We claim that momentum is conservh ko1/ 6v7qr+ x0febhot5w *oled, yet most moving objects eventually slow down and k+ 6o7ox/wb0ofet *v5lr1hqhstop. Explain.

When a person jumps from a tree to the ground, what happens to the momentum ofphzizh) n:m70) frh: r the person upon striking0hf)ph) i::7rnzzhmr the ground?

When you release an inflated but untied balloon, why doelt tg -m3kv6vuk3fg7i) f ihiwm(o,;, s it fly across the room? t-im7v6k)li3h,gvgf w oi(3km,; uf t

It is said that in ancient times a rich man with a bag of ;y/mdw w4iod hik4 t4)gold coins froze to death while stranded on a frozen lake. Because the/hok44 iy4t)dm;wd iw 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 space and is ess) /1ml9i cii sbnqtu*dcz3,u )entially in a vacuum?* sinlc9 ic3tqu/ id)u b,)z1m

According to Eq. 7–5, the longer the impact time om8-devz 3u6wff1 gl9 gf 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, ex fug8mgl e93w-1d6zfvplain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Today 4m4z8fc* wwnr, though, cars are designed to have “crumple zones” that collapse upon w 4nmf 4*rzw8cimpact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than oz:35dni 2p.kosvf ;h a ball tossed in the air by the bavfoi .k5;sdz:oh3np 2tter?

Is it possible for an object to receive a larger impulse from af8+0tc wj jd.z small force than from a large force?jtzcf8jd. +w0 Explain.

A light object and a hemu(y u7/ k8wjz4*nmlravy object have the same kinetic energy. Which has the greater momentum? Explain.ul j*m7r n k(4z8muw/y

Describe a collision in which all kinetic eneo rnt9(hyu*h+;06taln ,ghx qrgy is lost.

At a hydroelectric power plant, water is directed at high speedcv, vb 1muco9( 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 thabu cvv(,m19 cot the water rebounds?

A squash ball hits a wall at crps 2cey (x)m1mzyj2(u i5d6a 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 fxnu5sp xl8qp(oo 67.h rom a height h onto a hard steel plate (fixed to the Earth), from which it rebounds at very n (.pl76u8honps x x5qoearly 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 backward when cagdgld vd10 f69 k-i-oilh3(x :m;enrj rrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is.xpe p 4yb96,5eej/tiq(jx7 dsqe j( b not true for y xe5ebpp(q/qb jeij6s9x 4tey (.dj ,7our arm or leg?

Show on a diagram how your CM tacu(xg 20 ,l1 sns8mtshifts when you change from a lying position to a sittit8,x 2g (mln1c0tusasng position.

If only an external force can change the momentum of the center of / xm 14za7jco3*uyvw cyn0wr 6mass of an object, how can the internal force of an engine accelerate a 1*/jm4y6rzaw7yu ocv 3nw c0xcar?

A rocket following a(n1 c 8ij(wcpjb di79i parabolic path through the air suddenly explodes into many pieces. What jb(ii8icnd 7cwp9j1 (can you say about the motion of this system of pieces?

  What is the magnitude of the :,+osj hq st3 *e1kkxxmomentum of a 28-g 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 skier for 20 s. What fybvi 5fnzcu80v80xnz -; j559iom vo is the skier’s change if-oymo fi vn5xzz 8 v;u9 85cji5bvn00n velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a hori*ixq io 8qp)dirdlb/xp+) g8n8 jxe8(zontal line drive straight back toward the pitchj ( )pd88x8/x*ipi8x+qednr )gqib oler 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 package out horizontally with a speed owbnd i6 d,wps/o +,4yqf 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, andd/ywsi d,o, p+w6q4bn 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 exp19sukb /k; 1ehhwv,0 uryukz3 elled zhub wk/sv1h0 ueur , 139;ykkat a rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moviiw +knf86c5sd5d9p knn0tz02 xbe 8 nqng 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 alevg 5r 0i.yio,hvel frictionless track with a constantr oh0, vg.i5iy speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling atv 1/u1oqm 4gnm i1s.xp $15 \; m/s$ 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 bxhj, :h.7jk ruh vm+3speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the forch:jr.mh3vk, x 7u +hjbe 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 ofzy;az );p) km)v: g*m8nsgcde 8.6m/s on a level track. Snow begins to fall vertically anz pgk*gvz )m)mcs)8a de; ;:nyd fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in the direhsdk 0h9k0oedz bar.1o+4 g4ection 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 t 0 .h+ao144hordegzkde 0kbs9 he alpha particle have when it is emitted?    m/s

  A 23-g bullet travelingk1qy : dx/c6lu2 a1vfu 230m/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a x/ku6ld2y :qv1fa cu1 frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speed ;f :jbu1lvh(r 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 travdn)*q*p4h n;qpmfvgzi/ 4 :pb2m z, ekeling in outer space with a velocity of 115m/s To alter bzh/vmkn dp*i p;f zm4)*4npge2,:q qits 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 q3 2dq09pqmhl 3he8q ytee at a speed of 45m/s The golf club was qqyh03de8 3p29h qmql 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 rl ft;8fbjah-*qjrqknj1;m: l:u( ge2est in a time interval of 8.0 ms. (a) What is the2;qla :l8j* erfn j:(;gtq-1hubjkmf impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s st,hlylv5ma:qg4f (q pp8 rve44rikes 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 a.i8irhl : vu)sd3e 8glutomobile 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 rest. (a) Calculate the average force exerter :dhlvis)g .ile388ud 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 rorw.5a*f7,gny9dp w a+fmum 4unning at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler runnio+y7m fwgf a*9 4naur, p5dwm.ng due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points in the +x dir4 5bqnyyly9m (ection and is given by the graph of Fig. b 5yl4mn(9qyy 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 rk c.sh*.lxz0fvc) :la 75-kg person jump without breaking the lower leg bone of either leg? Ignore 0:c). z.lcxrhfs l*kvair resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the 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 0.4403sfo :5cg+dq tt bt,+pg(iz/t kg moving east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision df3tg/ qzcg+tp ,+bo5t( it:sis perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, movim05jn0 z5b2lex u. rayng east with a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuman zb5250jruxlmy e0. ing 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'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergob(*tt0t,basb*/xkhut ;na :vx (ff +w a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the pos:* ab0 f;abtt+xwnv(kb( *hxutf,/stitive 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, movi67glsk h0 la:ong with a speed 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 Assuming a perfectl 7lko6: ahgl0sy 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 8.5m/s colliq5awwq .wl) 9d4kq.xc des head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with w. qlwx5w9d )qaqk.c 4a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as one cccj 56 ek4sq*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 differencesc ekjc4 cs*6q5 in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastizhf*:)f70d65 qlltyz*nkb,m cp -w rcwy39o z c head-on collision with a second ball initially at rest. The seco m9:3 fbzl0td7y *c z)wzc,yq-wkf*pr5n 6h lond ball moves off with half 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 frictionleemetm: kka0)3 ss 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, whek3) t:makeem 0re 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 o, vctp16xp8b 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 results in.;gym::ay(w mmw 4qhf a maximum height h of themy(f wqygw ::.am 4;hm 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 m) jtp6;d: nnw ve:e3kitself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which make;e3jknnv pe:6t dw: m)s 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 the4lw 5htnf 6c2 co8z/ (gczjvk8 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, one5kkx8 *crhje/ 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 lig/xr jhk8c *5ekhter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopgwi5g9hw h60b ped at a redw9h 0gih6bwg5 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 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 1tfz e-p /,m8f* h*a rxchlo;r/.50 m and rebounds to a height of 1.20 m. Approximately ha;p o fl-ctrxf **rehm/8,z/ how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects r;1bk5/lf7th r.y iu qk iag5i,l6v*i5zj1i nis the coefficient of restitution, e, hifity65,1k 5lnj u rqz1ki;7i.i5b*/aglvr 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 the ;va8fbwxi7k;s us3a)other. A depression is made in both8xkfb 3vua)s;7 ias ;w faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x di: tmcbj wtju1 8 gm y9kb4er5.-yn6j2brection at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final vej ycmb8em-9nt:6k btwy bj j15g.ur 24locity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest de4zpit::hf t+r y5c :1hapwj/ tujm1h,cays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emi4t1yi h 1j5h,j:ma :pt/c+ wt:hfuprztted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of mass 5rcpf n)s9sjv9la*hg 9z2 ch8$m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equal mass, eachz:9 c0 s vc:bpfe14rwy having initial speed the t01f vsrzce 4c: p9:ywbwo move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles ands:lv)a tc5(yb-q;e doy79i fo 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 th; 5(oeqdb9it-as oclyyf 7v: )e 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 perfect42xs9j mbowu,ot ve m3f,7/ pcly elastic collision with another atom at rest. Aftm3,/e4mwc ,v osub 2fpx7toj9 er 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) mr at2m/x,qd- ultlz ogtb*6() akes a perfectly elastic collision with another atom at resu*t)-z tlr m,d ax o6(btl2qg/t. 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

  Find the center of mass of the three-mass systxt w;f 3b7icobuh(rd 9e1y yme92/3io3f5i cb em shown in Fig. 7–38. Specify relative to the left-hand 1.09fwc/b9yc xetbmy 2d1 uh33eoi oi;3f 75 ri(b0-kg mass.    m

  The distance between a carbxcvk)ms ,3go.on atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of the wwbmhy6-r-xxs/ 0 peh +7nr/tcar. How far from the front of the car will the CM be when/0rw- nxe7ybp-hht 6rsw+m/x two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m bygw0bb7/ )y/dmz u go-k 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, u/ b/0ob )d7wkmggzy -SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesy; vq9mkg0+ecjex53w )t k,vl+c( azn $l_0$,$2l_0$, 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 pau j swmx:c3y25ste (see Fig. 7–40), each of which is a cube of length l. Find the center of 2y5s x:u cjwm3gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R9hpbpmp rbs0lfc-7 2i..b 8gs has a circular hole of radius R cut out of it. The center of t9s 0pl2 -igf pbrm7s. bcbph8.he smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the sa/pcs:q9v t p6gme as those in Table 7–1, and calculate the mas9p /tcg6vp: qss of one of your legs.    kg

  Determine the CM of an outstretchedk-2j)6 (,aq oxfdkctn 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 bent at a r13ryx z6xez vyfdrh9,g.dtd f-,/hz 2ight angle. Assume that the person is 155 c yxt163.fyrx dh,z9 z/e,2h-dd vrfzg m tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his armsp krx4h/q) y8w and legs are hanging vertically, )p8 wrkqhx4 /yand his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth a:s2b/ vo1,bramt9jg w nd 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 sta km7*2 x/btt+li zwz/and 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-0flkjr7 r lz2: t5zinx8cd0 d a uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle d5-tjli8f0c nz lk2x0 rd:z 7ris the point that will follow a parabolic trajectory?    cm

  A mallet consists of a ;gddnfyl+s h dckf8l+ pm.*mff n 45+6uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is4. +kcl6dynmf;gm p+s+5 fld d*h8nff 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 uf ddue2 +qxvdw:c+5n*xz 5v2(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 Mmi/cm , a+3zj1:dkrjw, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs ou j:iam1 c,/dzr3km+ jwt 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 stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is popthnj0nqnath.: +v c k6b2ozr85s1n m;ped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the averageo.t1nr52 bn: hn+n;ak 06mjt8vz sqc h force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling witj,ra 8q uj -+nyh-;pwoh 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 tezxz8) wzi g* w/qc5l.he corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about ez.5 c)xgz q8wi/w*lz 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 2.5m/s bd2ev obkc k rn 4z (mut2pc:oh;ve693*y pushing off with his le3o(b2;62pkvzcndc vmtroh :9*kee4 ugs from 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 the other 80 kg, a;wehw96xv b 7;zzq: otre initially at rest in outer space. They then push each other apart. How far apotq9 wbzv7w xe6z: ;h;art 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+ xskb:k sci t:;njs4, (at rest) and rebounds in the opposite direction with ai;s+, :cjbkn 4txsk: s speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a courthc9 et*dgrs/dx wg1 5yk *0u5r 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 hu5dw*0yrdrg /1x*5t9 ecskg 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 ofr m01s 3nq,z (kshvwl4f the top of a flight 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 different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches ,r kh4s0q 1s(nvmz wl3the bottom of the stairs?

  A bullet is fired ve)kat 23hvenw+7u /l* i rlyrw7rtically 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 will the block rise after 7ih3/ wny w)2ae7k+ lrtv u*lrthe bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedbfwutij8f/;mj./98)g h g koqded in a 1.35-kg block of wood placed on a horizontaltj)ujw. 8i8//gmff9 hbq gko; surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a r-n9a 6 xb8c)r3cnru wiowboat 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 directio-i6)8cbx acr r n9wun3n will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abopla83e 8q7mf mut $ 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 sudl2+1d;7p zn iemiq/- qnusxl9 denly broken apart into two fragments by an explosion. One fragment acquires twi m2 lun +x/qndipl;7-szq1i9ece the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is o; 9afl4 x,gpbgiven by the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses/*() jngagp+vkjs r4z4t ez 5i $m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha particle and a smi4ut1o sz4j) c xvj:i,aller nucleus. What will be the speed of this recoiling nucleus if the speed of,4:j4iitz)cvo1j s x u 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 dn*z5xtryq2h92 )zvp 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 dm *il68xk9an0mbtu2;5 wa j agown 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),1jn7/wo jsc.i 9zxgx-xg;b2 v what is the upper limit on mass m if it is to rebound from M, slide osic1zj/ b9g2g 7n w-xxx;vj. 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 7–47 shows tocqjc3 b,+ 5johe planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Satj 3 ,+joqbo5ccurn 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