We claim that momentum is conserved, yet most moving objects 0/hpz 5*:n4b(iyd,lyy jsd sceventually slow down and n:/5 cdsisz ( 0yhyp4*d b,lyjstop. Explain.

When a person jumps frt bex wv2do:0pug;t8;:. lq xmom a tree to the ground, what happens to the momentum of the person upon strik: o2tx;g:t qv8px bd0mw;e.u ling the ground?

When you release an inflated but unpaw7;tifafs j c-9l6 z (,h4 ght vr5;7hw2bbhtied balloon, why does it fly across the room5f(ghszw, w4 fajhplcht29h7t v bb r;7;i-a6?

It is said that in ancien/(f,yfji4fs :z7uvd p t times a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he:d/fuf,vs z 7( 4yfijp 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 o- *fs ,wreg25wcp6 gihut in space and is essentially in a vacuu6cp wr52,*i hfgwgs-e m?

According to Eq. 7–5, the longer the impact time of i gslrl1::(cv ;hma;txn ;ayly0 xz:9an impulse, the smaller the force can be for the same momentum change, andi hl;t:;zm1 rslxl; ax(c90vya:g:yn hence the smaller the 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 withstd od/n.59s cx thfb 2 du0c/dlwut0g-,and collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of -dou 0.tbdxhc/5fcgnlswdt/d 9u 2,0 this new design?

Why can a batter hit a pitched baseball furtu2i2 eec 2x6 1w;fsqsgher than a ball tossed in the air by the battereq 1fxsue22ws26 c;gi?

Is it possible for an object to receive a larger impulse from a small/4pfku: z6,vwfm8 b w 6fze4oy force than from a large forczy 6u4opfv6wfm4: e 8 /,kfbwze? Explain.

A light object and a heavy object 0l 86qcs 9qysdhave the same kinetic energy. Which has the greater momentum? Ex6qyslqs8 90 dcplain.

Describe a collision in v6qyqcrutwf 6r z.f.u n8 )((kwhich all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speef m(5 ziq:x.jqd 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 sto5qix( fj m.q:zp, or so that the water rebounds?

A squash ball hits a w1t4rc1d r/q*rnb cy4eall at a 45 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h t, cc/cl6 5cu;wo:kafan+qb+ onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is tnq,ctofw ; cauca6ckb+l/ : 5+he 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 carryin5 ih-f1e -jdjn*irrmtp gr ,4 *t)/ 53maldhlmg a heavy load in your arms?

Why is the CM of a 1-ykpij8d97n2b d6e/e um length of pipe at its mid-point, whereas this is not true for your 7udebky8d9jie/p6n2 arm or leg?

Show on a diagram how your CM shift+ ) h2mipel-ebsq/t )ys when you change from a lying position to a sitting po2y+le-phb/qte) si m)sition.

If only an external force can chan*5he0 nqxf l x9(jyv.age the momentum of the center of mass of an object, how can the internal force of an lx*(jh5axen. y9qvf0 engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes into m rf8+,y3:nrxc 6d mnxtany pieces. What ca3xt yc6, rdrf xn:mn8+n you say about the motion of this system of pieces?

  What is the magnitude of the momentum ofg lwm9d6fvh idf; uv1 -m7q-e9 a 28-g sparrow flying with a speed of 8.4 m/s i9em--l wh9;1u7 ffd m vvdqg6   $kg\;m/s$

  A constant friction force of 25 N acts o2q1eig/k -j vtn a 65-kg skier for 20 s. What is the skier’s change in-12i qj/tgk ve velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit onwig 9i8m cf8w* a horizontal line drive straight back toward the pitcher at 52m/s If the contact time betw w8c*i9mg iw8feen 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 oao h99mvowp-r5 u 6r2tut horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The velorpo-r9ut wv9o2 m56hacity of the boat is    m/s

  Calculate the force exerted on a rocket, given t 33:yjby ge-ifhat the propelling gases are expelled at a rate of 15gyb-e fy33j: i00kg/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(az9nl s ,*+ed)wn wvptw d9sil2tb48.1m/s on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same directiw9*t49psbad, vnz) n2 l+wtwl(i 8esdon, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car tr 9eg(;ggar p0chw.3jxavels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. jg9 gc0g3xpw. re(a;hWhat will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar at restyp sa 3ag(gk;x9i m7a.. The two stick together and move off with a speed of 6m/s What is the sgmkpi.7xaagy;93 (a mass of the second car?    m/s

  During a Chicago storm, winds can whaxvtb1+muz3 e e(lgi; -x k1,yip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg bee ,xta ;xim k1zvul1+-y(g3/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts al ktatgdj.118jong with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 m.k 8t1jjad1tgin?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in oy bs ;nr+ts:cjh7 2ky 3eqa2-the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emito2y7sr -3yj2 +kac;sbqn e t:hted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and eme,)ucen)f,i c 5ot6j hrr :kd3urges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bn e6f:3t rjh,i5cuk,d)ouc) rullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speed z9lqe y5c;h5v of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a velocity of 1(h (f)j, s9 luj+etn46lda dcd15m/s To alter its course by dfjsd) ((c+ajh9ul6 4td,l e n35.0 $^{\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 w2obn:ey x/1i off the tee at a speed of 45m/s The golf club was in contaonixe w:1 /b2yct 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 veloci+(p97dytj.u 1 efkbl cty of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) Wkeljc9dty(f+b pu 17.hat is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and s3heqt7;vzh z.)q+ aa w0w0ma npeed 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 crashwort v 9a 3ur8erx(irej16ahiness 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 average force exerted on the car by the barrier 98xuvj ae3a1re( irr6. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running atn-8(a s7 b7j70s9lp1m eh /slqdyffgt 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due t blm(l-sf7df s7j 9p0gae7/8y 1hsqnwest. 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 f)lb h4( nve*l8q8ob+9sdo kia tennis 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 graphical methods to est 8)(b*hesnkod 8lo+qb9vl4f iimate
(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 sg9*tmggj e7tuckqg*:80 ;qa lower leg bone of either leg? Ignore air resistance and0ag:c8tq gt7kge9m *uqs;j g * assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed3eu/p(6bpo kw of collides head-on with a 0.p (u/6p3eow bk220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B 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 s7jg (tcs 3w)awith a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and diwcs7jt(g3)a s rection 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 yc6 4lo23. gda)bqvxty4-:x5g a qfh;ncjr5 aequal mass undergo 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 positive direction.Let B represent the ball moving at 3.00 m/s in the oppt vc6agofn55)x24:qrj y y-cabga 3l; qx.hd4osite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s col t -7umeua:*ppk9+yt vlides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a pert-py ev9tup am*7k+:ufectly 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 spe ij +8(pvr,sct5e2vawr70edh5a q/reed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softbh s pe2,r5v teai/qrvwca8e( dj70+5r all 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 amusement park ride collide elastically as one apprgy :i5ubd go )fa .us 1.l4hu4a)5cefroaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg4fs5 ggfeuayuab rl)c:4)h 1 o.id5.u 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 ball makes an elastic head-on col( y ;ezypgy8uapob/ w0u8px7 )lision with a second ball initially at rest. The x0wbzp;8y7o8u / )g y(uppyeasecond 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 frictionless incline as shown inw g64f 83v-tjmqcy9(6wb8oqf9 j ke xm 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, where3 9yjxmboc8 m46f g wt(qkv-6f9eq8jw 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 ofn3vnb cb(x9 +1s0zi3;qw;-w tef uq s7hg3 geb an object 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, projectile 1 results in a maximum heightptk cl,3p - se)w52+fgg-jiot w,yln7 h of the pendulum equal tl icjtt7s,3w-2pngl +gyk- )eo w5pf,o 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 trav9af* qr(kf0o hc;3fubeling 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, w 0hff;9qakcob(f 3r*uhich 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 dvqg)/ ff7jj 03q:fem01vsqa for the 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 ri 2-.a;evnqv6l x4lj/ xtlsy8est, 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 energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter-a8sn4 xlty/v6vjx leq2l;.i particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear e*fogyy+ -r1 qnnd of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2qy*y+ 1f g-ron.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 ofjk0 pdidl q.vd8hsdm m)s 8t83e4xp8no zq9*( 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losingdd 8.mx9 mp0zdq8 3dljns8(t)sk4 p i*hq 8ove 90% of its energy?   

A measure of inelasticity in a head-on collision oy6) 4th b.2ybt bfiv w-1t3vvhf two objects is the coefficient of restitution, e, detvy. h6h vtv ybtbw-4f2bi31 )fined 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 piec.us5zbxs*ex g* 1sb 5ies, one with three times 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. Whebegsubx55 s**s x i1.zn 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-oa9 sobgezv)96f3 gfe7 n with a 10.0-kg object moving g of96sa3 gbev)fz97ein the -x direction 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 decays into a second nucleus, an electron, ppuov6 a-j0*a/m uiq)and a neutrino. The electron and neutrino are emitted at right angles and haq/ u pa ju)6*mi0pav-ove 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 ma kjpyh9ygu+u z/7o 1v.ss $m_\mathrm{A}=0.400$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 coljnrx cz+1y0k1y xz25ulision between two objects of equal mass, each having initial speed the two move off together with speed x1y n5+x01zurjkyzc 2v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles a pezt: ;remswkic:.-.dp r5n9-g* jb jnd 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 the95*etj:- k -wsm.jrei p.ncpgz ;brd: 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 perfectq6 xra7j9jhv26sbl1 bly elastic collision with another atom at rest. After the impact, the neon atom trbb9jxa67 h2sr v16q ljavels 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 collisi yk k lf4j4(fmi:+j(ypon with another atom at rest. After the impact, the neon atom travels 4 p(4yji k:(l+kfmf yjaway 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 shil4/qay) 4qm *;ua7wii4gdw nown in Fig. 7–38. Specify rel)ii4laa47qq w*n/ gu 4y;imd wative to the left-hand 1.00-kg mass.    m

  The distance between a carboh5z(6 /etm kuhy6gyg3di5o /wn 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 tx)d9 mfa z ;/3koh)ysrhe front of the car. How far from the front of the car will the CM be when two people skxs))9zmoahf3y dr /;it 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 by 18 m, of mass 6800 kg, is used asq ga2jp2asoivi. u h8 -qk;4z/ a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine th/j.pus 8v- 24kqz;aho igi2 qae CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidem/ m,-uyeb:pg)tfz-e4kta z* s $l_0$,$2l_0$, 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 identi;+x+*lvoiq s xe(u5ebcal 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 cranixo* e vle+x q5u;bs(+e operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circ w5zbbkn:/hees/u 9j2kxr9cy)l9 2 u fular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C: 2es9)zjukw2e9/y/ 5bufln h9bxkcr 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 sameq; .)h pm9jvnb as those in Table 7–1, and calculate the mass of one of your l;qjmv 9hp.n)begs.    kg

  Determine the CM of an outstretchaaox, u;d01xer z65ym ed 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 rivz-i- koo6ik)y(c t,vght angle. Assume that the p v6cti,- )v -k(iyozokerson is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs a;xib :zu(vm sp1n2gz )re hanging vertically, and his trunk and head ar2bsu;)pz(g1 ni vz x:me 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 and Moo9jw; oirh17/j ,raugx n are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m amvvzfi*hrgow8 ni 006a, d )n:part 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 head of mas:) uo fj7 w/rtux1sjv2s 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 ujo1/v 7rfxt)uw :sj 2point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical hemhn8t2r eewl- -i99nwad 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 rewhn9 -m 82l-9ewnit mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–1dwapa z 9,vl3q(zg x1utvz. 584 (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 ah3..xzu1 (fqhdsic4 u ir 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 b4d.x z fihq(uh3.uc1salloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat an voa4(fs7w4 r+ o7)(zdhxgnsn d is popped straight up to a height of 55.6 m. If the contact time is 1(h f dwng7sv) rxs474zon(a+ o.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling wit ,i6mrv6chr,y h 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 yksz8:2d4z0i*lva xg1evb (ythe corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the pla zkdyl1 8:02vs*xbzv ai4e(gyyer be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suitqa 3c6xxr9;8.qg1 pc)vk;fo 3 evgqwq) acquires a speed of 2.5m/s by pushing off wiw; f 3qx)9 .;cv cpk qxrgoqaqgve3816th his 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 and the oes dha*g f6 xd /.5iyk1ik/6cp/ wrc+other 80 kg, are initially at rest in outer space. They then push each other apart. How far6/h ydi+rwef.c 6csakkgp* 1/5 i dxo/ apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a*fcj :c 1vwpd6loi )eo+v9 ue8 second ball (at rest) and rebounds in the opposite direction with a speed eq)pc *o edi9jc+: u61f vowlve8ual 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 witn14jrx j m2yxelr255pov8c xiv ihn015 ess in a court case involving an automobile accident. The accident involved car A of mass 19 02y lhv 4x1v52n18xexcrjmiipor5j 5 00 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concr/xmu4m ps2 5lq 6ge4legm 4x+lete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horiml5e /6lxspgxeg u4l44 +qm2mzontal 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 abos w:lro+f3 c9tj).lav3w * gswve it. If the bullet has a mass.ag+fw9sl o3vsl c *w)3w:rtj of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block b)zty;o7.ey0-hz. j a jnxs3tof wood placed on a horizontal surface just in front of the gun. If the cj7e;-sjtnyz0b)yhta 3oz .x . oefficient 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 rowfb u:1ht ;xjz6boat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3. bj:1u6hf tz;x2 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 was ab mx0u7b834bqz oww- dg*8vzbnout $ 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 broke2)/h iiqp qn45 k;mmewn apart into two fragments by an explosion. One fragment ac4;/iq e2)kihm5q wp nmquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is 1n/ ao*gcr i-sgiven 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 -+i*ujwrqlsq w7(pi t4a9l)z $m_A$ = 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 radi,q ur: s29 ,vgf6az5xiqyqxlva(*sy0oactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucle:x l2gf6zuva*rq59 xas , y(0q yqs,ivus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an ao7wf va ;kx3oi*a z/c/ngle 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 slidesahj;+/31uk*p4ocrn sxh9 )0slw dfj t down 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 mass m if rke. uav,*ai9z3tx m*it is to rebound from M, slide up the.a3*v9xez,m *uraik t 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 the planet Saturn .) yisgmbk2e9moving in the negative x directi9igb ks2e)y.m on at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s