We claim that momentum isxhp c(xysea*kklsss,(p.q( 0u;5r9q conserved, yet most moving objects eventually slow down ansxy(r qlcksq *ph.upxs5;90 ska, e((d stop. Explain.

When a person jumps from a tree to the ground, what happens t: v a6btbj e8aano q6,(dm,uo1o the momentum of the person u,ua1meaqojod, :tbn6(8 b6 a vpon striking the ground?

When you release an inflated but untied baea1b7b - - 1jfsug-uorlloon, why does it fly across the room?b-e o-7aug -ru js1f1b

It is said that in ancient times a rich man with a bag of gold coins f q5 p sp9zgowluer3*38roze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himse wo8s9pl33ru p e5zq*glf to shore. What could he have done to save himself had he not been so miserly?

How can a rocket changq3p:x5 vwsm6a/m28jf x s;hwce direction when it is far out in space and is essentially a:x/msqhm pvj 68ww23cx s; 5fin a vacuum?

According to Eq. 7–5, the longer the impact tqc:p an5jxl bj5 6*nf1ime 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 bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or d*nc: qax51njfj l56bpeath.

Cars used to be built as rigid as possible 6fg1lfoy q06g to withstand collisions. Today, though, cars are designed to have “crumple zongo0qffg yl661es” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseb-8quxj2ast :uall further than a ball tossed in the air by the ut8j -s: xq2uabatter?

Is it possible for an object to receive a larger impulse from a small.5awb8 rv /4 ;bkvrfva force than from a large fvb.84v wavb5 ;afr/ krorce? Explain.

A light object and a heavy object have the same kinetic energy. Which has the fo,g d5-wp3itw9rl :a*fu .imgreater momentum? Explaiawil g *r:, f59idf mtpwou-.3n.

Describe a collision in which all kinetic energyu;oef0e2rs1rl h31m n is lost.

At a hydroelectric power pqmjpd m 5/0 hn:a2/ptqlant, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generationd0/:np5 2mphm/aqjtq , should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wal11myk6i r w(zbl at 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 ha afrf/,i:jnttzrt.2 . rd steel plate (fixed to the Earth), from which it rebounds at,t/n .ar.iftrtfj z2: very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean 2 tlnb4 8plhk3backward when carrying a heavy load in your arms?

Why is the CM of a 1-m length 08 o ;j p) xu/.ejrb2ldiggcx l-zx84jof pipe at its mid-point, whereas this is not true for your arm or leg0 x l4xjxgd8 2.)p- /liu8zeorjg;cbj?

Show on a diagram how your CM .apvw6hyg94 iq :qw0 qshifts when you change from a lying position to a sittingqw9 a4gh6 yi.p:q 0wvq position.

If only an external wg 02rf 6 d56pn:x rdp, +-ye(9hqgoy id/ztedforce can change the momentum of the center of mass of an object, how can the internal force of an engine accelerate a caryh2 dydp,wnr0q6 o:9+5d-(f dei reg/ gtz px6?

A rocket following a parabolic path through the air sudde3xqsxo62f 14oqgsft ux8w311 unj:y cnly explodes into many piec3xuo8:x11u qcs2foxjngs 1 3 wf46qytes. What can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of evv+gqkc, ra)/ /er p/a 28-g sparrow flying with a speed of $8.4m/s$    $kgm/s$

  A constant friction force of 25 N acts on a rk8e:gb) mk9bz8puks7a q(7z 65-kg skier for 20 s. What is the skier’s change in velocity?7 bg)7:u9kzk askme rq(pb88z    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit onfx,+jzn k-k8p( zuu)5b,rs hn a horizontal line drive straight back toward the pitcher rhz8unkj k,-f(p+b n)sxu ,5z at 52m/s If the contact time between bat and ball is $3\times {10}^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a speed of 10w( p2lmgk63r)xpg 9a )/mj rpi 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. rwjl 36 pm 92i/k()ag)xgr mpp The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling g.s2j jcmul9utfb*:h o 6(qt jb.vo9k 4ases are expelled atc vqt:2mjh ub9.k.f9 btl*(6jjsuo 4 o a rate of $1500kg/s$ with a speed of $4\times {10}^{4}m/s$ (at the moment of takeoff). F =    $\times {10}^{7}N$

  A 95-kg halfback mov6pog) i hsccn- e;f*f1ing at $4.1m/s$ 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 direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on aleve+wtqsz2ece3 3s0bi wa(1a v /kl frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, q3 vc z 302aet(kawwise1/s+bis dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelina,7 r, y,dfdkkg at $15m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of 100km/h If the0+n,clff;yv8r 5pl fh 71utio air strikes a person at the rate of 40kg/s per squlr 0fclp5t uy1,fo+ nf87;vhiare 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 $\mu \approx 1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{onperson}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a ctw( opyf/2bsa dp8 p-e.;0.j+eekf ae onstant speed of 8.6m/s on a level track. Snow begins to fak +bfe0(dfapp ej8-tep/.w e2; yo.sall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpydb043 8kd7esilrr8v ha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a masld e8kdy43 0vb 78rriss of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and emergefo+xfa:iu y.o0 v es3q+*ts+ ds cleanly at 170m/s I*+ xf+0s+d vutf.s3i y oo:eaqf 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 r 3t)1kbnw3c3l1jipdhp 6tt a sd2e 0;jocket is traveling at a speed of $5.80\times {10}^3\mathrm{m}/\mathrm{s}$ 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 $2.20\times {10}^3\mathrm{m}/\mathrm{s}$ 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? $v_A^{\prime }$   m/s  ----待选择----away from the Earthtowards the Earth  $v_B^{\prime }$   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? $a\times {10}^8$ a =    J

  A rocket of total mass 3180 kg is6k 14(hk ggrxc+; kqhedjh*5r traveling in outer space with a velocity of 115m/s To alter its course by 354hkr(d1 gx6+k r;ch*jkh5e qg.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 m-1pnp12i,he4 c d wzrz pm;*pis hit off the tee at a speed of 45m/s The golf club was in contact with the ba,;1 p2hpd-cnmwr 4*zp ez1i mpll for $3.5\times {10}^{-3}$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+lxr48jpgm 6y and comes to rest in a time interval of 8.0 lmy +grjx48p6 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 wal /y83*b dncglyl at a 45 ${}^{\circ }$ angle and rebounds with the same speed at 45 ${}^{\circ }$ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthiness of new vgexyvp 8 rc8 4ab/9,qautomobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kgq49gvav x,8er /c y8pb 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. $\approx$$a\times {10}^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 and is stopped in 0.75 s b1x aje6tatj6:znw j1 9y a head-on tackle by a tackler jntj1e xz66a:wat19jrunning 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 o 5u(t:qpiopw +ttu u2ln,)4pvn a tennis ball (mass 0.060 kg) points in the +x direction and is given by the graphppt,u(lwpot)2 +5vqnui u:4 t 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 per91zuqbq8 q(pq .bdihut.jl3u6p4.hw son 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 from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is p q8 uqu .j.6dt41ibphhzlqb 3(uw 9q.$170\times {10}^6\mathrm{N}/{\mathrm{m}}^2$ and its smallest cross-sectional area is $2.5\times {10}^{-4}{m}^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direc4 rgy6hkv,d; vtion) with a speed of collides head-on with a 0.220-kg ball at rest. If 46krgy;vv ,dhthe 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. $v_A^{\prime }$    m/s  ----待选择----eastwest  $v_B^{\prime }$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s ha3:mpjdr db (d9s a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represd: bdp3jdr(9 ment 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 elaslz)lcjubm-)k ;va1k0j- 8nsxxyp8uz zm . ,/e tic 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 a)j,k mk/xzzcjb; ux 8-0)yls lz1mun-p .e 8vat 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-on with a 0. s*ox.fq ylwf-kb()9a090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tenniyx afqks.o*w( -bl 9f)s 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 withhy(6 - jq:js vtafv,r8 a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.f :v va(j-ytsj,hq68r7m/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 a(acrmm*9uw aabt*90nxanp98n amusement park ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Caw*x mrn apc9b 80*(a9a9tnamur 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.$\mathrm{\Delta }{p}_{\mathrm{A}}$$\approx$    kg*m/s $\mathrm{\Delta }{p}_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on c4(rz( q;vcq1i x g;hzrollision with a second ball initially at r(c hqxzig 4;z1qr( vr;est. The second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\mathrm{\Delta }\mathrm{kE}/\mathrm{KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as shown i :zd-ujv8z;qun 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, where does each cube land? [Hint: Both leave the inclin q z:jzd8u-uv;e moving horizontally.]$\mathrm{\Delta }{x}_m$$\approx$    m $\mathrm{\Delta }{x}_M$$\approx$    m

ake the general case of an oby uv ,w(htq2/eh 6u2ocject 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 experimennj-j6 t 1u3gbk : kahqr6kp0/ft, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the t-n66 bkp/uajrkq: k hg3ft 01jhe 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 behcwu - w)l()curies itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vcwhe-c)l w)(u ertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kin2ijlzbk-spvk -en0 2 lg.*n3. imhm 7aetic energy lost, $(\mathrm{\Delta }\mathrm{KE}/\mathrm{KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, pd90 o. 9hl8-zhyvbvm6cv 8bd tcqr:8into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released it d8bh9p z 8y-dmlb:6.9v0 rch covqv8n the explosion, how much kinetic energy 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 reaujkxvvv;f (pt+2n+ p4sa) 4-bttu7for end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked,+avft u7 s;2tt+ov4)ujxk4 nbf(pv -p and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a heighhs 25j95hs egkt of 1.50 m and rebounds to a height of 1.20 m. Approximately how many reboundsj9ss5hehg25 k will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two otpfui/ e(jo ;nq woh)7d9c,;mk:dx3 k bjects is the coefficient of restitution, e, defined as d7e:kpduqo /3o)(hf;k,j;cnt 9x iw m$e=\frac{{\nu }_{\mathrm{A}}^{\prime }-{\nu }_{\mathrm{B}}^{\prime }}{{\nu }_{\mathrm{B}}-{\nu }_{\mathrm{A}}},$
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 wit(cek2+i v ng0uh 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. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travel i(nu+ ecv2k0gs? ----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 foq2 n(k tn-t ohunmy .h0s5*+with a 10.0-kg 5 0*h.koys(n humonqn -2tt+fobject 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 a second nucleus, an electr-od0eulau1a p 6 t. z-2r)xxbnon, and a neutrino. The electron and neutrino are emitted at right angles and h)bul pa-xu1azt .d2e6-nr x0oave momenta of $9.30\times {10}^{-23}kg\cdot m/s$ and $5.40\times {10}^{-23}\mathrm{kg}\cdot \mathrm{m}/\mathrm{s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $\times {10}^{-22}$    ${}^{\circ }$ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed ${\nu }_{\mathrm{A}}=7.8\mathrm{m}/\mathrm{s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at ${\nu }_{\mathrm{B}}=10.2\mathrm{m}/\mathrm{s}$ 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 mass3yu/++tpg p mrbn7*kznex-.x $m_{\mathrm{A}}=0.400$kg moving with speed ${\nu }_{\mathrm{A}}=1.80$m/s strikes ball B, initially at rest, of mass $m_{\mathrm{B}}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 ${}^{\circ }$ with a speed ${\nu }_{\mathrm{A}}^{\prime }=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'${}_B$ and angle ${\theta }_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. ${\theta }_{\mathrm{B}}$ =    ${}^{\circ }$ v'${}_B$ =    m/s

  After a completely inelastic collision between two objects of j+.svamd05h 8se fi-lequal mass, each having initial speed the two move off together with speed v/3 What was the angle bd-v 5imhf.ej 0a+s 8sletween their initial directions?    ${}^{\circ }$

  Two billiard balls of equal mass move at right angles and meet atyp z;ru99 e (bswe5c,yy5on 4k x*:dgyuz/7gb 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 speeds? directio9nz ;ybryw5s/9gy(beo*c u,4zxg: uy57pekd n 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 perfec8 df vhdmqm5x*d2z5o:5trw +q (r8kr ftly elastic collision with another atom at rest. After the impact, thr:8md t ddvrq5*(qfkwrzf5 x+8o5hm2e neon atom travels away at a 55.6 ${}^{\circ }$ angle from its original direction and the unknown atom travels away at a -50 ${}^{\circ }$ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly eav.,hp .(tovelastic collision with another atom at rest. After the impact, the neon (av,p hvo.et. 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 system4.9v 7 mx 7oxjic:kbwm shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg mbmcxw7 oijm:vkx 4. 79ass.    m

  The distance between a carbon atomj z2num/,kux p83;l sqren9;:kji4wo ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times {10}^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times {10}^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of the car. How ft 9 2mcs9ulvli/tqx; )ar fro qvt 2l );mcs9uilt/x9m the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, 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 raftmm)1* ql)e5hzt-jge vj mht.:(d ,qfg jz 5x0i, 18 m by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and S)j1 m5.lhe:hitm0 qfj(mxgtj5) * e,dzg z-qvW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side3ol+)rs,wq*t 4uuisvw ze8 +3vcj8yms $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_0$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of tomatomp4/d ,6 cu3ldufnh esnczm/n;4* +ad 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 openlue 3u *cs /pmfz+ad/d6 ;n4,cmh4d nrator 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 outnttp ,ojf/)kde kxh-9r( ka08ui-c/my: 9 toj of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hi/ -9u i9atp/rko( jje fhnm-:cxk,y) dt8tk0ont: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calcuvy.d qq.hd:. dlate the mass of o ..dy qq.hvdd:ne of your legs.    kg

  Determine the CM of an outstretched arm using Table 7–1 hzj0 qr o.z8zsj6ej*-x5.we4 hip.fs.   % 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* yt/vy4(m8wjz fx/l*7hr zfu-i,cnvnt at a right angle. Assume thawjtf7zcf(n iy* -z u/y8rh lv,/vx 4*mt 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 r05aqr9laa +odvu/q 1 legs are hanging vertically, and hi/+alqv0 1 5ar9qr udaos trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moo*s1t*b:jra snujqxp85uc h h)3q(b d, n are $5.98\times {10}^{24}$kg and $7.35\times {10}^{22}$kg respectively, and their centers are separated by $3.84\times {10}^8$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 frictioncwn- +t;w (dl+zrr-fu less 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 mass 2nw.2(48yx5go pf x mpe.00 kg and a diameter 0.0800 m mounted on a uniform cyle(n8o4p 2.fxm xwyp5 gindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of massenmc)m x0i3 u bpj6*,nke hff:yyk7.2 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, fky un:.ki0)7emb2xmnhjf3 y6 p* ,ceas shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29:p4p2gl va ay,), $m_{II}$=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, ahzjh p2: 6/xzlre 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 respect to the balloon. With what speed anzj 6ph/hz2:lxd direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizogu) pbc+3o)kp-un f :qntally at strikes a bat and is popped strai 3-:uong)pfk qu)c +bpght up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    ${}^{\circ }$

  A rocket of mass m ti,7az/v gf+av raveling 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 fa35eq q oxbl6t7ced with the corner pocket shot shown in Fig. 7–43. Relative dimensions are 7l56xobe tq 3qalso shown. Should the 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 (including symnco.uoa t.vl .m **1pace suit) acquires a speed of 2.5m/s by pushing off with his leg.von. u.m *alc*o1t mys 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 :. 6vip/drn lfkg, are initially at rest in outer space. They then push each other apart. How far apart are l6:/vnr idf. pthey when the lighter astronaut has moved 12 m?    m

  A ball of mass m makegmo/ 84eo-g x k0ygz- 0,c egckeua54os a head-on elastic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the seczogg cxke/0cg y -,5o8-ag4e40ke u moond ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court 6hd f ho(d6.rgmz)kw2 case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. Thg(dw)mk6.h ozr2 6dhfe 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 flig u8u/dzyhm,on9 kd ()eht of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth boudokhyz8 ,9demu ) n/(unce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood :xev(ss6.atzi *(o0f5yq o im,9f tpzat rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rim((i,a izt.s95feop6 yt*sxqzfo : v0se after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embeddavr90c xo8ui 0ed in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?9cro ai08u0 xv    m/s

  Two people, one of mass 75 kg and the4v36lypuxz1g fq (v23bg; s idl-+c fx other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite2dfyll3+3xq6c( u gfvp;41vig bzs- x 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 a65u.:u +k*vlqc vlnsqhg sv- 8bout $1\times {10}^8$kg struck the Earth ($m_E$=$6\times {10}^{24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $\times {10}^{-13}$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $\times {10}^{-17}$
(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 nq dp/ tv; 6q1yb3aul )1bikn:apart into two fragments by an explosion. One frq:/b1;6l)nt n daq u bvyik3p1agment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the foc61zgb3 -7hv+ i zodwhv08wadrmula F = 580-( $1.8\times {10}^5$t) over the time interval t=0 to t = $3.0\times {10}^{-3}$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 masses4 uxg2e;pq7 r;b crow; $m_A$ = 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 de((/d +zhm ) tbys3cbwxcays radioactively into an alpha particle and a smaller nucleus. What will be the speed of thiswcd / m+ byt3b)xh((sz recoiling nucleus if the speed of the alpha particle is $3.8\times {10}^5$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) i5imb j we5yihc/+,kc, agb*v.s fired at an angle of 30 ${}^{\circ }$ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\mathrm{\Delta }x$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides dolc* asu; nf:)ld r, /doqyh*,ghlv;4t wn 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 thi14 gg6y9 a;xt/r1 xip7afp yee upper limit on mass m if it is to rebound f gxpaxpi;61a/t4 1y y7eri9fgrom M, slide up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot efk+exfa/ 6b qi2c-)eg vfect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The massqx-k)62ai g+fc b/eve of Saturn is $5.69\times {10}^{26}$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