We claim that momentum is conserved, yet most moving objects evenqr7 tdgxv ib77.0: jretually slow down and stodrq 7e gx07t .:ir7jbvp. Explain.

When a person jumps from a tree to the ground, what happenn).y, b5n l )j:albl(yjife v6s to the momentum of the person upon strikin)bybn lfle.i:v njy,ja )(5l6g the ground?

When you release an inflated but untied balloon, mfb/jlv6n:h./x yb- kwhy does it fly across the room?k6m /fxnyv. bbhj-:/l

It is said that in ancient times a rich man with a bag of gold coins frozmfxv9s ioikz 6 b.)iq 1acyan1:pg*9(e to death while stranded on a frozen.im69:pa) bk q nax*ov 9f (1c1izgysi 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 directio jmqh)mks (9o;n when it is far out in space and is essentially 9qjmk s()ohm ;in a vacuum?

According to Eq. 7–5jmyca /yilx;:. y8klsc ).ph) , the longer the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the pos pxylj)8c.al; yik .s:)hmc/ ysibility of fracture or death.

Cars used to be built as rigid as possible to wig( dg4,yhck ,+ sr:vaithstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this new deycg(+4,vasr,kgd h: i sign?

Why can a batter hit a pitched baseball further than a ball tossed in the air qlgd5lwnuhxq0+ 9 4*xu1 bzb4by the batter?0w4qux1+q54z l gndxh*lb bu9

Is it possible for an object to rece3:dh6,sk ke aatw60 2xg 9ju :ouf4eyn4e-qusive a larger impulse from a small force than from ajuq 9 6k 3 se4 etu2nway:o-keuh4a:0xg6,fds large force? Explain.

A light object and a heavy object have the same kin2,e.qf sb /b9jyac).fq8.hnfe 6tfyz etic energy. Which has the greater momentum? Exp/fah62.ecf n.t8ysze,bf jbq.f9) qy lain.

Describe a collision in which all kinetic energya p8(iu1mv3 zm is lost.

At a hydroelectric posx9v vrm;7c8 i p5y*jbwer plant, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum pvs i5jm yvpr;8*97bxc ower 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 45 ( ahc7 eqs8,4p/pjel rflq3+pb0jyo7$^{\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 heightin5t60a5 bqcq h onto a hard steel plate (fixed to the Earth0 6atbnq5q 5ic), 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 putty that falls and sticks to the steel plate.

Why do you tend to lean backwa5ynr /uip4 7wcrd when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whenp6e gkp.7b c rws7/25oph 2tareas this is not trueo5.ra62pbgt p2nc w e7skhp /7 for your arm or leg?

Show on a diagram how your CM shif2fw ;+z je vew:vqho(l89tf* ryg)po+ ts when you change from a lying position to a sitting positlovpe *rw:v f) eohjfzq8 y+w9t+(;g 2ion.

If only an external force can change the momentum of the center of mass t/:jeii0xt)o e/db6z of an object, how cazt e/tx0i io)6bje:d/ n the internal force of an engine accelerate a car?

A rocket following a parabolic path through )rsyx7 */yov qthe air suddenly explodes into many pieces. What can you say about the motionoyr*)7 /yvqxs of this system of pieces?

  What is the magnitude of the momentum z hpxsvc80ng37pwb;6uk) 1lp of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction fod xn9 )k5ou5c*1x owiie3y gi5rce of 25 N acts on a 65-kg skier for 20 s. What is the skier’s change k1e)9do*3x wuon55 yicgi i5x in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is o03cfe n)kgjs6ca/ q-hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contacgjks0 cqf) /63-oen act time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with iso(7jp(g 6omq0/hs rhbi.t9a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, m s sho.9boj(60p(ii 7gh /rtqassuming 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,s . vpww jfr3/s6h*1no given that the propelling gases are expelled at a rate j/ws hw.n613 ofps*vr 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 moving at pn6qz ukt4,)c $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on ale s1(vs;n ezgqsg, 84;ky )inprvel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dro(k 4y8 qnsgevn;zs;,rpig )1spped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling azw:qs q1r eb z;*r.+hzt $15 \; m/s$ 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 at5)ql+3sfw png speeds of 100km/h If the air strikes a person at the rate of 40kg/s per squarpns)f3 5glq+ we 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 3 cxkn1p3zktae3o/ /5qxks 8aalong with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of/3 oapqk /1ek33 s xan5xck8tz the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle i(qf w4e0xi(ndo*eya3;e eg; in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alphxwge;i o3eyn0( fdiae;4(* qe a 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 when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kn:v6e + ejq85 7 mp2-i bodtf.rv7msodg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does.o+svtonv:d6b5 m fe e-27q j r7mp8di it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at ;ux i03fbu2mk,p nvw,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 velocity oi :pbk.nb4 w7cf 11iw b b:ckn4.7p5m/s To alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed 9jb h5i;w 1g.v4ou w 6 v8zxu;mgoyu,hof 45m/s The golf club was in contact with the ball for huyv1mx,6 9wz uh;g;j5o u4b .8ogwiv$3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a vz q z.zmnn(t6q:k;8u8 -wlmgad qhr9 5elocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to theh:q8z;rdq m 6a9tn .q 8zgm 5-luwn(kz 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 f)q1d uc1-de8aiy.pb l 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 ceu3et bjn3,c,+ ps dqg-d()mcrashworthiness 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) Calculatn u dj+,-(sg q tmep3e)c3dc,be 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 a .-wvm ,c+0arse2ztlxt 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tack,w02v- .meslzcra+ tx ler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (g 9pygx c6fw*m5dxvi::m tw9 5mass 0.060 kg) points in the +x direction and is give5*6mwc :5iwtd pg 9vmxygf9: xn by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking the lower m 7jjh+ 03rropleg bone of ei7 ompj0j+rr3h ther 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 $170\times10^6\mathrm{~N/m^2}$ 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 spebp icu(m(tvwm -d*eq 149q)tf+c ukb-ed of collides head-on with a 0.220-kg bafq pmm1c 94ki -bbq(*uc(d )- uevtwt+ll 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, mo eg: 1kagu-5 rxhe/mmluo 297kving east with a speed of 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 collia l9ko /:uue h2mmrg1x7ge5 k-sion?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 hej 5mbh54rbxrtg1 .qmhzu8e9yarr/ 86 ad-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 direction.Let B represent the ball moving at 3.00 m/s in the opposite/xu 8 b5b4z6h5regr. mjtmh9r aq 1r8y 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 wpg0) (tr:e ()zu9 oadsybq 7zwith a 0.090-kg br0z )g du(q9wso z:y)bp et7(aall 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 is moving wigy tn94ado 4w*th a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterwar9dowta 4ng4 y*d the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as one approa(vb8kws ; d(uu 16 uj22ooql8tepn;mc ches 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 passenger mass. If car A approaches at 4.5m/s and car B jdwbv(6euskcuq lo (po2 8 m1;8n2;tu 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 g)l;y1gjuk4 g a second ball ini glgk u)4g;yj1tially 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 frictionless inc84.e ao.x9d cj3cncv 9kg5yaq line 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 30gc. cykqanj.9 v9cead38 o54x 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 oes :d 5x 7xj8l5sinwz/f 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 maximum heigh s v:yp 3o: jsn7cz5myg6*s-lut h ofs 6vy:snupgj-5 3:sy*lczm o7 the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buo7o8 z-n/ay zje-+tqmv/iko6gp v( z;ries 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 horizontal components of the pendulum’s displacement.va igz; pto + --nvqzkmjo7ve6 8/(oz/yertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy los5v -qb9i2a(,mv 4 it ndgeup4st, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object,h.z gqzp04kf zk dh2.0 initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece0gf4kh2 pz.kzdz q.h0 acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car co-wz7 1:kbf igjr:i sq6llides 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 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 ther:k 7z:siiq61f-j gbw SUV) $\approx$    m/s

  A ball is dropped from a heu(: 1 94h pilpjmeb;ulight of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its ener( jphi:e 4ulpl9m1;u bgy?   

A measure of inelasticity in a head-on collih zhy4c1,mp8v 1qhwqudw/ss; v.z5 t4sion of two objects is the coefficient of restitution, e,uhc5q 8svtm s 1 wpz;h yzq44w1vd/,.h defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces4yjmu. / gjcyy1js7: 1wata8x , one with three times the mass of the other. A depression is made in both faces of the cut, so that a fireccs8j ygay wta4.1yu7j / :xm1jracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object movinw px-5/f4 wb 6iufr:lpg in the +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s/f6lbx45w-iu rpfp: w 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 nucleq3 xc4jza;gw nrk *4)nus, an electron, and a neutrino. The ele n can ;xz34)rj4*wqkgctron and neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of may kyxptvd3 tv/n pz.7vf.1 (nk( 8ra2mss $m_\mathrm{A}=0.400$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 y)59mxof ok y8equal mass, each having initial speed the two move o5yfm)yxk9o8 o ff together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal gtgh d1-d 3,5.vlaezl mass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–3,ezldhgvt1 ag.d-5 3l7). 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 perfectly e5gwc*7nqt h,knlkg3 rk 0pf9;lastic collision with another atom at rest. Anch79lg3gk t qkn5; 0*r,kfwpfter the 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 perfectxztxc63f/,c/y jg(i h r x/gb.ly elastic collision with another atom at rest. Aftxgix(ctzr/6x. /bc ,/hjgy f 3er the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mp he1*gj5-mawass of the three-mass system shown in Fig. 7–38. Specify relative to the left-hand 1*w ea1h-jpmg 5.00-kg mass.    m

  The distance between a carb5 rqwmot77 x50g nf 1:zipi- ojed3w)bon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m b:g7 q qjv03cq:h2s tylehind 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 seat 3.90 m from the front? Assume that each perjltgq 3qsyq:2 h:7cv0son has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, got2.c r.lu r8(wr l eql3-pl0of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determinlllr.el(rt03p or8g cw2u.-qe the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side: bo qfojb4p4m4twn9sj4w- h7 s $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of tomato paste ( xw:h*v2+nh twsee Fig. 7–40), each of whw*hx+2v:hn t wich is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a tqa *v*nga5+2vt z uvvuqf)3 8circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the czv)avg* + 2 q* vtua3fuq5tv8nenter C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same aa9o1nq ,,bc dxs those in Table 7–1, and calculate the mass of9qanx,b1c, od one of your legs.    kg

  Determine the CM of a2wg +2av s)du5uf pssru,;lo0n outstretched 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 an arm bent at ,;,.tansebe0v8*n-djeac jx a right angle. Assume that the persoc0,ed xa ns,-*.vnat;eebj8 jn 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 hanging vv:e,d jpd1ldv- y+ p7mertically, and his trunk and head are hor pyv7pj 1lem,v-d:dd+ izontal, 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 ae8 gs6mcl,9;cs,/4lyq iebjh re $5.98\times10^{24}$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 apj d y.gstc-f,m-,p/baa n6;pgart 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 w1-xmi9/d llepx eh l/*boeysw 56kai l9w 8/+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 thi bea*9/h8y ldx km+ xwil1slp/e l-o65wew /9is 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 mngwmm7:)e.2gr1m d rzass 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,g:n.)m edrmwg71m zr2 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 (Figu,iknm i .-phs2m i 3mbq9-g0o. 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 gondo. )w8j nrokmg4j0a uu-la, 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 passenu4ug jk-or8j n m)a.0wger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is poppemc-ct w)wmiui q 4q.:4d straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculat)i.iu-mq m:tc4ww cq4 e the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling1qe+ xhf-q dez86m7h x v6fhn; 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 shem)(z gn,( pli) ew qn*8y)igpown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried aboe*m)pq)i g y(p(g8nez,) lni wut 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 speed of 5k0k pei sa6q62.5m/s by pushing off with his legs from an 1800-kg space capsusak6 6k5e qp0ile.
(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 8a4f qwj 8y4fel 96fqx30 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut hasefxawyf4 q3q9j 6f 8l4 moved 12 m?    m

  A ball of mass m makes a head-on elastic collision wiucn7,e. e5 rrlhygjr3q8q:m 0th a second ball (at rest) and reboundsrq ,73e q.e url8m5ny0hrc:jg in the opposite direction with a speed 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 cou sta2w 9oy/9ih1)hhwurt case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of 29 awh1o)/ihhuwty9s 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 1aimyc6g 06c frbc2m; 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 elasticby1mcr6ci cg;60m f2a , what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg bloqc3it2z,o wg (zo5o+8cyup7hck of wood at 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 rise after the bullet becomo5z+itooh 7 cz w3(8u ,py2gcqes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood sw qi-vq1hi(i( ;xw q2placed on a xqv 2 1is;iihw(q(-q whorizontal 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?    m/s

  Two people, one of mass 75 kg and the othrgi3z d)-3 52c49hizj xj6juz/gz j nuyr 6f:her 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 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 mov-3xijzhzyf6d)ru j 4: 6 z9h2jizgr/cu5 g3nje    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abouc6l;b6vbo+tl oz -y (et $ 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,hrbc dxx4ufyg kc 0pj986:.o fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio opr84bf k:yc0u , c6xo d9hgxj.f their masses?   

  The force on a bullet is given by the formula F vk+7j 9 i2w24sflrag,ykc 6et= 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 massesn) xr 8ep cd13*b;urcq $m_A$ = 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 radioactivelrmh,(q og :ks-ivcry.l.h3*ry into an alpha particle and a smaller nu h-r:mg,(q hv.*k3 lrc ys.roicleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at anlzqp +2znhr:: 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 downo ;be 8rlh q)o.s4vt4j a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mass m 9 plcrr8vqos(1(/tojif it is to rebound from M, sliderc/ls8( ( ovq1t9po jr 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 effect. Figure 7–47 shows the planet Satu)hevc2ah -lq1mwtc m) i;s 519lgjs0orn moving in the negative x dilc )lqjmc)2o 0 -vhm9hs1w1a; teig5srection 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