We claim that momentum is conserved, yet most moving objects eventually - 0i9ol2rp)byajlblj m/d*+ovr/ uu3wg)o u- slow down and stop. Explain./3 oi)+ 20) g-rayulbb9j/rjup lmo* wdvl-uo

When a person jumps from a tree to the ground, what happens to the moment:)oyw 6,- neapq gd0xeste+15ds5 k pe+ ianm3um of the person upon striking the gro d nyn1te6:5g 3 es5dq-0a+eso a)ip+pxmek,w und?

When you release an inflated but untied balloon, why doey wt5x9zr m:s*s it fly across the room 9*r xsy:mztw5?

It is said that in ancient times a rich man with a bag of gold coins froze to d6nol .,ivf (x.(*ilkonv (rrz eath 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 no(oz*f (( nrvlr ni6xi,..olv kt been so miserly?

How can a rocket change direction when it is far out in space and is essenm:hn-)6(kg eu8 ka ccz6 u(mls bp(ql)tially ia(( plmzu6()k )un8 k6csmgq:cble h- n a vacuum?

According to Eq. 7–5, the longer r2tug 3i t2k)vthe 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 possibility of fracture givtr2u t23)kor death.

Cars used to be built as rigid as possible to withstand collisions. Toewwy/5 u/ affx ac gr9/g+p2q:j6p.kv day, though, cars are designed to have “crumple zones” that collapse upon impact: w/g59fp6uyc.aa erjq/ g+/pw2v xkf . What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in the air by4rfpo*, o b4da the ba4da4o, opf *brtter?

Is it possible for an object to receive a larger ik pimo-52pe+ygq hov hl*+)+smpulse from a small force than from a largep* hph s 2i )ovek+g+-m5l+yoq force? Explain.

A light object and a heavy objecf.pb3 y(o*jx rt have the same kinetic energy. Which has the greater momentum? Exppb*r 3jx(f oy.lain.

Describe a collision in which all kinetic energy isz(r.i 9zudyloe , -uu( lost.

At a hydroelectric power plant, water is directed a nhdr(:i2xxr (r sr2r)r,ni.gt high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades ri.gsnn)r :rhr d(r2 2xx(, ribe 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 vd v:xz n1ao/9*cx5uo$^{\circ} $ angle as shown in Fig. 7–30. 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 st ;t xznp9a 7 m0muo05ilw,q9sqeel plate (fixed to the 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 that fallsm ,o0;ta 0n5pqm zs q7x9l9wiu and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in yzwm(. z, -ce( kd rjx;vug3c3your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereub +k*tut6 mq4e2v1xh as this is not true foh1 em2xbt *kt6vu4qu+r your arm or leg?

Show on a diagram how xd, v z.i6 ,5mj:qbiwa(;g4ixz gw6afyour CM shifts when you change from a lying position to a sittizxg .fa4xvi5;j6wdi, gbaz wqim6( ,:ng position.

If only an external force can change the momentum of the center of mass of an )zt +ozes7dt5 object, how can the internal forcett dzzeo57) s+ of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly expl*.uu0b,cgdw6ru*ukq c 8 h,ndodes into many pieces. What can you sa cu*8huuwdq,* . ,k br0un6gcdy about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flyiduskpi ./ 2i- i(e1lrpng with a speed of 8.4 m/s 1k(lrui-ds2ii pe./p    $kg\;m/s$

  A constant friction cir dgl8jie8t2d* v74ce71ir force of 25 N acts on a 65-kg skier for 20 s. What is the skierlct dig1e74i8 cr2dv 8ri 7ej*’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizon 3vs 4 bhe,s3hm-b( pms6ch8yftal line drive straight back towhsfh,cy3(-s8mpbv mb h6s4e 3ard the pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally j cu8a zu;he7* ifdj;2with a speed of 10 m/s Fig. a;7 uz*;ih2efdujcj8 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 velocity of the boat is    m/s

  Calculate the force exerted on t zc ww5/qi )ng3as7j:a rocket, given that the propelling gases are expelled at a rate of 1500kg/s with a speed ofsi5) n7/jcz:a qwg3t w $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an apparent brem h e3dle)qgvre8 sew +mv60,c3e*h.uakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg corcwl+, eee)0g.md3rqh muvvee *3 s8h 6nerback running at 5.5m/s in the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad carb2tzyl+b,gy( w 5nualc a996f travels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is droppeu+a g fwytl2(lz 5c6 naby99b,d onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s str6hkqym+ky +4(j fghd(ikes a second boxcar at rest. The two stick together and move off with a speed of 6m/s What is the mass o (4h6j( +qfmgydyk hk+f the second car?    m/s

  During a Chicago storm, winds can whip horizontaf/r2 mw,h r4 1lrbj5yl3l. tuclly 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 1.50 m high and 0.50 m wide. Compare to the typical maximum force btr5f u3 jwc2,l4l.1r/mlrhyof 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 al-up)s zsuh5 9qong 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-uusq5hs)p 9z 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 a .pg4qlr,dyh5, i(ololhj3d4lpha 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 ay lri5jog.4,dql 4hl hp,(d3 o mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetripzw;hvt 8;cvvdg r 4otka9v .,0d+5oates a 2.0-kg block of wood and emerges clead89+z4oarh.c dtkgvvo,;wt v v5p;0i nly 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 isf(wnxtpo3 8m 1 traveling 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 traveling in outer space with a veloc**gx9 iyl9k4zz kzq j0ity of 115m/ki0z 9ykx9q z j*4lz*gs 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 5(pfkv o4gy1 oat a speed of 45m/s The golf club was in contact witf kpo(vgy15o 4h 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 8.5m/s and comes to rest in ayo2cb/gkeoo38,j i8r time interval of 8.0 ms. (a) What is the impulse given to the nailjorgkboie2y o/ 88c,3 ?    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 wall at a 4: 9fw-utufl6zhk q2g05 $^{\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 crashwort n(rg(loi x 8cq/tmyzql5 t /14*sggr8hiness 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 exerted on th84t qg5 (1nzyglclroxqr/ mi( g/*st8e 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 in 0.75 s by a hu.yn+l43s ,9bx omlzz2ars,a ead-on tackle z,2y n l3 s.bz+4,9srm oalxauby a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) pointagvbp +f//63 xp/of 5 dru/y ze(vb cb71cwkc;s in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Usdf cxpw c fb/b;vec7k1 //r( /bovaz+6 pu5gy3e 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,vquewi 7 p7)efm3*s w jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) o,7s3uvp7wewim*) f qef 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 collides 0mya s pv2ryn4,t/du, head-on with a 0.220-kg 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 thes/ p24yt mv,,yd run0a 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s )g* w.. jh3 . lalza5flgl-6jlk eib+shas a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, whl3hljl-g6 iasj5a . ) .kwlf.z+g*belat 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 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 perfectlp gm 0 2or(wvgtjp2nmqv6bur ,77g1+t y elastic 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 u72jvrq o+mpng167r(ggt wtvp,02 bmthe 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 0o t tzhtxw7;k0n(bdy(v 5a k/speed of 2.5m/s collides head-on with a 0.090-kg ball initiakt/0( kv( x;dohtw5a bzt y70nlly 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 mo* 9k ag0vhb(dhusu.7z ving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate 0hd u*gkbavuh(s7 . 9z
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in a,n 4u6uj lstn5:sqcwo/( p q8xn amusement 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 4.55o uqncp j4q:t(w l 6/xsn,u8sm/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 secon cp/l+afqql88 d ball initially at rest. The second ball moq8q8lpca lf +/ves 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 incline as shown in ,i )(hhhh2u ak esg7h8Fig. 7–35, and elastically strikes another cube at the b, hk2s)eh7 hahg8 h(uiottom 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 case296 sbufjw )jk of 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 experig j,3e j)3qcbzment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum tbjjqcz g,3) e3o swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itsa hrq-2kwc 65welf in a 3.6-kg pendulum hanging on h a6w-25kq wrca 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.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of .zfh,f m1zr o3kinetic 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 breaks an object, initially at rest, into two pieces, oneifvch8a uzs: 98 n87qrl(; iip 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 piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. )8s9ir:7 f i(h;i pnv8cqlzu8 a KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into tgg f35vc6k)zrfy:x x1he 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 c163cx)vfyf 5:r kgzg xar, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds cvy,cebax d;cl5e 2mq-x1/r8 to a height of 1.20 m. Approximately how many rebounds will the ball mledexc,b/1c2m;avx58r cq y- ake before losing 90% of its energy?   

A measure of inelastic d+en0 cmrbrz2t44utgf 6vy*;ity in a head-on collision of two objects is the coefficient of restitution4 nm*26y0 vt;f cbzt+udegrr4, 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 the 3uzmg)o)i hmxu bb /e/1 n3u7emass 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 reassembh7m)oiu/u/z )m1e e bxb gn3u3led. 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 movigya6d(n//u. hb. aonj ng in the +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at n a.jnduo(6h b/.g/a y4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second ns;/ , pymyah 0s3ktbj9ucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momenta of3p,tshays /0by j m;9k $9.30\times10^{-23}kg\cdot m/s$ 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 (bm)t nvt0dmty1he;4 $m_\mathrm{A}=0.400$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 ixga5+ xld3y e6nelastic collision between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial directions? yexx6la3+dg5    $^{\circ} $

  Two billiard balls of equal mass move at right angl5-c srvc.4bd xes 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. 7–37). What is the final direction of ball A and what are their d.cvsb-c5 xr4two 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 elas9n1nu8j;jr llgbsqbt 90(.w ntic collision with another atom at rest. After the impact, the ne;9 lnwt.q80 gu1rj (9sbnjlnb on 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 collisiond4u.*z4t 2on(t4 6ihqs.b e a*j hlcve with another atom at rest. After the imp4 e csab*6*.2td itu.j4lhz(evnqh 4oact, 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 mass of the three:3akout 4fq zm.7 0 fdlvplml11.p j4v-mass system shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg mam flpl1k1a0.v7j.v qoptlumf 3:4dz 4ss.    m

  The distance between a caljds7 r+vknsq/) 4k3 fy3 gdq9rbon 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 isv bi-:,(.b qu4mxzknj 2.50 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three peopqzm xib -j:.u4,k (nbvle 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 m(hka0)powgm 5b5no u2g25e qz ass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine then5 w 5 2mo0p5ag qz(ebh2)guok CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides / o2m;x-u4 b-dpmxjcf $l_0$,$2l_0$, 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 lonkg8a j +i5vkb.g5u8 nei 97rww0 fe7dad of identical cases of tomato paste (see Fig. 7–40), each of which is anufbig0ekj 5 gki.875der +nw78 9vwa 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 a9a mw6sn5mh2ec 2uo )h0j6wpp circular 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? [Hint: Try subtractiommh 6ej2ch6spwa92)0o u5 w pnn.]   R

  Assume that your proportzgq234ewuvk n j3 11rpz41 hkp. qghk4ions are the same as those in Table 7–1, and calculate the ma1qv1h2u3zkenzj p w4qg4 4 3hp.rgkk1ss of one of your legs.    kg

  Determine the CM of an outstretched arm using Ta8xwjz b 8gti47jqsc0b)y0c n ;ble 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the 28fslpt ml4i:.f1ru cposition of the CM of an arm bent at a right angle. Assume thatr. lu2i81ml: tscfp4f the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a poxr23wel * yewaj wlj+fv(:4/dsition such that his arms and legs are hanging vertically, and his trunk and head are horizontal,ye w34*lvl w2+(rex:fw ajd/j 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 Ea;mj-w*bf z- n2oz:9w4o operirth and Moon 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 frictionlsy5 jhx5il5t 1ess 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 dia(e-lo6a o)gpqx4c ylh yr4+ta,yx /r,meter 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, a cq6/ryylp g4yr-o,4aet+h()xxo l 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 cegsz5by 57+3am2wa/:kr ahkw ylindrical 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 rwh3mw:s eaya+7kz b2a 5kg5/shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29),abno0q w6 z,-o;t1p5 qpj6kvj $m_{II}$=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 in4-g 3bhmlo5 gu 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 (relatigo3hbl u5m g4-ve to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and pxvmjx2rv+ a,pu 1ru4:2y7;u mmx5 i zis popped straight up to a height of 55.6 m. If the contacu:a 1u5x+27 mvpuiy ;4jpvz x xrm,2rmt time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with spewj qqqv,08+4dkqq k8s5y-9z 6g zeyqted $v_0$ 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 l mz2i6wtm+)oFig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which thtmo z+6m2w)i le cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by pushi cd.lpwj ias/)3f;-gc-w p m-sng off with his legs from an 1800-kg spac.cws);casipw f/- jmp 3-dlg-e 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 otherda-4at b*t fc) 80 kg, are initially at rest in outer space. They tbt)-aa4fcd* then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ballusc io* :w o2qpl6p-pmva*j)1 (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the second bp *o uj*oq2lcpa -)vm 6wip:1sall? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expey0 w(zpoiaqbl 6*;r7(c-pfv db rs 5b4rt witness in 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 c(;o z7w-f(l6 4d byp*cr baqrpi0 vsb5rashed 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 stg 0 4p jvxeozd s()8z9q+xes+ueps of total vertical height 4.00 m. The ball hits four times on the way down, egp4 o+xdsxe+vu (s z 0)zj8q9each 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 1.40-kg block of wood at rest direukq7e7oj32v r98cm u lctly above it. If the bullet has a ma2 u 9rujv7eckmlqo78 3ss of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kbhq1l2bz3gsf+ 1 9gurg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kg gfq211brsuz9+3 h lbinetic 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 a7 cjahk,+vle;h 0z(ko nd 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 a+h,k ;z0(ojkc 7elvh exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abn zm+fq2 w7wv;cvm/y-;c d: ioout $ 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 fragme4ocu0s l0gd( gnts by an explosion. One fragment acquire ods4 g(u0l0cgs twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the for9 2lt qmzh i8c3ywk81omula 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 kq 19 itw.n6sqd.ehnn j,0-kw$m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively i2wz nzn(q*36cu zmih1nto an alpha particle and a smaller nucleus. What will be the speedi z(z*mq6zhwc3 n1 2nu 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 n/q xq1:ce )nei,kw (79 eljvaan 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 slideyxty1vr5; oi1s 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–zogk8s k9e -)yhz0zs146), 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 with M again y8z gse oz-1kz0ks)9h?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47edx sw,vs pi9pn19z662 +oyrx shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s T1sixwp9p62osxe+ yn r ,z6vd9he 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