We claim that momentum is conserved, yet most:6wp +r qhw32i .wvrr1 ydtlv: moving objects eventually slow down and stop. Explaiw:q+: r2p1rv3vwr.ytd l6w ihn.

When a person jumps from a tree to the ground, what happens 8 /veiqg;(exn;a q oz9to the momentum of the person upon striking t9;8/(eovqe; axin gq zhe ground?

When you release an inflated but unticp g,jfml 7 lvqgvp0bp*p* rd--s438 ted balloon, why does it fly across the room**0tqg-pl dpjrg8c7mv fp3vb- s p4l,?

It is said that in ancient times a rrh5g5t h ,/qglich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he c,rq lg/5h thg5ould 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 o*y 6wrca*1ybmwcrqb99u 4.shut in space and is essentially in a vcq9h r*9cr4u 6msayw w*.1ybbacuum?

According to Eq. 7–5, tgcjetlx i2x- 3vdw)k(ka0s +)he longer the impact time 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)t x a(3xj +0k-edgv l2iskcw) 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 ri/-bkar5sjjwx : 4x,uxgid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage a4xx sk/jrb5 wj-, x:uof this new design?

Why can a batter hit a pitched baseball further than a ball tossed in thf6zi c9bsp5q;2 mxla :e air by taszicxbm9 f :pq256l;he batter?

Is it possible for an object to receive a larger impulsa 6: )jgvruau2e from a small force than from a large fora guav ur6:2)jce? Explain.

A light object and a heavy object have the same kinetic energy. Whic veasrqsy,po3 g-pswym- 9z0 v8,qr* 2h has the great2,y9a-g,ws0p3vqq-s ypse vomr8r *z er momentum? Explain.

Describe a collision in which all kinet4iyi8r1jl m)kz p/j5zic energy is lost.

At a hydroelectric power plant, water isb-s/1 ycdq 0 3wnz5sys directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the ysc 05s/13 nywb-qsdz water rebounds?

A squash ball hits a wali2e0+;ek,y l/ z6xvqm1 kafino8lep l,u+1url 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 heigh 5--rn9itbk-oja7ar xt 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 thij- 5nt- arka7bx9r-o is 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 leza.7e od7gu5a an backward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereasb ,om8bdf/p+o6*hpos ;g) y n3( bggru this is not true f8d3r ub+6osb/(;f p b)mogop,gy*h n gor your arm or leg?

Show on a diagram how your CM yva -4ephmwi wtzgx;g*34m/ +shifts when you change from a lying position to a sitting ygw;me hma 3vp-z4 iw4gx*/t +position.

If only an external force can change the momentum of the center ,6vl;j. qhlyi36twp jt. r;v7iey p*z of mass of an object, how can tht7,*;tqevzw 3lrl yj6 hyip.;pj6i v. e internal force of an engine accelerate a car?

A rocket following a parabolic path throzheu (0;in,fxugh the air suddenly explodes into many pieces. What can you say about thfh(xezun0;,i e motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g7q/ 4gd xis5fce) 8puu sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg ski 79k5 ab2d:mq0e /mnoduyay9ver for 20 s. What is the skier’s changeyaa/2kb 9n7 qe0dmu59:d o vmy in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s z1 t0ci,)nuncy /nak9is hit on a horizontal line drive straight back toward the pitcher at catk9/1cz0n,uyinn) 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 x n,xci03 qi3d6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediatqx0 ,dxn3iic3 ely after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propellinujpfs+;h.e mw: oy+ r1v 0ca0ng gases are expelled at a0n +1yvuprc;a+hs jo0m .f:ew 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 movt8cgu2yua4;9 1ggek bing 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 on alevel fr:okp1 8s1+nu lc+w e l)j-ipxnictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What wx 8j:k11s eu n-wl+)l+npicpoill be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 6 ux-m3q:rpog$15 \; m/s$ 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,)w.y evwyaq/l 6-4ysp winds can whip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/sq/4-ep.w awy)vy6 s yl 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 o ib x6v -e//4j ;ndliei(0poncf 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 xi6 4le ( /div-pneb0jn c;i/oof the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving a:r)t/ffkw1annlw3/0zoy- ij t 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus sl kn0r1/yzaf)n 3-ftwj/: oi lwows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wo-x;*4 ltz j x*wtrhv3lod and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emevt*3wjz-x;4hllxt * r rges?    m/s

  A 975-kg two-stage rocket is traveling at a sp72jxto p6c .vteed 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 3.mmf -2 ntccem1k8iz/ rclf+7 180 kg is traveling in outer space with a velocity of 115m/s To alter ititm c2n17cm8m/+fcf- e. lrkzs 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 golf cl p3yi 5f7 k6vtiex6/mp(ssb ,hub was in contae3ifib766 y xv,tkp(s s/hm5pct 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 6 *pqudog r/sy9, yu9y3g3w x)pe08lf gxk +qya velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the wq98,l*ygeoyry 0d9u gp6qs) 3gk/+ xuf3 py xnail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and)yzd+f7e26h1dzdr bs: r 7cx.brlkz- 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 crashworthiness0y0ou v2k34z/vq;3mxhem :nzt dox;i of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km2itxe dxnq 03v; /ozh3mov z;40k:uym/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 at 4m/s to *kz9 yn5oec w*h8**nho ,t3bzwrreqdq rd 0).the east and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Calc * c kntq5ezoedwr0,zbod3r**9n.y *hr q)h8wulate
(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 tei(; 9q5wlpeb*wges8dv sv 9+r nnis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use gwl* i+e5v9(s;gp8esvdr qb9w raphical 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 withoe0y8tbhq 8hq +ut breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing tetyhqh+q 88b0 o 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 7,t7/ i5ck-w3t vwvddpim-/ hmnxb r9u/e-qp east (+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 /hvbxwt/-td/v9i5dcm7-,iewk 3-m7 q uppnrthe 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 3m2s :p0wzq:l tz/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a pq:0 ptw:l2zszerfectly 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'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass z5f5aipr2*twd ic :vxey2n:/ae:q 3hundergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the v f:/ y2i:w 2qn:pa*i35zedte xh5rcaopposite 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 speedi jon/7qs;ns8 of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assumins sn7jiq o/;n8g 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 t;was fg3ko923 iaiq0 mhat is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a s3m;qwigak0 3 s9ai2fopeed 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 colli0e f3x *fax(/cz-jb pslbj8f. de elastically as one approaches the other directly from the jfl -x bp a*8(fjcf/sx0.z b3erear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet bay* 5gv:m teo kyor7xlq*m8gg spu2(; .ll makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with hal* q e mu52g;kt*(gs gom7o:yxp8l.vryf the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline bjb )w1k (z xgc)vbwu, fjr6+)as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. jw()c)6 vj +, fbgub1)zwxbrkIf 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 mass 89q2snlod /hp m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 reshk;ms )c6knftwtu7+ 0 ults in a maximum height h of the pendulum equalw)+k0 7;t htk6msf ucn 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 itseg0i w twed7fm7wh l)88tcfp +1lf in a 3.6-kg pendulum hanging on a 2.8-m-long si0m tl+ )7pdf1f8wge8cww th7 tring, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy 7t/-qaw+ zp jblost, $(\Delta\mathrm{KE/KE})$ 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,7f(uxgs g*p *p into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic* *fg7p(ugxsp 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 col km gn /,ky5le:ksu 89i)7xqojlides into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic fricti/:kkk5i )xg8,lm y u 9nse7oqjon 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 rebouy;+mk4- ;x2i vlvi t(ug 41f tumob/yynds to a height of 1.20 m. Approximately how many rebounds will the ball make before v;4ytu fmlv tbm4 -(yo21iky u;i+gx/losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two object*d xbmonf 77/4l6(mbh/k:iou ko 5bfbs is the coefficient of restitution, e, defined ai/b kbudfx/b47bko(:n6 o75m fl oh m*s$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
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 tim-5ouivf nx(9 ies the mass of 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 o -5unxi (oi9fvf distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on with m ,+uj gukcymhg;,*)4)/ujor qf x.qx a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass if:,j x;f. go)mugqxq )h/,ru*ykmuc 4+j
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an electron,9ye - pnu(b;la,f:ka w and a neutrino. The electron and neutrino are emittedua af:- nylw (9,pkbe; 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 mvh3 g 9hgvei (y+sxd97ass $m_\mathrm{A}=0.400$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 inelan 0uexzn*pqa992ikn l /u.8 lkstic collision between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the an*99p n.z2ll0exi8knuun ka/q gle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right tg-end1u :wgd.nhj9 -j5d 8isangles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ba9g tdd:gjn5-- 1h wju8d .nisell 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 perfew*+4 pa*75cn;j azsz 6 ;okwff 7 dy8jzg(kxzpctly elastic collision with another atom at rest. After the imp*w p +yzdz s7c4kk(f zw 7;85 x*fpa;zjaojgn6act, 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 va 4eh; yi:b(ai,y: p3vcz n1gperfectly elastic collision with another atom at rest. After the impact, the neon atom travels away at a:i ,pinay:c4bag e3(hzyv ;v1 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 sho2s,r( dr y;;5non1iuduq )rm lwn in Fig. 7–38. Specify relative to tuduqdr; r1o; 5iysr,() l2nmnhe left-hand 1.00-kg mass.    m

  The distance between a carnvu8nqdw )p gohosim 06/dr-h+e 0k ipr4l351 bon 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 w)n vsm290y)kax f(kv2.50 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 wv0v ))mns9(xa ykf2k the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, ya7wnec l 9,2pis used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine ten,cy a72wpl9 he CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides l2v; co wb4le:44 1kvzllw5jy$l_0$,$2l_0$, 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/1u2gkkn( s (vq:p;xhk /qto t 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 c/t2kx uh1 s/tkg v((p;qknoq:an 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 cux/ qqmrd/w)6zw+, jtut 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? [Hint: Truqx q m/z,+w6 tr/)jwdy subtraction.]   R

  Assume that your proportions *l3s*(ta 5(m6da68ylnbz n eq qas5g aare the same as those in Table 7–1, and calculate the mass of onetbq6a5 *ly e (gn*ql m86nzsds3a5( aa of your legs.    kg

  Determine the CM of an outstretched arm using1541s ftpjvqrw2 p:fsy2c sb1 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 bentb9m4 ff6eyyp1hs vn/ . at a right angle. Assu16p4 svyyhe9ff nm /b.me that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms 0 xqkv1 g tcyr*io hwhihs xk0;x)+;y/g-cl :,and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will tkrcci-0 h1*;/,gl ) 0xwh qyosxvh; :xgiky+be. Will this CM be outside the body? Use Table 7–1.

The masses of the Eartj;k8h9ivnx2+,g ypwa9 s) us mh 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 mpqz)nqnbe8r 0r.-, btan stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical he(nu)a kkgbv.d5;g:w::9aos :w tuk lsad of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and lega )a kokt b9:dsgu.5wv;kn:w (::lsu ngth 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?    cm

  A mallet consists of a uniform cylindric/ra b4liw. q0 xsc.9ohal 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.l0qa. .rw ih 9bosc4/x 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 yo3zq3(sdc hr7 c,1e m7–14 (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 mas *+m zq8g;5gyfeoopp3 s M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stfeozq+gyp3 85mp; go *ops?

  An 0.145-kg baseball pitched horizontally at ss9 .gxm9lzikc161jjltrikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate .9zk6iljjc 1g9 s lmx1the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with -oz0+/wyptgm omv6lkykp ) gyc0a1u0o6/jz5 speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown ief6 hn(w j70yun Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall in7wfyjh n(e6u0 to a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a sphr00 2zsuhp5 ceed of 2.5m/s by pushing off with his legs from an 1800-kgs2ch z0u 0pr5h 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 the other 80 kg, are initi :1o6zvlwddux*/l: 23ewdzw ially at rest in outer spac /zo*:u1w2 l6 wzx3dd viled:we. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic ckyb/.+gxv;w w ollision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original spe .wk+ /wb;gyxved. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as aln 7sb n38k8by xnz(9kn expert witness 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 exceed7n9b 8 n3kszxb(ny8lking the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of 40n ;ysz/ * ghquptnl-v;+xzs 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 bouu-qgpnz 0 y*h /lnsxz4tv ;;+snce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood b ,hvo7ztze7 ;.0zae. wy/wvs6k0wacat rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it? wee07zvb a;hc wt07yzk6z.ova./ w s,    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of w9e( mnuhaxhy5*pk5. hu p jt/;ood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance o k h p5tex .j5/hnphumy9u*(a;f 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 th +iwcxf9vxi 79ccsluye4:,4 te other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at oppos c9iw,esvt7 +yc4uf9cxl:x4 i ite 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 3t78tz 7z.6p5-tiwntycvmem. v e+scwas 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 tuxqmhn/07 ni rl t1,+bwo fragments by an explosion. One fragment acquires twice the kinetic energy of the othenrm 7xlbh +,0i/u nqt1r. What is the ratio of their masses?   

  The force on a bullet is given by the forcl62dtloja/qi3m,:c mx ;ij 0mula 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 masses8sh- ct imnvci *)..awa91zno $m_A$ = 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 radioyp0a455r cfajactively into an alpha particle and a smaller nucleus. Whaar4y acf 5p5j0t 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 targer9.h- rc3kh0 sefxz(-s+8mf 0h ieoekt) 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 a 30emp-6cvdu -1f1i 5q.zo7ymkh8+ wc uz.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mass m if it is to rebouny eqpk3lg 2x(69o ic6wd from M, slide up the incline, stop, slide down the incline, and coll3qxclpkey (66 w92o igide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn m xlvp6 d1fmgz1m91( /ducbo8 foving in the negative x direction at its orbital speed (with6f9 vuf/ 11xbpm1 8mc(g dlozd 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