We claim that momentum is conserved, yetgn85 i(8thj-) p tz:od85koqt3 hdtb k most moving objects eventually slow down and stop. Explantob(k5-i5:8q h) ptk8 jd gzhttdo38in.

When a person jumps from a tree to the ground, what happens to the momen)wk43gvn46l *zg 3+iluqyudutum of the person upon sdvy 4u )gzq+ugw3 4n*6ku3illtriking the ground?

When you release an inflated but untied balloon, why does it fly across the room2t4yl inb.u,l yu btn.il,l24 ?

It is said that in ancient tim.vxy4gl4 fgmz2wmi8c( *bu 6qes a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because zwcxi8.4 qu (f4gbv6l mmg2*ythe 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 whd.z q8o wq;am0en it is far out in space and is essentially in oq0.z8aqdm;w a vacuum?

According to Eq. 7–5 gax)w wxc 9by ))a7d4 vb,3kxdd8yo y,vxh-e2, the longer the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air v7h)xb g39dv4yawxk,ay dyex-,)82 oxdw)cb 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 d7v h +qa;(1ucu*j/g vufsw,nwithstand collisions. Today, though, cars are designed to have “crumple z cu*1aghj n(w,u7ud/v+ ;qfv sones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in6gv5+sh; g swx the air by t5;6wsh g+gsxv he batter?

Is it possible for an object to recmk;p 7n(qgh9u eive a larger impulse from a small force than from a large force? Explainphn( mqu97gk;.

A light object and a heavy ob jdg7hub7b5j yrk6j1*eudd+ y2bh) 7bject have the same kinetic energy. Which has the greater momentum? bhr ykyb6 7uddj17jb 2ed 5*gu+jh7)bExplain.

Describe a collision in which all07p kzf;jy/s2ya ig0f kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed a1oo+y.-hw gz*iwf0 m3 gxgo w9gainst turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbing y*.mo-xwgh0 zw ow 3f1g9o+ie 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 araqjdg65y1f 4u i8b;x t a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixed to tzekn 2 *sm6i0ttj ;/orhe Earth), from which it rebounds at very nearly its origint2kms0t z*/ijoe6r;nal 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 carrying a heavy loag7,tkc+squu 9d in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas th+b-u )olsffgy-we- j*e ya)7r is is not true for your arm or legy)a*e u-+-ywe -bg)fr jflo s7?

Show on a diagram how your CM shifts when you change from a ly*fh6y+ymar/ uwcy/d4; euc t+ing position to a sitting positc ry*/+e;ya 6c4m +fd utyu/whion.

If only an external fors :ovcq v(05g3lartj3ce can change the momentum of the center of mass of an object, hows0q33 ralo (vj tc:5gv can the internal force of an engine accelerate a car?

A rocket following a parabolic path through th a22s :l9nchg m+ jg lw.gn;;evpde53le air suddenly explodes into many pieces. What can you say about the motion of this system of pie . legn+c2lg2 ewlmvjdapg:;n9 53hs; ces?

  What is the magnitude of the momentum of a 28-g sparrow fgrdpi-t(wvr u*6 8zb 6lying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kgt.( wftioigj0a/7 +1 vbpgz a xgc*5t. skier for 20 s. What is the skier’s chan/oi *c0. xvga(.1ptwa b5+7itfgjt z gge in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit o 9 n0ddbs:/vjbn a horizontal line drive straight back toward the pitcher at 5:djsb0 v/9dnb2m/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 spezka oh9h5) rc;ed 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 ihrhca ;5ko9z) s 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 pw3z l4h 84ifpuropelling gases are expelled at a rate o4 h3 pi4uzw8lff $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movingn(dl+icpgk6 ;*vl-ko 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 ale*5lk /m(q tnpevel frictionless track with a constant speed of 18m/s kq5/e l* pt(nmA 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 ovqnp3hz9j p x), kmsy.2s uf,44s, ecat $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of 100km/h If hix 3r n70,c6on;jmkpthe air strikes r, i;x0h km7p6co nn3ja person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along 7va,2tli z dv81imzs6 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 ca 6z im, s1vzdtal8v7i2r after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in the dir lj7y3e+gkn0 7mj m*z-6ilppx ection of its velocity, and the remaining nucleus slows to 350m/s If the alpha pax6plz ljnmep+y m*0g i7- 3jk7rticle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg b;4 y2qqw21)oxhlhnl-rd z6r clock of wood and emerges cleanly at 170m/s Iq w q;1c)rdlz22h4 on yx-h6lrf the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket innu1xni; vz - vg jp e5*-q m-4dczpqe7dbo041s traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a velociws b 4k ,veq13*yozvt9- v1nkf(6atyb ty of 115m/s To alter its course by 3(wtb,k4v* bo zy9a16sv e- v3tq1 nfyk5.0 $^{\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 3 yth(+, ux2/cbk 1e;doobjgcgolf cluoc3du/c1jbek+ 2,t hyg ( o;bxb was 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 rest ina:xwt +czecll )a) *p khe:l5* a time interval of 8.0 ms. (a) What c:l*al epcwlt 5 akzh):e)*x+ 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=0.06kl 4av.8ehccv (g and speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer9dl,k8yk40 6krftv ir in charge 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 irk6tr , f8l4vkyd0k9rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/j:ohl hftji0,b3 w0bvjlhrj5ck 0; k 7++:htqs to the east and is stopped in 0.75 s by a head-on tackl7iqbjlb0t00ljw+3vj ktrhc;h, h+hj5:: fko e 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 ke fdvd/*8xikzza0+r9x /)sr mg) points in the +x directia+sdx80r) e* k/vz9ix f/ zrdmon and is given by the graph of Fig. 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 a 75-kg person jump without breaking the lowetps6 2 qzn1+wtdh+0a;kjgcx0r leg bone of either leg? Ignore air resistanceadtgx1 n0+ htcqjz0 s+;6wkp2 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 0.440 kg c5q/;i(1ik x.n .vfyg8marcnmoving east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction n8 .cy/c.vi;ga qi(fn1rmx5 kof 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 with a speen9r9konfg v (r :ta61fd of 3m/s has a head-on collision with a 0.900-kg puck initially at res 1k9gnf:o(a9 fnr 6vtrt. 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 peroe+ 18nrv-w8vy;:z pskc2exsfectly 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 coc1r k-2n8 :;p8vzv eoy s+swexllision?(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 )pc7ccf70 lpk1pe5 3jyp, sql-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 p3jl 51,kc7pc l) fspy p70cqespeed 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 th x1zqsm; j0pb-at is moving with a speed of 8.5m/s collides head-on and elastically with another baj0p-;1bzq s xmll 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 amuq:1jj 3sj/z dzvk yzebf:8f8r w;* .+sqbo 7rgsement park ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Carz*8j;ow+z:ze.s8k qj3frvbrs 7: 1 d/j byqgf A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elakm+y,jg. atl ru5+k*cq yj27astic head-on collision with a second ball initially at rest. The second ball moves off with half the orig7gqayukt,ym*. jjk5 cal2+ +r inal 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 showncb52x abf-d 1*cunx e/ in Fig. 7–35, and elastically strikes anotheb/xu5 n-*ccxead 21bfr cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of )w75be t3nskmh)cj (w l262j z yj6karmass 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 f)xwg o77 cte .7izurdtzl 4..1 results in a maximum height h of the ped7tur 7.ctow. 47lfx)zg e.izndulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-wa:l *8oko -bpzhkw7 /kg pendulum 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 di87*-p awkkb hzow/lo:splacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fractionk*d ,odj)r7+. -ov p6rjv iofq 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 objxum27twwjb2 79o p 9wbect, initially at rest, 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 9p9wwx2ub7jm bt7 o2w represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides intblc mg-i2,xi;r5nes ;o the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coeffi-g ;l riic ,bemsx;52ncient 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 1.50 m and rebounds to a height of 1.20 m. .p9en)jd1t4avvil* v Approximately how many rebounds will the ball make before losing 90% of its enid)e*.p1vjl 9 nvatv4ergy?   

A measure of inelasticity in a head-on collision of two objeczw, gcux9 choe 11i. rl.e-anm b;60phts is the coefficient of restitution, ,u.-w6 z; cme0ern xpb1chi9hl.g1o ae, 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 tw:k7 /- so1sg5 .fn tn2q 9f;uobueknawo pieces, one with three times the mass of the other. A depression is made in boufsg :b. kn ;w/n27q1u9tef-5noosk ath 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 directi fkq/fib7j3d - xjua ospxz+4 f71,so1on at 5.5m/s collides head-on with a 10.0-kg object moving dq7, o1j sbk4-ifzf3po +xj /7saf1uxin 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 intcmp/klo(e v:gy(/ vlr 5 c2d8ko a second nucleus, an electron, and a neutrino. The m( v/y c(oed:5lclvkrg /82pkelectron and neutrino are emitted 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 massyv+ + ;3+mcdd7h bfkxh $m_\mathrm{A}=0.400$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 cws upgj,:eqr2,2w ,g rollision between two objects of equal mass, each havi,sp,gqr u:rg e22,w jwng initial speed the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass moiyq-na3 ;z g6sve at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along 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 ys;in 36-za qgspeeds? 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 collii05+mzdqk2rad 9d:n b sion with another atom at rest. After the impact, the neon atom trarnb9qa idm+d:0z5 k d2vels 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 wifv n9a*ua,7e)qcn o+hvvf s /0th another atom at rest. After the q7nf0*o +avcs/a f)vu en,9hv 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 system showngb)b +(7 z 4beeo6f xaf,5gfze in Fig. 7–38. Specify relateo46e+b bgfzx,a ef(b7g)5 zfive to the left-hand 1.00-kg mass.    m

  The distance between a32p p wsl-* o3ghohyqvwa)v4+ carbon 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 ofngfqwn6 +969ge ytug5n,* hxi 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 fg q9ix g69nw5gyhnn6*,+ute 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 (fp(4jx z7g7sel.wo 5jb+l2xzrz l0o6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine thejwzfp e+xzlxzlsrjo( g72l b504. o7( CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side -fqz7wq1vjps tn0 )4 +cs35xxgv(phv 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 loayq,g(3 :d syvtd of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find theq3y sg,td :(yv center of gravity 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 2R has a circular hole of radius R cut oulu;cmjj -z1-l t 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 o--cj1ul lm;j zf mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportim:/p x,7dy nh;kgs g:wons are the same as those in Table 7–1, and calculate the mass of one of your led kyw; xp7sh g/mn:,g:gs.    kg

  Determine the CM of an outstretched arm using Table 7–1. /f2q z0b d wvvxj ql1szh2*qg1u2a5 9q  % 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 (c+r 2wtlnkst7xjp 3z.nw;: xbent at a right angle. :t+nc2w r.xnk7sjwx(z t 3;plAssume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and leo-))9:pzycmt f* svs wgs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be out o s f)9ztw*yscpm):v-side the body? Use Table 7–1.

The masses of the Earth antd-ph15 ;p.q enjtbvs46 ph(xd 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 stand 10.0 m aphx2/zr/*(lqb wd; yavart 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 ofp:m/ /*vgmj*c+ve jnf 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 is the point that will follow a parabolic trajectoryvgm+ f :j *m/*vjencp/?    cm

  A mallet consists of a uniform cylindrical head ofsm5f ru1 s :vg-k+cl1c 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, :5 +1c-l mfusgr1vksc 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 3n-czqg6 ijjd)(k/e qExample 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the/tl 4y6 k/usei air and stationary with respect to the ground. A passenger, of mass e6t4i/ksy u l/m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is poppp e-t* bpenc034 6klgved straight up to a height of 5vp-*bn t4ecke0 lpg6 35.6 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 trnq9kg y4,s tf9)va*um,l 1w kkaveling with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown in Fig. 7–43. Reafrf7tvy *g9q3y +s/r lative dimensions are also shown. Should t fta rvsy y/+*793rqgfhe player 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 (includw ;7gl8jwhq9ding space suit) acquires a speed of 2.5m/s by pushing ;8hdq7wl wjg9 off with 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 other 80 kg, are initially at rest in mnyc8 s, lk5*ejxi q0mg*j bn1*67sm mjmn**5i6qm n8sm , mk7cjl0sgbe*1x y outer space. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic colt:yzv(k xsq(- kd)j;n lision with a second ball (at rest) and rebounds in the opposite direction with a speed eq-n(kvzxyd;tq:ksj)( ual 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 court case involving an automob(m,at7 les 9dp(cjr:c ile accident. The accident involved car A of mass 1900 kg whit( 7rs,9d m (leca:cjpch 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 concrkh2 h 9l2t,gmzkwkjmxav./ *5ete steps of total vertical height 4.00 m. The ball hits four timesk,jxhw / gmkka52 ml2 .zhvt*9 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 the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest dc aqrrmh2/ s5 wyweb,y02n1x :irectly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s hosxec21w m , w/ 0qn:2abr5hyryw 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 blot,. ac--vr /jajl rwoyrybq8+k k8*+bck 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 qryrb8+b-a t.kja-r/8o k+y,w*v jl cm 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 b j+t3p58q djg60 kg, sit in a rowboat of mass5b tj3j+p dqg8 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was aboqf rpav-7 q+yv6y1zmu24voi 1 ut $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fri- z )q0h/,qvna*55rpilw1u k pwd 8ziagments by an explosion. One fragment1uzdq iq8hpvlnr)ip,0w-*wz5i /5 ka acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula7bm c8zvn (f+b66uj((leld /r ,dbi xw 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 masses9q v3gg j736xzwhx,jj $m_A$ = 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 atbl 2 bj(z5dl4c rest decays radioactively into an alpha particle and a smaller nucleus. W (db4zlbjc5l 2hat will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is firedw3n:x25oxg+-q s pfi l 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=2.2kb4bm8.qs t**)gh q.c v,ehffwg slides 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 it is to rebounds3;7ybczr pv 5 from M, slide up the incline, stop, slide down the incline, apvzcyr;bs 375nd collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 32 yueyim46,n.uiqy mshows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s Theq63iu yy y4iu.,m e2mn 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