/difw+ s)4 de up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure r+2l xcq.fxt*7–47 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 Satu*xcrxqt +fl. 2rn 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