We claim that momentum is conserved, yet most mova wy,bzgtzlv.*m :(;wq75ww eing objects eventually slow down and stop. Explaw: ,vtgzbmla *7(ywe.wq;w5 zin.

When a person jumps from a tree to the g.naes,8iv o+ (x9kzj9iys5, 1 rrqxohround, what happens to the momentum of t9,ie zkra9 8xnhs+s1ivxo r,5 y(. qojhe person upon striking the ground?

When you release an inflated but untied balloo*;qit3 ;jj typn, why does it fly across the roomq tj;j*yt3 i;p?

It is said that in ancient times a rich man with a bag of gooftjvfi3h0slj93; fgj qiu (+95h+tuld coins froze to deh+v+s hlu(jf9 f u3tii ;jf05gt39joqath 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 had he not been so miserly?

How can a rocket change direction when it is far out in space and is essenb6 ue)b4xc-z:ats n/j tially in at:b6a-sj) /excu zn b4 vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller t p4exwd)(x) h0.lzown 7nvzt,he 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 en7ov)0hx)( dw4zw,p.tnl z x collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand colliew: : kp/btaj wy5zv*,sions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this new deywtv 5* j /ka,we:bz:psign?

Why can a batter hit a pitched baseball further a cm *;3pra7fs1qb+f pgh w/0bthan a ball tossed in the air by the batt;/3rp haw7*p c+sfmq gfb1ab0er?

Is it possible for an ob+vo : 47eypykjfkd v/lk 5mq01ject to receive a larger impulse from a small force than from a lark d5/ 7yq:lj4emo kf0v1+vpk yge force? Explain.

A light object and a heavy12n t(wlhrsd 102cngn object have the same kinetic energy. Which has the greater mom gn12snr( nd 02ct1lwhentum? Explain.

Describe a collision in v5y 7.lf;nbx bwvqi :npnq7+ 2which all kinetic energy is lost.

At a hydroelectric power plant, water is directevl 21z r,h/lp73 u n rfsj(ki-f)lt9vdd; 9fahd at high speed against turbine bladefrn h ll2 1ra;s(zh7kvdf)tl9u-d9/pfi,3jvs 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 the water rebounds?

A squash ball hits a wall at a 4u ybc/bua-(.i(z/oxqwf r (0h5 $^{\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 E+fszj q: zhlr3xdn,6:1c kdn3arth), 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 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 pu r1k:33j dd n6+z :hlqfsn,zxctty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying abgs(tz 4vfr4/ (nx ti; heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point,a tk yfh-39i.*n8/jc jwcvat* whereas this is not true for yo. t /cjw an*yf hk3atjvci9*-8ur arm or leg?

Show on a diagram how your CM shifts when ,zkq/:n c;sf6m hg a9jyou change from a lying position to a k ;gc:sj,n hq9mza6f/sitting position.

If only an external force can change the a67 )wjgq2stcmomentum of the center of mass of an object, how can the internal force of an e gws6)q cj2t7angine accelerate a car?

A rocket following a parabolic path through theh. j406(z:fxxyer lbzu mjs:7o6t5nt air suddenly explodes into many pieces. Whatfy ej bt 6u(tn z:sjxh0ro6x.5l:m7z4 can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow fv s)ku5q 0+)pq chk)u4q ,sl 3z*qhzdflying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What is thecz e-uuk p71xq z)-(as skier’s change in veloci-e-pcu 1q(7 a)z xzsukty?    m/s

  A 0.145-kg baseball pitche j3,9 jjh*mvgoxr(e.zd at 39 m/s is hit on a horizontal line drive straight back toward the piog3jer9m*h .j (j v,zxtcher 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 packw3b*dc,xk1,t 9gncrn. 1tmimage out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of thegk. dtw11b3m*xn,9m c c, itrn 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, given that the propelling gases jw 5o--gb+anp6* dqvnare expelled at a ra 56dwngp +jv abo*nq--te 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 i,tsf 4aq/2hying 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 alevel frictionless track z2akuy jf-sef)io6 .;(ml+f o with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the+ (usm-j k;fialoo .ez )fy6f2 car’s new speed?    m/s

  A 9300-kg boxcar traveling atl t5u0e 3uv-gq $15 \; m/s$ 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 horizonta) cy9kru.ckbzmn f(omse;n 5 /5h31wally at speeds of 100km/h If the air strikes a person at the rate of 9n5sckr(nu/moy ;).c 5zbewak1 3 mhf40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constay8/ zg8ust 8 zjr;f6wznt speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car zz zj8/u8 ry8fts w;6gat 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 partic(kbw:;irk+jg /, inz cle 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 th:g/iz;jwn c,kk b(i+r e 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 emerges pu osnm.tl(20cle0omntsl.2 pu(anly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at+n g 8 mr:gaeqb,b*6hs a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a jfv 6y:2lyw*v z*-l gkvelocity of 115m/s To alter its cou6llw:-k*zvy* fjg2yv rse 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 hy2aqs yg1 qyc. ic)04mit off the tee at a speed of 45m/s The golf club was in contact with the bal4a1. cim0y)y gqqys2cl 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 8 g s.2 p c5kwep/caihs-pg3-la nail at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nais.w8/ klpaip53- ghpg-c e 2csl?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg sxd.+6a5o(inj3fxsnf 6g;ir b0t e5 g and speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer inoxuvhe x u /z4bt47wr0fb.+y8(jgl3u 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 average force e8+/ 4xzfw.t bul(o b h4u7xug y3vrej0xerted 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 inrt7 b9 59e1mt+byfzkv iqd 9l2 0.75 s by a head-on tackle by a tackler running 5 79rb2b9+ fvy9t kmdtz1 qliedue west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 08 b8fa q4a8hmaya45ys .060 kg) points in the +x direction andy8fysa8b4mq5h 4aa 8a is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum hei4du 7gu2 n+x-gbio.-wazpdd yx -f, gcr)8xa 4ght can a 75-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distan2p bodayg ,7.- 84gc xwg--z4+ad u)ixrf undxce of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of cdz1z) )0oh gakga /m-e5 /ygvyollides head-on with a 0.220-kg-g mg1zg5ov)h0)d ae/azk/ yy ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed o/ vzz0wfv1. uef 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B repvezwz0u/1v f. resent 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 )b g4 z laf90gcoe8jo3d(isf2+n-nvaelastic 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 t-3lg)n(ds b+4foj0fae czavg oi982n he 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 ba9d33-l)rda djkizq1p dur d5.b1rj*- phvev0 ll, 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 Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(ddbr- pa31rju5d ekd h10d j)pzvlr-v93*iq. 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,e h (8eqmuu 4euot*:o moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softba4eu:o8uemht(euo * ,qll bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as one appro :2ctejw 5 c4j bu.ap,lsj,,gyaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passengew,. uj,gt2:p y5 ecbc,4jl asjr 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 secondsuppcmr )al7 85 *sv9a ball initial 7rc 95s*p) pvsl8amauly 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 gi.bvg3 tx2g6slides down a frictionless incline as shown in 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 cube6v b.3xggti2g land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of u3-)eut hz o4gmass 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, projec ; qc+gyyfe;u6ae6y j)tile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulu; e)g6+f6qa ;yjcy eyum 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 tl8 tbnt 1ljrd1,5a p3mraveling 230m/s buries 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 vertical and horizond pr3n8 a51m,bltl 1tjtal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic e4:s- rk+voed6 f:h8bkl)hhgt o( f7o cnergy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initiallytst)j mr/v4y4 njk;)f at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500tnyf) 4mv4 jk;)trsj/ J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kgmza m2u5p2nln /h2a(c SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forwardu /n 2n2mhaza5cl pm2( 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 height of 1.50 m and rebounds to a wy2yss /ln-c;qsj6a 8 height of 1.20 m. Approximately how many- q;6nwsl sy2y/ js8ac rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head- 8e3hv53tglfy on collision of two objects is the coefficient of83 fty 5ve3ghl restitution, e, 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 q 5erro5r6)4yg:lve b two pieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the twolroe rgybr5e)q5v 64: blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head- ngqm0j+ 5p1omv+t t)mon with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass ifqmp50n+m vo1 g t)jm+t:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an electron, anq v7c3oy gia*r3;.1 mmidvy-hd a neutrino. The electron and neutrino are emitted at r- ;cadqymg1 hr3mov3i.y i7v* ight angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of mass)slo)7xu roueg n37 n, $m_\mathrm{A}=0.400$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 bet1)j5 q 3fh5k(ewursene) 2t qhween two objects of equal mass, each having initial speed the two move off together with speed v/3 What was th e)tqr 5j ehe)f q521wnhu(sk3e angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass v2 u8/v rwj,ri:oy3llmove at right angles and meet at the origin of an xy coordinate system. Ball A is movi8 loj v3,uyi/lwrv:r2ng 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? 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 perfectlyff)*a8faw8 p dtzgv)vhqrlq /- 8k:7df c-wu4 elastic collision with another atom at rest. After thf) wuvz 8c ga*f7qk 8trl:/qf -fa-w 8v4pdh)de 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) makes a perfectly elastic collisij.l mg 2l:mlb,on with another atom at rest. After the impact, the neon atom trlj.mm :llb2g,avels 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.gep2((13v3 nfso c)ar ,ktdtr Specify relative to fgtc( )(e3d3, knstrvo p2a1 rthe left-hand 1.00-kg mass.    m

  The distance between a carbon atom (:1 oa t0dppy.l$m_{\mathrm{C}}=12\mathrm{u}$) 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-k 1)/vz i7wudtoc(+lf kg car is 2.50 m behind the front of the car. How far from the front of the car will the CM be when two pedo/l) 1cukt zi f7vw(+ople 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, of mass 6800 kg, is used as a ferryboat. w 8+z(jskb+8m)yqodb If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, de ojdzb8 (k)8qymwb+s+termine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides asi4;2efmtmzsh9a . 3e6bms-h7- nhf$l_0$,$2l_0$, 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 idi zbh+2p31tyjr,ho1vwkh9 b0 entical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of 1i0vy2kzth 9r w, hjo3+1bphbgravity 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 c ;i:+.e3wow8atwv yvf);qmy lircular 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 center of mass of the plate?;l .v8iv)w ;ww: teyqf+3amyo [Hint: Try subtraction.]   R

  Assume that your prop0)l hr(e)3wtqo +qy ftortions are the same as those in Table 7–1, and calculate the mass of one of youo0lq 3t)hyqr)(f+wter legs.    kg

  Determine the CM of an outstretched arm using Tablemhvrxyjh0sz1n+8 0p * 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculaod0vwb5q k;+r;7be l nte the position of the CM of an arm bent at a right angle. Assume that the person is 155 cm tall. q+o;e lwrnd bvk7;0b5$X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such tiir)*5 gfk7vnyzz p85 hat his arms and legs are hanging vertically, and his trunk an7 vk 8inr)z* if55pygzd 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 Moon ar( ty,e nvu -zpswt w-t7mqcpi.6 5/:hze $5.98\times10^{24}$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 xn9sj un72k1g apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a d no t8pgijp0ik as4+6+iameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, so g tpnpa68jk+i+i40as 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 uniraawh0 bt0c(5yl ) af;form cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectt;wl0 (h0baaa f yc5)rory?    d    d

  (a) Suppose that in Example 7bb-r l5d qq,c*-zo-eg –14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola/ rkxgf /zd+:n, 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 Earth) does the balloon then move? What happens if the passenger sn+ /gdfrkz: /xtops?

  An 0.145-kg baseball pitched horizontally at strikes a bat anwnvwec z.g o:w).:*nx8 xth*qwhe4 r *d is popped straight up to a height of 55.6 *xwh et*qw) hwgno rw4.x* :vn.ze:c8 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 traveling wit64xz3loodzw9(*u v psh 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 f n );fg63lpy5hc ;aazah,do -qaced with the corner pocket shot shown in Fig. 7–43. Rey3;-,) hng zlo;ah fa p6cdqa5lative 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 details.

  A 140-kg astronaut (including space suit) acquires a spe17q60ps eky2iqp :tcg (2sn iued of 2.5m/s by pushing o60nt k 2i7qsuy ce( qpsi2:1gpff with his legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, a99 2y3 kt,m z4ly(.dhvoqgkb zre initially at rest in outer space. They then push each other apart. Hoqh,mkv.9d( 32zk 9 zyo4gtylbw 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 snzcs qi2 lt(31l1q0 xbecond ball (at rest) and rebounds in the opposite direction with a s(n l10qq tzsl2x3ibc1 peed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case in9s. v: uv bhi-yvi+h/hvolving an automobile accident. T-uivs+ y 9bhivv/.h:hhe 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 while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of cux93bf7e l f6total 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 fofb 6379uelxfcurth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg blooh037v spy nujj+uh)(ck of wood at rest directly above it. If the bullet has a mass of 29.0 g and a sp)( ohuj3uhnv +7s0 yjpeed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and biwp bm uhan+2+25c7vqecomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetiam bqvnw+ 5 +hic27p2uc friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in atwym8;pb )7cd rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the bo cb7 w8tm;dy)pat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abou s4o*enw rng04t $ 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 explosion. zr 0 laodxj233ed8;7ckjui8nOne fragment acquires twice the kinetic energy of the other. What ijxcr zl3oj20a8e8ind k d; u73s the ratio of their masses?   

  The force on a bullet is given by the 6s qgg4*y t:ovs en-5 -rkeum8formula 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 o(n gpwfc+d35$m_A$ = 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 k/p aft+n1rcprq2 1v9 decays radioactively into an alpha particle and a smaller nucleus. What wcrvt1nk q+appr91f /2 ill be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clayvk54(6pjb xvjax.t5w target) 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 t:;w:p3ttnhm.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(nqn() vqlf gwqq5+ 3q–46), what is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide withg)vf35qq+q lq(wqn( n M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect.v3cnnidre zd r2(:9 /z Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6kc( ve9i dn3z2z/rr:n dm/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