We claim that momentum is conserved, yet most moving objects eventuall0h opg fz(9dl*u13 ezky slow down and stop.p91 0 zgez3uh*df(lok Explain.

When a person jumps from a tree to the ground, w+m crwxo1.mr cs82d;y plz72phat happens to the momentum of the person upozmrsp ;c22r+1c ym78pxdwlo. n striking the ground?

When you release an inflated but untied balloon, why dx rqllyl 8 -33-8xfh rq.oqfi 2r5shh4oes it fly across the rooms.4xq2r5hr ll ifh y83-q -rqoh3fxl8?

It is said that in ancient times a rich man with a bag of gold con4q,8vv fk m+n;h fho*ins froze to death while stranded on a frozen lake. Because the q48non;hh +,kv *fvf mice 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 oggyrcvj y8*3ko jfg br /vbd0+2 t-l;8ut in space and is essentially in cygtor+k fb -gj3g d02;b*lj88 v/yrva vacuum?

According to Eq. 7–5, the longer the impact time of an imvecadqwz-6u u4;8tdo j82 c7 cpulse, the smaller the force can be for the same momentum change, and hence the smaller 2-ewd7ju4vcq;8td aozcc u8 6the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Today, tho1 wez8y vn5n ph4/bu 6yv8*(v +fxosld2 eiyi;ugh, cars are designed to havu+1i64nnhvvv w/oi2y8 ;(fz bds5ple * y8yxee “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tosses9j +ki1kdt. dd in the air by thed tji.9skkd +1 batter?

Is it possible for an object to receive a larger impulse from a small forcex:1.prf8i:i wfp0yqo;h pxc 8 than from a large forcf .;xxpcy:fqri1oi 8 0hp8:pwe? Explain.

A light object and a heavy object have the same kinetic eney:1sdp40w ee8n4 8a 7elrpcto rgy. Which has the great0le wdaporc 4nt7ey8es 14: 8per momentum? Explain.

Describe a collision in which allt3uz9;d s lm++vyoxn q(v/ om nxs(szb(7.zp 2 kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against turbin b6k)/4 g5ifgxuirrp+e blades on an axle that turns an electric generator. For maximum power generation, should the 6+iukbi)4gr pg5x rf/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 at ad+tjwlk )e31 ruug/*h)lt5w f 45 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a h0mi3rsn qw8 i f,-*jfrard 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 m38*-r0fiwjf,rsnq i a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in you:smay n qh-2r5 )9x;t guz:ukvr arms?

Why is the CM of a 111w gttl ixf1jed/. ,m-m length of pipe at its mid-point, whereas this is not true for your arm otmd1f/x1 1 jw ,l.tegir leg?

Show on a diagram how your CM sd fp su1zh5h7/hifts when you change from a lying position to a sittizhf7u pd/5 hs1ng position.

If only an external force can change the momentum odznl/5kslo 21o 8tz, of the center of mass of an object, hz5, tzoold s/l81 okn2ow can the internal force of an engine accelerate a car?

A rocket following a parabolic pa w/f;hc09dlgu th through the air suddenly explodes into many pieces. What can you say about tchwg9 d;0u/f lhe motion of this system of pieces?

  What is the magnitude of tl85zabqw ;.r whe momentum of a 28-g sparrow flying with a speed of 8.4 5z;8 qwwlr.ba m/s    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What in +k086og l)p h8 zprd4zunfd8cii:u9s the skie40pnzp9od):8 g6 ku8c nzu8+ hfirdilr’s change in velocity?    m/s

  A 0.145-kg baseball pitched at qp9a7(ds p2(poxd fa7 39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If xpsa7 pf7 dq29p(oa(dthe 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 s jv; 3eec3hm2horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the e3eh ;cv23m jschild is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that thgjqnl j,u1ci9 ;8sx9l e propelling gases are expelled at a ratelx,1 9 n8jlj;sc9uqgi of 1500kg/s with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an apparent breaka4ez01z.eabr6 dqjgy6jrk(vjp: h3q+ way for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running a6 e:63 grv p 1zj0rdyzjb(q.qj+ahe4kt 5.5m/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 am389(ljioe g(3 v2xja ey piy2level frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped ont3mog(p2x9y(3 ji eljya8v i 2eo the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a sec4wlh5f y 4s4ux ym54 xogrs-zu5f/ z5dond boxcar at rest. The two stick together and m 5f554ug/r 4uly-z sy445womxx dz fshove off with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, o8eze0 v7x0 lnqds 7b/winds can whip horizontally at speeds 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 force of the wind on a person. Assumbe dqe80z l7x/vo7 sn0e 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 artyiwk .a51hijgonhc8 d 0. *( constant speed of 8.6m/s on a level track( 8g o0yidtw1.r.jhi h5ca k*n. 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 the car after 90.0 min?$\approx$    m/s

  An atomic nucleus inio o: iyih:hj-8tially moving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has :8:oh yjhioi-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 woodr n:h eknj)m2c)u- 9wvg75mwu 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 emer uevjcnh7m2 -):r)5mwk ngw9uges?    m/s

  A 975-kg two-stage rocket is traveling at a x:l-4mdx vra5.ae g 5z8li3l nspeed 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 318ci 0 oepr(b/39fyl,ub 0 kg is traveling in outer space with a velocity of 115m/s To alter its courseb0 (r/ ypobu9l,fc3ie 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 cumk )m qcw(6-27vcnr ilub was in contact withqm-26km)un ci vw(7rc the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes to rest ii.,v vy ax17r i/ kwgh,hudh*-n a time interval of 8.0 ms. (a) What is the ighi7*dhuiy h ,1/ -vr,.vxwkampulse 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:n1e,a iq6vj t. pj0 lsdx)9el 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 chayr(k5t. 6ko xca*h xohd7c d83rge of the crashworthiness 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 rest. (a) Calculate the avx8c codd(tk 5hh7.a63rx*yk oerage 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 theeq;uglu9hp9gmk 7p+8 east and is stopped in 0.75 s by a head-on8p9;9luhuekp 7g gq+m tackle by a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 k,ydoup u)c: 3pux-qg m 5ya94gg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time.m gpx u3u:4qy5c gpyua-,)od9 Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking the lowkdiszz4l0a+ q)6)(wwg:kz mmt 7 vy7l er 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 to the seated position (thatyiw(g l6kst0)l: kqdz zz7v wa) m74+m is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of copgb5g- b*o:ow je+)tqllides 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 be+gowp q* : b-to)5jg0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-on collo3bre,r-;i zd +k;j vowf1l b4ision with ar3;k,z1r4bo + e -f ojbvd;iwl 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'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastic head-on coll 98xbiee*xfyn5.kbjn( *9up yision. If one ball’s initial speed was8ukxp 95ef. n(n*jbiey bx9y* 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides head qr2q/:2 a k/m e*anyum4o+-v :wymh9sl y5ynd-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and directio*/: mywq :-msdyv ay 4umn+ honyera92 25l/kqn 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 isa 9vu6sp.c. b3h w-tm wa1.paa moving with a speed of 8.5m/s collides head-on and elastic.cpmuh 9. a.tabwsa3 a 6w1pv-ally with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusemenbj. h8ayp+ci8a cnw e)02e- rgt 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 ng.8icjp0 ra+e-8cy b) 2hawe 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 ball makes an elastic head-on codjh*ebtfl t4 o(n6zwun5 z;9 .llision with a second ball initially at rest efo4dhn6z95.wtu * b(;ztj nl. The second 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 slidepta76 zf*1lr29qop96tokmw;i wd(xes down a frictionless 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 902x97p6 wwqzf mpt o*6ri l 9a;dek(1ot 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 obti2 y6 5fvc3n;ofgj98j:roj3lp9yanject of 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, m q-u1f gb1h :ih)5srgprojectile 1 results in a maximum height h of the pendulum equal to 2 h5 h-bf) r11usqiggm:.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 pendh0ta+ w*;:oplxxqe7v d/ 15kaihnds7 ulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.5qn a7k:;a+ohlxix dtdvp7 01we/*sh vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fra+:4d1 ;rsbr yfd6co ofq9)mx fction 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, odp o-c0l;q j6hrp,b7yne of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energoc qbl y7r,h0p p-jd;6y 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-knoss7 nv*45uwp k*a*eg SUV stopped at a red light. The bumpers loo* u4es5** svnkaw7pnck, 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 1hhm a9uej4 5gheight of 1.50 m and rebounds to a height of 1.20 m. Approximately how many reboungh 54mj1h9euads will the ball make before losing 90% of its energy?   

A measure of inelasticity in)bvn;exqzyvh, 1p 4 y8 a head-on collision of two objects is the coefficient of restitution, e, definedz yq)phv ; ,y4n8xvbe1 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 dsibd-,va :+ mwith three times the mass of the other. A depressions ,v:-iddam b+ 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 +x direction at 5.5m/s collides head-onjb8; n/p;f(z(wm *ov tip,l zi with a 10.0-kg object moving in the -x di;t8zlm ;b*i iwp (v/ n,ofpj(zrection at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decr*esgc(oyu+prej-iek.yyj9z636 p 6p +w e4o ays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have mop.e+ 6+syi9*wypc z4 (-e yrr3oujp66goekej menta 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:l7eo1c k1fqb $m_\mathrm{A}=0.400$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, eacme) -pi rt+-zp6ech z+h having initial speed the two move off together with spze-cr pzh-m6 itep+ )+eed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass8 jso 8d9g.7 b2bzrjw9qcz7 df 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 alb 8f7.7d9gs 28 b w9corqdzzjjong the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with another i1iy9d /izr+uy r r;rce2a-q;atom at rest. After the impact, the neon atrrz q9yideirir+uy;a2/ c;- 1om 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 collision with another ambl00)er -4gg -lz4pyc mh+l stom at rest. After the impacb sl4gc+m)lh py4l-me z0 -0grt, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. Specify x)/xsm; 4f1htqt)e6kko1oxj relokk1;s/ xtte) x )6ojqh1xf 4mative to the left-hand 1.00-kg mass.    m

  The distance between a carbon atore1)8q, m)z2eao ogok dif6m6m ($m_{\mathrm{C}}=12\mathrm{u}$) 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 1(/o0/uzj hqyjoo f 7l+050-kg car is 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 car, andzoj 7qyhl+0u jf/o (o/ 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 qr*6aom3y jt :ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and S jatmro*y6:q3W corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides ze jj e(0r7s6 :jpk,bq$l_0$,$2l_0$, 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 o** k0gvv+xii yeqrs;qcq d:b 73t2now 8b2o3mf 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 can pick up tv ky+te2bro7 *i m g onxv*8qwsc0 bq;33:idq2he load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular jp ,r*t/a,led 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,lptaj /,dre * the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same a25 s6 xdd*4g18/xf i vtyzcdhls those in Table 7–1, and calculate the mass of one of your le5/zl 4x*sxf yh1id26 v8cdtgdgs.    kg

  Determine the CM of ay3 5p:ves*y9ceo ti0hn outstretched 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 positio3x cm z)o/8saq xuy( w.mmy()lnpda/9n of the CM of an arm bent at a right angle. Assume tha/am msml)zy/ (wnq3xy odu)8(.9 acpxt the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his ar4-e,cuwp8a xjrs bg* ;ms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below t g8ebaw4srjc*u,; px -he torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Mou zf9rs(o cxnon5;,-eon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand x+ w 8xd4)wabl10.0 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 heac,p;mu.yq.3 hevbk4 to5ug y4d 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 is the point that will follow a parabolic trajectory g4 .;phmk,o bquyt y3e4vc5u.?    cm

  A mallet consists of a uniform cylindrical head of masxtbq o/*ig3z;s 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 is 3b;qxo gzit*/the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–m- b5ngtvejfin 59u7; 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 withb3(yy76)v :gl:rahxe h76iz np ;w .ab7wvdvr respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured w7rdwab(6h i;hrzp6 a.:l3xby vy vg v7 7e)nw:ith 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 strik,3 hm1x*vl-x: os(ag4oge gcz es a bat and is popped straight up to a heigh l gm- gxo:g,h4 a*(xcos1zve3t of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling wi8(9ti 4 vo;*4kc yvurydp9gnrth 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 wit x3b w9i.tlwc:,p/gcsh the corner pocket shot shown in 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 into a pocket? Givesx g9wlic3ctp wb,. /: details.

  A 140-kg astronaut (including spac;+ny5smnlaw .e suit) acquires a speed of 2.5m/s by pushing off with wa.m;+sy nn 5lhis legs 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 a;uq3wh.j-.+cti m cct nd the other 80 kg, are initially at rest in outer spac.c ctm- q+j.c;huiw 3te. 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 elastih azc 00j- juhxukwc479-wbet 0h3s* bc collision with a second ball (at rest) and rebounds in the opposite direction with 00*--j xsc 7bhuazjhe9k0tcw4h 3wbu a 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 experllrxs8g o )jj : nmk+w-),lb4it 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 driw ) bkl g+lsjomn4x-:)j,r8liver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total vertical he dt1oehz;wz;uye i.9 /ight 4.00 m. The ball hits four times on the way down, each time strikd/w9.eu;ey o 1zihz; ting 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 the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest directly a1m5ujzodu x87e (x4y sbove it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block 4soxde(yx m u8z u75j1rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and bj1*a3hut-hi : h-(6v*yn q oppwxx 6qzecomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the 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 i *-v(:wot6h 1*xya-pzjpxq h3u6nq h muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mas om:jh-9+u rlruhj+g9 s 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at ophr:-l99+mju hoj gu+rposite 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 2 u7+ymg)e gjynd/up*was 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 dcfxlfboqyj2a00i km) )90cp+ywtqe 0u1p/ 6 broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of t)q001jum0a)yecwypqpf2/9 o f dx t bkc li06+heir masses?   

  The force on a bullet is given by the form7-z1b 4/faj3 q,xi5fio jprntula 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 massesff;dbc)hnw9, zrc;mgm14y t* $m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha part3 3r3yxv wy1lqicle and a smaller nucleus. What will be the speed y3wl3y1xvqr3of 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 targe-2avj uhg;9 6waxh uy3t) 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 dow7hvj 2f qb(jkc8b)9ss n 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), what is the upper limit on maa)ddjh5e7o:2m-:ha6 xjyh,f ng sm w+ss m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide with M agahad e,5 f7 axhhns)jjm:md6yo:2w+g- in?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 st7s-g 4 zi8q1ws8kgdehows the planet Saturn moving in the negative x direction at its orbital speed (with resp -g7s81q8tk se4iz wgdect 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