We claim that momentum is conserved, yet most moving objn4t 71z2m zexeects eventually slow down and stex427 t1zenmz op. Explain.

When a person jumps from a tree to the ground, what hzu zf yb6v4xi oy)g8-kn-*xa5appens to the momentum of the persuv)6a54f- xzb8xozi *ky g-nyon upon striking the ground?

When you release an inflated but untied balloon, why does it 9xa0 jqff+ mng5;f 7fklqh:+ vfly across the roomk9vqa5 mn: f0gfjfqx+; fh7+ l?

It is said that in ancient times a rich man with a bag of gold coins hmh b4pl gt v1)2azbx5c(x2k/ froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had )/ah(x lk5bz2gbphmxv4 c21the not been so miserly?

How can a rocket change direction when it is far ov9ndd;h3;ilf dd5 cv.n hk4 ,,3e.xdumijz6qut in space and is essentially in a vanq 45nv.di 9.hkd f6dhd,l;mx; ze,jv3u3dcicuum?

According to Eq. 7–5, the longer the impact time oft61x)i mgtyhq6r.1 iy 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 automobilerm1t1 i66. it qh)xyyg collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand colli qu6hqjk jpyo2;+fi2,sions. Today, though, cars are designed to have 22oi+p, uj6 ;hqfkqyj “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in tho+g/h0lggb 2oe air by the batter?golh+bog g2 /0

Is it possible for an object to receive a larger impulse from a sm79d*r xwqi;/ufpg n z51o;usf all force than from a large forw7 ugrn; qi;uo 1fp*zd /xs5f9ce? Explain.

A light object and a heavy object have the same kinetic energy. Which has theoe w2 d*ei;0rz keeok(jhs:v-p wz/:8 grev::oeo ;*z(s/ zdkpe w rw8 0-kheei2jater momentum? Explain.

Describe a collision in which all kinetic ene6xisn +hm25i vrgy is lost.

At a hydroelectric power plant, water is directed at high speed against tut/1j-s8y d ,+z az2;lhtam 4vn57;wxl muxmo crbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so thcoy/wmv nad- a +h; 1z7m ttms8zl4u x;lj2,x5at the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall a3x:yo d6 j2pcblq2v+3 wab 3iot 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 t u/85e*i veab cq m,v,k2x,xzihe Earth), 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 thavm ib2 ea8/q,*kv, x c5ze,iuxt falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in your at.vrbodr4znu9 c.7ja dzr/ ;/rms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is not 35y. cu -uutmdtrue for youy t 5uuu.3dmc-r arm or leg?

Show on a diagram how you wc,)dsys*b4da7 7xu ir CM shifts when you change from a lying position to a * cbw ax74,d)s iudy7ssitting position.

If only an external force can change the momentum of the center of mass oy*ijk;ohu .f 4f an ob;h4i ouf k.y*jject, how can the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodu 9-kng9a .fytr. 0tihes into many pieces. What .9 tyu r.a tif-hn9gk0can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speevvc) gsu yh):7e4w xp9d of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. Whawp m4qsik72 vor9.a7,w gogb/t is the skier’s chanok m .7s4i/qb, agv729 oprgwwge in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive straizz:54cqwr*)kejkqy0 41 edu qght back toward the pitcher at 52m/s If the contact time betweeqyq ez1k)wj4 *5z0:u krcd4qen 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 n ++.idu8ypsm horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The+pm8nui. dsy + magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases are exyml4cg6y y.+opelled at a rate 4y.ygl6 +omyc 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 movcv3e(m-n5 5;cbl bddaing 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 alev ww0we ,h3lwo-gb w.hxmkx-.b:fc )p1el frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?,-)lg b w:chomx.f 1x.wp whwk0e3b-w    m/s

  A 9300-kg boxcar traveling at lt. tvzm 5s00;xpc e4e$15 \; m/s$ 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, winds2ugg p ;3l++;4xzhjh1gxb rhz can whip horizontally at speeds of 100km/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 person. Assume the person is 1.5 z1jzxhg huh r2l;b3;++px4gg0 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:a*9ph0txhvf9wmvul 6k w 7z+r6j4n d.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction: khwxj u +*09vwh9zpvtl 6a4fnrm 7d6 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 egd 2t6 dzpgvl;m*q+n 1mits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle 6*gvlt+dm dg;12 qzpnhave when it is emitted?    m/s

  A 23-g bullet traveling 230m/s 001neer0po v jsyr(t b e90 l;xa60tsbpenetrates a 2.0-kg block of wood and emerges cleanj ;6 pe(rl r0b90en0e0 0ovtaystbx1sly 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 n8w18 bn- ) :baemjowar;o0bstraveling 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 is trave)2rwuxlt37 ric)a3gn ling in outer space with a velocity of 115m/s i nlt2)ac3 gx)r3uw7 rTo 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-1 vfp fr*5gc:v+de3jso w6ah at a speed of 45m/s The golf club was in hjf- 3s*pr1 e5fowa+d:v6cv gcontact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8mq2emq29a y:m.5m/s and comes to rest in a time interval of 8.0 ms. (a) What i:aqm m2myeq9 2s 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 spee 9zxnbme4a: 2sd 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 in charge of the crashworthiness ofjf rqqi-6 l+khqn6y+/ 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 impactqqf +l-h+6ir jn6/kqy until it is 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 ibfcv4t +v eaaz+0 3e+wn 0.75 s by a head-on tackle by a tackler running due west. Ct3 c zbev0w+eaf+4+vaalculate
(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 7d+)v52xmekdl 1q(c *qc is2fb o/bdfa tennis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to eskdb+si /d*dm 2l cf1c)2be5( qvoqx f7timate
(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 7lu -kzxc56 w/a5-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in zuw-/xlca 6k5 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 s w*/; y/t;/: nvaboaef mz5auopeed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what wil/oyba atvfz: *; o5m;wanue// l 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, m5ld5iwjdg9fz ixu a;d2dws+*kl 1n g cg--1c8 oving 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 collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg d g nw;lwads 2fi5951u+x k-8l ccgddi-zg *1jpuck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastic head-on c) gpohv4pry* mbc+ cukf-5l8j(q )v1 zollision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speckmb p-4))fvq zpy*+1 g u(5v or8cjhleds 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 direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a spvc)73 cgncab0 eed 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?(Let A represent the 0.060-kg tennis ball, and let B represent3)b7g acc0cvn the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.2216zfq:tis h l+0 kg that is moving with a speed of 8.5m/s collides head-on and elastically with another ball initiaq+ sti lh61z:flly 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 amuseme04f+vlhh3.v cqmqxy zm cq7 5:nt park ride collide elastically as one approaches 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 is mozlvv qq.70+q:m 5cyhh 3mf cx4ving 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 buh)sn.by0h5 0tb9feijn, 2 y iall makes an elastic head-on collision with a second ball initially at rest. Th0nyit 0 u .9ef2n5bybs,)ijhhe 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 ov2e :as6l sr0mnn 6 qrj)l (u9htx;ce ;rv.d9a frictionless incline as shown in Fig. 7–35 oq)sl669n 9e0( rc mlraj :suvnx;;vhe td2.r, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an 3,/p0,mrdpkpp zs jh1cr1ar ( 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 erhqo iz d60 h..dou4,gxperiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causei.o.0 ozqdh g4rduh6, s 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 travelin xbw+uo ;nd94 vbmoz5(g 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 horizontal components of thebou9 zo b(+v4nwx5;dm pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction o7ii p kl.r43z (rsxtj8f kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion, oc u*6(dqe mto+lam1 breaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy di,oad1*+ mtqm( uc ol6ed 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 of6i -/u,dv8sz h0ifwn n 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 bet/ v,w hn8u-z0f n6sidiween 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 m4nw 6cb:m8rri2a(uh0+ jc zwr. Approximately how many rebounds will the ball make r24 ciuba:nc rzjhw (8+6w0r mbefore losing 90% of its energy?   

A measure of inelasticio n6:*)adxqc01pomuvty in a head-on collision of two objects is the coefficient of restituti mn)qa*61 dp:cov x0uoon, 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 two pieces, one with three times(xwja. mlwp j)0c8l6l b im0o0 the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it withbwl08ia 0pcw( ol0m6 xj ).lmj 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 moving in the +x direction at 5.5m/s collides *h1j42 lamu mjdo*r (k(nkx9ghead-on with a 10.0-kg objec1 n ahldm42k(9m*oujrx(kg*j t moving in the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a secondz28 qi hv6+g ki-yma:w nucleus, an electron, and a neutrino. The electron and neutri hy2-6+vaikm ziw8:qg no 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 massn)q uent8 o(jcqmhw4j1- 4;gcm(i/g h $m_\mathrm{A}=0.400$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 nz,wyw- o rp9+vn8cm-collision between two objects of equal mass, each having initial speed the two move off r8w9pm+c-n vy z-nwo, together with 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 originhj: s,tr,x 0zf of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is movin,h ,tzjfxsr:0 g 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) me65ltfb *(1b jo;zu rqb-m7mjakes a perfectly elastic collision with another atom at rest. After the impac-1lbb z7f6beo t rmjum*(j5;qt, 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) ma 5 p.we,f7sbyh -00qqxwv;9 zkrbnzv;a8gk ,akes a perfectly elastic collision with another atom at rest. After the impact, the neon atom ta. s7pzg08bk r ;yab-qv0qe;wz,x 5nh9kf,wvravels 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 sys4 ze72cwsehx. tem shown in Fig. 7–38. Specify relative to the left-hand 1. e4wes2hz.7cx 00-kg mass.    m

  The distance between a ca l/wu .b8munu+rbon 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 2.50vhxgw;b yfru/ 3h)o 68 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 ca/ wr xu6)hhvbf8;g3o yr, 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, 0kxl09f xxdw5of mass 6800 kg, is used as a ferryboat. If three car0kl xxd0w9f x5s, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidescol0 nsy5:/ ep $l_0$,$2l_0$, 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 c 4 o8s,bydd2mct x*soyq)9y /of identical cases of tomato paste (see Fig. 7–40), each of which is a cu/yt 9yb cy4c,dd*oo )m8 s2qxsbe 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 d+* h(n7 /4qrlc;yi.oyixmma has a circular hole of radius R cut out of it. The center of the smaller circle is acl 7mix(in m; dhyayq*/o+4.r distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and c8b2trkb8k/ sdik:,a -yh qgxv lw f4,+alculate the mass of one ofi4 8y8v-kd: b ,r tbk +sxgwqh,alf/k2 your legs.    kg

  Determine the CM of an ote .wbn 5lb/i7utstretched 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 positio8wz.zv)i 5;)zyv:vo dxov/pe d2le/on of the CM of an arm bent at a right angle. v8)i5 2ezo e.xo/y)ozlv/p; zw :vvddAssume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs a+ud od k/ 2 w;wjf4z03xx(etxdre hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Ta( oxxf3/4 udewkd0x;+j tzw2dble 7–1.

The masses of the Earth and Moon2qc. a8g+;dj2lthco -dkos 3 z are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on fri fz9a8ot;mb- wctionless 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 headb5. g,:xdn* nol avmg2mwkt +5 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 wi.v:+ 2l5b5tnkox*an md, wg mgll follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of/ne jbopt/6 siy 35r*wc 0lu0o mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500/c ot30yr5j s0bi6* opu nle/w kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–2e;b q:6p4o qpw9), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air-dpuq006)xqtz2t ss5/.fftf qhru 5 w 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 the2qtfu zfhr05 qx sp0-s 56wtt)dq /f.un move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat co0 8scl:n1lvm6 bh d1and is popped straight up to a height of 55.6 m. If the con1hscn8l od b0:vl mc61tact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travett5 vtrct(2 h ox0)q nt-3poyii) h2i*ling 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. 7–3hl 7aik9 .8vwz *ygfs43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in whiilfz 89y3* 7hk vswag.ch the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acqu5c b fnxwi+ j;:,gbu8n 9s8tzjires a speed of 2.5m/s by pushing off with his legs from an t: xcb8 i9+ug;jw,b 5njf 8nzs1800-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 masjy9 b1qndn6.l s 60 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astro ln9.nq1dbyj 6naut has moved 12 m?    m

  A ball of mass m makes a head-on elastic col*, ,a fhu+xsuulision with a second ball (at rest) and rebounds in the oppuufu a+sx,h ,*osite 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*ysu5ozabi; lpkfguxk3 ((9 0 a court case 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 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 exceedingzb (x3(p yg9a;u ik5kls*fu0o 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 total vetqyl +q600tc ertical height 4.00 m. The ball hits four times on the way d+tc0qe06qly t own, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a m:wxi v jo9 shx9 ccf28)-s:hx1.40-kg block 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 rxoi mw:h :s x ccxf99)28s-hvjise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and bw0j,yd o)kep1 ecomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front o 1oj0pdwke),yf 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 mass0axi6m br57swie d- z* 75 kg and the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in wha7 iiwe6 zr-m5dba xs0*t 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 wasqx6s usx7+ew2asw*d 8yoj1- d about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragmentg-yxtw:5u,wi9 ore,u2 tep a,heu9) as by an explosion. Onyw age5 a,xwou:etu)up,t h,9r i -9e2e fragment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formulao (yqhttl mk2 wbi(ou2 ( bb/xqmh/t*e/+i t4* 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 ali9 q7 an)kh+$m_A$ = 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 radioactif:b7d.4 a-n9h.tvcp42 dret0r trfqively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alph.hp0atn.i fet7v-d4dcbr rt :4f2qr 9a particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angle of v6 bcmvq:2 .vq30 $^{\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 sli mn,v2i49dad b,.2y3jlx9e u. q utosldes down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mass meam /yz*bsdalp :8;qiq02+:b rdbmr5 if it is to rebound from M, slide up the incline, stop, slide down the incline, and collidi 0rab:qzb/;+a8s d5b2rdmymlp q * :ee with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the plane1p- gacv h-m6wt Saturn moving in the negative x m-gc1hw-6a vpdirection 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