We claim that momentum is conserved, yet most moving objects eventually slow d 30ug-azu2 a yh6c7pfeown and stop. Explf0uc g ahz 7ae-63pyu2ain.

When a person jumps from a tree to the ground, what happens,h9 (fufjt*io-n smb9 to the momentum of the pers9s f* ijbu,om(9n-f thon upon striking the ground?

When you release an inflated butt,5 ps;wtx,da untied balloon, why does it fly across the room?;w,dt 5px ts,a

It is said that in ancient times a rich man with a bag of gold cod46siq8 khy an.3p 6t.x kcgx+ins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself hap 8q6x+antgsh36 xk 4dci.yk.d he not been so miserly?

How can a rocket change direction when it is far out in space dxi7i8g: +bvy and is essentially in a vacuvxi:8 + giy7bdum?

According to Eq. 7–5, the longer the impact time of an impulse, the sy7ru9qj s(xs 1maller the force can be for the same mo9(7uyq x ssj1rmentum change, and 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 dt6h d+b sn6/brigid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is th6bd/t+hs nd b6e advantage of this new design?

Why can a batter hit a pi zv9fiqj8pze-+o d t9j*8a6optched baseball further than a ball tossed in the air by the batterf9 -zzp8oajq+dj pvt6 i9*eo8?

Is it possible for an object to receive a larger impulse from a small forcef3 fsll g*7a( 1;zwr.b4wkqxu than from a large forcl1ks w*.z frlab4w ;7(fg3quxe? Explain.

A light object and a heavy object have the same kinetic 70a0 iq yq7af :pkjz2eenergy. Which has the greater momentum? 0aqqp0 zf:7 ike72yjaExplain.

Describe a collision in which all kinetic energy is 4w t)*(sbxctn , 2xa ant:pk-c8gu;u jlost.

At a hydroelectric power plant, water is dir1rj 7.xwo(zb b:i:/gft bv75,x kksx cected at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that 5:1ro zx.:(7, bj xvb/tkx7gcwfs b ikthe water rebounds?

A squash ball hits a wall at a 45 v x;;zxswts/7$^{\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 the Eac+kisx6a l;iqyq8g ,js646 kdrth), 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 cils66xi ;+4qqdky8s ak,6 c gjonsider 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 load in your ar5(pvj qq czaiz:m2 ,dw8g. n0ims?

Why is the CM of a 1-m length of pipe at itd;).v7;k6 1lr3tcanv hhxgll fj l7 b:s mid-point, whereas this is not true for yourv7hal7 ncxjbv;; f:hd6gtl1 )ll.k r3 arm or leg?

Show on a diagram how your CM shifts when yobi6fxs+lr,0c;f nx- ou change from a lying position to a sittingo+r 0fln -c6 s,;bxifx position.

If only an external force can change the momentum of the center of mass of an ob xr.bseo2-2eg6vs6 gcject, how can the internal . 2erc2-xg6goess v6bforce of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes inhqnm7 1t q mv4eg7d0q6to many pieces. What can you say about the motion of this system of pieces?4 n 7 q0g6medqh1vm7tq

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed o k/5l5-g t9xwpds* eezf $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What is the sck+9 yizqn) /dkier’s change in veloy+k9q ic/) dnzcity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive straigh+-2ko (eyoksot vr,z 3t back towa3o r+o2k,-tsy(zo kevrd the pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horl8q3 es (c2qnfe,sus 9izontally 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 resi nq,2sfeue(scl8s3 q9stance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gfhs5+azjc ;x1ases are expelled at a r;aj+z h5 1sxcfate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movink,ap3 id e2;qwg 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 q( -ctl5lm+a wcar travels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new cmwtl (-+q5al speed?    m/s

  A 9300-kg boxcar trave yj0ee4+ tjbx9y f; nz2/;z *yyzof2lkling at $15 \; m/s$ 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 thxusgx+ y(9men7ib u -qx,yw.59rp)p be 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 um x.xewub,59 xysng qp+b( ripy9)-7. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constagm,3n5 9nm n1- eysdugnt speed of 8.6m/s on a level track. Snow begins to fall verticallnmns-9g, g dy3mne 15uy 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 initially moving at 420m/s emits an alpha particle,n xrr;dyhlrf5mnc q5jk2 7nvc :( *8q8onz-c in 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 alnr8 hylmc q:fvdk-c, ronx n;nrqj(5 8z*257cpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230aa xci s3joue-n e82m4e*ki 05mr -zy6m/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullkay 4u5-2nie ie amjo3m6-c*z sex08ret emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speeda22oam50ntydfxhc-dz g n8*. 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 kgae +w )i t;w/y*w3zxixd sg:s, is traveling in outer space with a velocity of 115m/s Ts :e xwi*xywwi)d+ gas,z3;/to alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0(bwo::iwx m0q .045 kg is hit off the tee at a speed of 45m/s The golf club was in womb: w :q0(xicontact 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 velocityb b/y1h0lwe,we3vi7pe 2 4y((coxewpplmr .- of 8.5m/s and comes to rest in a time interval of 3ew/ rwpv- cey0y,l1i hebopp2ew x((l. 4b 7m8.0 ms. (a) What 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 speed v=25m/s strikes a wall attsiod7bs602p8ga b c 5m7 of2v 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 engibbkg4xmqu pvr,g7 ut+v1 fkng4jz -b;( 4:-oeneer 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 rest. (a) Calculate the avj m:of+4qg 4z(k1u7--v pvke4gn,t;bxbugbrerage 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 the east -fcnv 0 wkr5ux fb-:wi(p bc )k;i.is1and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Cal(pfkifcsw-5n vb: rw10kxu -ii;c ).bculate
(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 0.060wa(xz0yc e* c; kg) points in the +x direction and is given by the graph of Fig. 7–33 as a functi *0aye;w x(cczon 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 75-6h 1h caw.xxp8:uf(ogkg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m o1x:wgachh .pu8fx 6(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 speed of cr*35-is,gqa n asqh67i xp2 kgollides 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 0.440-kg ball, and B ri ,pa-27n 35gi*q6 s qhsxkgraepresent 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 h an) w)ae4km:ie3yu:6 2noggefl( w*pead-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and d(gf*wa:: uomn eng4k6)2 iaepew)3l yirection 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 collisioj1hul q*;-qfq n. 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 thef-h q q1;u*jlq 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 ballnu 1(7zl2yag/pd q/*oygks d.zi r3- p, moving with a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assum.oz /2- a3rpgk g *y1py(7d/dlinqz using a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is xe)3y 9nnkf)2 -sfgjhmoving with a speed of 8.5m/s collides head-on and jnfkyf e 2 3)hxs9gn)-elastically 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 amusement park ride collijwfh4 ptz .(5tde elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg4tjf(.z wp5 th 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 collision with a second bally8,hj, ;vzpws60 cmobvy *m,tc4qp 7o initially at rest. The second ball moves off with half the orohtb 46yyp q,z0,s ;oc*wjmcp,v 7 mv8iginal 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 5hh wy.ghzua/06/gt j cube slides down a frictionless incline as shown in Fig. 7–35, and elastically stri5uwhza. /jgyhh t/0 g6kes 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, 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 of892wtw n: 7qtxu(oqp n 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 res4gp cchic0g: qlc91eb2a9u* ,tif ,heults in a maximum height h of the pend c9fl:4th9ci0,u1g ,*qebe 2acg chpi ulum 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 im zaoa;q6ghoz62w. *ytself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pe amoz6q2*wo z.6h;ayg ndulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fracti)) 3ky,qh0( hld en+bb)hqm p;i8nlleon 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 a9ktg6p6l*rw u n object, 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 enep9*gu 6wlt r6krgy 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-kg SU9l8 x12 1srw( 8uik w3vebjpniV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction betweenu31pxi b(ksv8w9e 2r w jin81l 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,,ju9bi 9zmvng-ru7r4 dxhf , m. Approximately how many rebounds will t rd 9,x ,z7n4, jh-fugumvb9irhe ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the c ;6neln 6vbub48fy he 1ejz.y/oefficient of restitution, e,/f4ube ;lh8yy6nv1ej6.nz e b defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the mass of the otf-aanqh1;p * 5bp,rd,uky s t(b7 ebl;her. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels,5(f; r*tbhbp- ; ea yudn17p ksalq,b? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on (0c f0t:ig:rncu ;2ctu ) httswith a 10.0-kg ght:i t0 t0fc(nr t;:2cuc)usobject moving in 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 ldnh/c.a7 dn)b8yx t*a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and*yl7ht nbad )cx/d. n8 have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of mass 5av 2 f)(xbut; joru:qtr/+pm$m_\mathrm{A}=0.400$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 inbkj((bf 7p s6hc4 ww5felastic collision between two objects of equal mass, each having initial speed the two move off together withfwh(w4k5 jsf 7 bb(cp6 speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angle6plli*k y3jg64h8 ypn8z zi0bs 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 zhb 8py4 3 pjyl6klg6in8 i0*zis 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 collision3 pp8n+ 2 ix6mytf3xkm with another atom at rest. After the impact, the neon atom travels away at a 56+3 xyf mpm3i8tn2kpx5.6 $^{\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 anoth (ixzm:jrx /+oer atom at rest. After the impact, the neon atom travels away at a / jmox:z+ir(x 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 r/:s0o-3vy, c4umu n -ntw kqcwpp*h1yelatiuv n wywyq t:3 hp*-,4snk1- /cucmpo0ve to the left-hand 1.00-kg mass.    m

  The distance between a carbon atom (ln1v u hd37hta,7+e:n y5h tkv$m_{\mathrm{C}}=12\mathrm{u}$) 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 iu15hrt51,s cxc 0u cyps 2.50 m behind the front of the car. How far from t y1 rcc1s ,ch55uxtu0phe 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, 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, ox(k(ix4;d z d(y 5awelf mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loadeexl( (5dkya zid4(x;wd ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides nsmo9ko-dw6c e* . sj($l_0$,$2l_0$, 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 ierrq3kpu (7s*dentical 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 canp7s *3kerrq u( pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of gje3,6. z ic r(wu(xjiradius 2R has a circular hole of radius R cut out of it. The center of the sm3r(gc6zi,(jij .xw uealler circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proport9s.)(g doyu (xze8u evions are the same as those in Table 7–1, and calculate the mass of one of d(9zesu8g oy. (v)exuyour legs.    kg

  Determine the CM of an outstretched ar (8if 6j4apg*f ea-7vcx hyq1vm 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 be x(sshx7qx b7z +:p9tgnt at a right angle. Assu p(xxs7+ qxb hz9sgt:7me 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 legs j6w 5;uhd;s1m i+b+uojmj2u qbl+gd2are hanging vertically, and his trunk aswqb g ujudm+j+6j u 51+m;2bo;hi2 ldnd head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth lg .cn+ q 85kd(9q 7ttzlxo4xpth4)v kand 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 apart on frictionless ice.:k*vu87 .hqii,sd aq2e4 quag
(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 mass 2) goet o,1fzin)r7qbw s1 0al::;bm vt 9cr:pv.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, spinirvga z b:r,)t)n f0 ;1wpcmo79t loq::bv1 esning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diametph eesw*4cw 8:er 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 8eh*:cwp we4sthat will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14o cx+.bqch**ta*y b86 bhorn4 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mas+i /0noru+9nhfo 9gq,)c3re b: khe8b+arykbs M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect9 k rhnrb+ hca8q0y ebb : g+oue9/)oin3,k+rf 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 strikb vd2 6wmaq7(;mlqx 6sf7c8d ves a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during th(av6vxd7q8;fdsc 2lmq 6bm w7e contact.    $^{\circ} $

  A rocket of mass m travelinp:kuhjdt*i;eg88. w ,;tnwkg g 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 poczg 1z 2m6y.pynket 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? Give dgzn z6y.m 2p1yetails.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by pu7nay552vkr 1yel rmj/)sd; hmshing off with his legs from an 1800-kg space capa2r5rn5 mvd/ j;esk lm7hy1y )sule.
(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 at1jnu(82xfrtfj wj2 a 2 rest in outj2rnj u tjwxf1fa8 (22er 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 collision with a second atk4dlhku vnyz)3g mb-b(+t3g9bm; 7 ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What k7) -vmhz;lab3gb 9 yu(t4dkmg+3 tbnis 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*52 8pet(yk:ud ryp(u) rc ap8jtvxy* automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. Thy*xppvd)2uartcpry:*(t5ke8 j u(y8e 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 ,bljx; l rhk3+of concrete steps of total vertical height k ; ,3jl+bxlrh4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of(4 i5r sw1s-bnhmlgn6 a8bq)u wood at rest directly above it. If the bullet has a mass of 29.0 g and a spegqu8 slna1 s-4b6wri( )hbm5 ned of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embj,h.s/f b pjz* 5suq/tedded 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, andjz*,5 pht.sujf//qs b 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 rowboat of .9j4 u ;iidigamass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends o ;iaj.d9gi4ui f 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 waa,4e 2 ,adp.32veosx8 kn jzlhs about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments by an explohcr00bgesk9*ao8ze 86ioj9 psion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their masses? sc9 ebekz apro6g0*9h0o8i j 8  

  The force on a bullet is given by the formula F = 580-( c- zzfvl msosfi.ruk)*/32e -$1.8 \times10^{ 5}$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 x9uv j5f5ql w*$m_A$ = 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 in :1jsfw6bfy h3ld 1,agto an alpha particle and a smaller nucleus. What will be the speed of this recoiling nusf6, 1w dajbf1h3g:ly cleus 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 angle onga2 d;b n5u4ef 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 9kd/sdzys )c 38+igtj 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 jh2b/uzot.kx cf*5y7 to rebound from M, slide up the incline, stop, slide down the inclin7.zcuf5 yb2/th*xjk oe, 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/ hx jj9,h;asv moving in the negative x jvj/,9x ;hah sdirection 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