We claim that momentum is conserved, yet most moving object ,vvb+, zq/ 9amfmbk9wlyti(bta, 9e1 s eventually slow down and stop. Exya9z,, 9 mi bta,1(vb/kq fe+bltv mw9plain.

When a person jumps from a tree to xvq, kcnw436)yuq-c gthe ground, what happens to the momentum of the person upon striking t) cnqkgvxw43 6- uqyc,he ground?

When you release an ivls,.dd/bnm6 x28 rn b5lnb 5gnflated but untied balloon, why does it fly across the room?5d.b 85gl,ln6m/n2 bn b rdvxs

It is said that in ancient times a rich man with a bag of gol+k7f i .o7yzny(nt; nu26wfvhd coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could heky.( on7zt7 ;2u 6f+nv ywnhfi have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is essy+pv ) +, ka9olnzr*wsentially in a o*)y lk++r9w sznpva,vacuum?

According to Eq. 7–5, the longer the impact time of anf/e8m2bpa ld dk *8k1 8dagr 8w05pxhl 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 odp/hld1r fl88 8g*kw82a k0 d abpmxe5f air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstvkvmoh/.,( te c))xhc and collisions. Today, though, cars are designed to have “crumple zones” that collapse upon )cev .(tcxhmhokv ,) /impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in5 5n g;wm/nmj3cav-0(tl9qy3gs aby8 hmv) q t the air by tqmtn-gtca wjbg ha5myq3y(s5m3n 80/v9l v );he batter?

Is it possible for an object to r za x xsbfzovq6u1j88f/8 (6n w39rsobeceive a larger impulse from a small force than from a large force n6oxx88o a3r96 bbuswz/(qv8 jff1s z? Explain.

A light object and a heavy object have the same kg fv8k;suu)) minetic energy. Which has the greater momsk;vguumf8) ) entum? Explain.

Describe a collision in wh7 w;qz4hsu1pvtv4 b k,ich all kinetic energy is lost.

At a hydroelectric power plant, water is directe/t+i ufw p)j .:yf-xpwscb1w;msve4 *d at high speed against turbine blades on an axle that turns an electric genem1s /tv:iu;sw-fpc4 ) +wf .jpe*wxyb rator. For maximum power generation, 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 wall atd*1 f-qm0bv58ou sl zt 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 tc0)ggz1f 8mz +s mr/umhe Earth), frcm+8sm r/ zmz)g0gf1uom which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for 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 arn+s1v7. cnvsww y)/, s;,mmvcdqbc+zms?

Why is the CM of a 1-m length of piphbryaa3uav60l4d, 1 gg6 zx6re at its mid-point, whereas this is not true for your arm or6 gzr14 dl0gyu,v3x6aaahb6r leg?

Show on a diagram how your CM shifts when you change fiwj0 t 3 )zulwh);af2yrom a lying position to a sit 3;)zy0w uti2lw)jahfting position.

If only an external force can change the momentum of the center of mass of an6 ceda(*kn,jj object, how can the internal force of an engine accelerate a c*,dc kajj6n e(ar?

A rocket following a parabolic path through hk f8 d5rua*,woqxi+l6 g0j) cthe air suddenly explodes into many pieces x* jkurwf6ago+l, )dq 50ih8c. What can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying e1,3nz ws ber 50wg0idwith a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg s0+ d c9ru+wb iyd2cf0pkier for 20 s. What is the skier’s change in velocit di02dby0pw c fu+rc9+y?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive stracb4sbxe0jg 7cdy+onfs1 b:92ight b+d1c oe4j7 n9y0s2:bf gxb scback toward 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 o52v4dwucpqygso3t)p w wg 69 n- 93itjut horizontally with a speed of 10 m/s Fig. below Calculate the velo 9jptg2yqww3 s6i3do c9)npw vu45t-gcity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, 1xx- lghd6 si)given that the propelling gases are expelled at a ra)gxs-hid 1 xl6te 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 mov;rfu0b :kab 3j/ad *7:wbi4s hxb i5sy0f1qhqing 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 al l /5def7lmjt n+pezjtlo+(u:52gcy *evel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is droppedjeto uec(j 5:g5ymdf lzn*lt/+ 2pl7+ onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at;9m*1-u-gmewx wfwkpg w:i j / $15 \; m/s$ 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 10v*2 d;a-lrv dn0km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a per* drldv;2a-v nson. 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 constant speed of 8.6m/s on7sket)h,n h* 3 6ffyes a level track. Snow begins to fall vertically and fills the car as*he63f) se7,nfkh tyt 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 in srvk2garm- ;;uw :l-pthe direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have-; gr:lp- a2us wmk;rv when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetr6fc9qu:hm0go/ py ynj b.j 3;rates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, hphj:r/ ;nfbu 93g0y6 ocjqm .yow fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is travxlp bopyhi+93u2 x* -peling 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 neorp,w 1vb6o00m .pbis traveling in outer space with a velocity of 115m/s To a0n,6rbbwe.opo0 vp m1lter 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 0.045 kg is hit off the tee at a speed of 45m/s T4c gyl- /zvnl8+.h zwd1di/h xhe golf club was in contact wit+zi18xh.dyc-hgn/ l zvl w4d /h 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 atr kcvf6eu/ +nre8,5by a velocity of 8.5m/s and comes to rest in a time interval ok/+ecy5 ebr f vu86n,rf 8.0 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 wa,bk/ qxe ppfm*- 9cs4zll 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 engineeuziekv/ 6x*y2r 8o 8c; geuax,r 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 ix6u*8ee 2zurgykoai/,8x ;v cs brought to rest. (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/s to the east and is stopped *pp/e 1m 37g 9rmvyaxwin 0.75 s by a head-on tackle bwp*v 3gyx mp/1m e7a9ry 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 (+s30xdwu,gbrz vuwce3 hv27 ball (mass 0.060 kg) points in the +x direction and is given by the graph of Firvcv 3 3wwue+hs 7ub,(0gxd2zg. 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 f60sa qb6xd:elower leg bone of either leg? Ignore air resistance and assume tq:s6eab 0x d6fhe CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction)kih .a*y ri) :9+iqzn;:nojbg3h t yd. 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+ j*3in:.a:)hid;9o kir zygy t.hbnq direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/z5 h:h oki1h3fs has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the spzh5hf3iko1: h eed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastic k ;efsi: tr-:fhead-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive di ;: s-ferkft:irection.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 18uab(os-k*, k ucciqwith a 0.090-kg ball1oua8k cc(i s b,*-kqu 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 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 c; obgqj,24jo is moving with a speed of 8.5m/s collides head-on and elastically , ojc24gjoqb; 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 amus*ektec:9 yggpoj cm,n.) w .0jement park ride collide elastically as one approaches the other directly from the rear (Fig. 7–)jomgc9 ngp0w *e.c:tj.ky ,e34). Car 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 elastic head-on collision with a secon2ojodk5: 9hjfvh9( qx d ball initiallof:9vd9o( x qhk5j2j hy at rest. The second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionlexu ,.zvo/lpl(n2s /iess incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is onlyslzo,2.v n puxl (e/i/ 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 o/8njmltzps 7c) m8e0 kf an object of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a max vs.g(mp,1hqkodaxt k:, / hf)imum height h of the pendulum equal to 2.6 cm. A second pr,q)hxk k.ov:,fd(p/ gt1asmhojectile 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 i1qbd iseze4tu( 0 9tg4.v3svftself 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 verticae4f3s es1 9 u dvqt(.0gti4vzbl and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lo,ql00 x:w9i7mkc0r ss9b momrst, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an o2gejov4 m +vjo4dxb (rm3b9/h bject, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J jroevm m4bv x gj4o/2d93 b+(hwere released in 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 coll v6fhz;e c;t-fv9o dhj6r:rv1ides into 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 coh1v 6zo6 jevc;d;-r9rfhf: t vefficient 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. j g.,l2w o crh84jjzun.ri5c;Approximately how many rebounds will the ball make before losing 90% of it.8gr;,425jlorc j.wnuizh cj s energy?   

A measure of inelasticity in l lgmz-7s990vka rvlg,2,oqaa head-on collision of two objects is the coefficient of restitution, e, defined as 9glqal9zlav0o m,rg ,7ks-2v $e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
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(9 ktmo(n-a.hac3 ibp9 nq)ys 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 sepa-3 ncm nokbps.9)a (a(h 9qiytrate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-u bzkbe,l1zvbpxh, qbvgc7o :n*:93,on with a 10.0-kg object moving in the - zb 19cb*nvle:gv,b zuk :q o73x,hb,px 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 decay(w/rgti 0g (f,wtz2iyb1) o3m tricd9s into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momentaotyif9bztt 2i(03r c1wgriw/, m ) (dg 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 mas-/a adw2e- b ym+j2wfss $m_\mathrm{A}=0.400$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 oz,i5o3 cyi o4nf equal mass, each having initial speed the two move off together w3con5oy,i 4iz ith speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the origafc/.grq9b5*oxb h/g in 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? dir/b5.ah cfg bqrgo /*x9ection of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) dk6- vctf.1i omakes a perfectly elastic collision with another atom at rest. After th16focdtvk. i- e 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

  A neon atom (m=20u) makesbk /wkxd48tv/x 9y73d8f mk:ml t8fza a perfectly elastic collision with another atom at rest. After the impact, the nkdf f39ay8:d/7 lkbtk48/xx tm8v wmz eon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. Specify 7 m4i.d6aways relatia. a4y w6s7idmve to the left-hand 1.00-kg mass.    m

  The distance between a c:o7b-k /qv)oomxx 5wpmk2l 6 xarbon 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. f:akr0jp )9 nr4rh/hg50 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back se0/r fn9:rk p)hgr h4jaat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is use8j xtcu kqkm g/2*w;8cd as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboxg 8jt 8m;uk/c2q c*kwat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides o4kmucvti. 6 4$l_0$,$2l_0$, 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 tomato v0k73r0e fjaj paste (see Fig. 7–40), each of which is a cube of length l. Find the ceejkaf3 v 070jrnter 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 ci6t zt/0h;zaqbbs z4, kv:1qle+ t wjb-rcular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the centbq6+l 4;j/q zwb k:zt z0b1sht-a, veter of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those insj:n swrc3ik:5p sa0 7 Table 7–1, and calculate the mass of ow:3as7jr sc:s0ni5kpne of your legs.    kg

  Determine the CM of an outstza7bo1hf39 vbg; oniv tv/- 2tretched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of g-l3h7e1 sr(zkiye/lr mi(kw /q8 :a ran arm bent at a right angle. Assume that the /:8hqrei w-/y rklem3rkg( a7z l i1s(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 are hanginibs:,frhs* l n):w :iag vertically, and his trunk and head are horizontal, calcs: :i,)s*franb :lhw iulate 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 Moon h1ij 8,vgdwcj 8m8q 6qare $5.98\times10^{24}$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 iz.58ux* cxi ;gcprp4 q-6cb iace.
(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 cylindmi37d w3dbg-w, 1 rhfbrical 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 trajech,3w -db7 w drbfg3im1tory?    cm

  A mallet consists of a uniform cylindr jqg hsm;v.wlm-gxt: -i,m+2iical 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, sm;,v+l wgx hmmtij-.2-s:q gipinning, 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 7–14ovenox)x twz ve eas+)k+1)22 (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 g. ykle- u *wruy2/j8ch o+bvr.ondola, of mass 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 respect to the balloon. With what speed and direction (relative to rvhe y2k- +.*8jw./lu bcr yuoEarth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat asru ;38e,tqf ond is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on3u8oe r;fst q, the ball during the contact.    $^{\circ} $

  A rocket of mass m travel8wpm bxa )m)0ming 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. 7–43wvx b4vfauc /3,8c.(m9 v1pzh0v lpsc. Relative dimensions are a0.p3lvu8b/1 pc (cvh4,9azvmw vcsxflso 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 space sufxc0h r x2 07mavxm5s(it) acquires a speed of 2.5m/s by pushing off with his legs from cm(a 70 mxxsxfv5 0r2han 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 on1c jic3z5n ;(vs b3fhf mass 60 kg and the other 80 kg, are initially at rest in outer space. They then push eacf jhbn53c; 3v z(i1nsch 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 3 (r4slngpuo4dv162 u y9u6ijkkwgj2with 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 seco2gu2l4ogk6n6 r(91upjy3dwk u svj4i nd ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court ca4lz5gph qi t/8se involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m whil5pqg/z t8i l4he 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 92hrbrxerzx e cm*ris)/g) x97 .-zc ik0x)cj 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 bounce when the ball reaches the bottom of the stairs. hee/irxr9* z0xcbmjrkgr-))) 7cc9sx2 zix ?

  A bullet is fired vertically into ac,c f e6mj8+so 1.40-kg block of wood at rest directly above it. If the bullet has ,sj8 eo fm+cc6a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becoju80g+ a)mg/5rx nwq lto+mo:mes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it5o 0mu+lrqtwo8x+gjn/gm: ) a comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg anx 7wi8x 5f vp+ze2r;arhi4h /dd the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, there2;x7r4v+a/z8f5 hidixw ph 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 aboz12 t(o1vwwwe8mgo31 vs,lmnut $ 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 8s9 1ymtdm*ddpv, w 5m* o2oksexplosion. One fragment acquires tw9y*mp sm5 *2o1 tdosmddv8 ,kwice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is giivdluo; qu )j01 :j iuoyz*9v/ven by the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses 4*7ok ex)y (lwden lg:jf)2 jw$m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha particle andb :x+pngj8tv7g() ef. qqcbd( a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle i(.be g+qfcbjq pn78:dtx )g v(s $ 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 tarmsos6 fo-4yb3. wq kk3get) is fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.0p,0vuj6lu3 . dssfg6f $^{\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. 7–45 mm8f s6+z82zhc8yf*ts zg wt6), what is the upper limit on mass m if it is to rebound from M, slide up the incline, fs+ttw 8m5c *z2 m88f ghzzs6ystop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the po dk.veht v:snj u8x4wr20, 6ilanet Saturn moving in the negative xr:n8kjxv u2e64 . doswv,hi0t direction 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