We claim that momentum is conserved, yejzhkq 2g/j8 +iggu/w x du9* 0r.;cmpet most moving objects eventually slow down and stop.w; di .u0 x//e8rgp gjjgm*hk9 2+zqcu Explain.

When a person jumps from a tree to the ground, what happens to(q34b*qrx:b;j i*x t+xaq 7p9o iwztz the momentum of the person o zbx3j a9 rtzq iqb*x;*(4:t7qpi xw+upon striking the ground?

When you release an inflated but untied balloo2r).tlmdlv ym 3b.f 6iqh.l8 an, why does it fly across the room?bd)hi m83l.vt6ly ..a qm r2lf

It is said that in ancient times a rich man with a bag of gold-2 zapme4gfgo ((wubvo d1.-f coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shor-au4-gvf(mo.z1(op ge wfd b2e. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in w x;jzkc u:xn6f- )*ofspace and is essentially in a vacuumcz:jf nxu-); fwx6 k*o?

According to Eq. 7–5, the longer the impact time of an impulse, qi0rn/)pv 7rsthe smaller the force can be for the same momentum change, 7)n/ spirr 0qvand 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 or death.

Cars used to be built as rigysu)e6xf7,ofqi+ l+ rid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upol+r)fis q,6+uxoef y7n impact. What is the advantage of this new design?

Why can a batter hit a pitched basc0k1)bu:;:)c v gfjhjs)hh hbeball further than a ball tossed in the air by the batter?h cf:h );) ujvk:bh0jgbchs1)

Is it possible for an object to receive a larger impulse from*z wg+kn8 6ev2fyf6zhr )x zel-,f,l z a small force than from a f 6 zx2l zg-wyz fnvle6,*+8)rfz,heklarge force? Explain.

A light object and a heavy object have the same kinetic enenqe+3ghz ydee svtj393va8q 099qre 6rgy. Which has the greater momentum? Exple +6 vdenzqy 0 3e9qtg9s3h 3aerj8q9vain.

Describe a collision in w cgrmex7kfuvu3zt z7-)*)mtd odtekuq7 *+ 70hich all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against turbine wl nss:qswnk936s lfw 857j2z blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is bs2l 9l w:sf7ws5z68s3wn njqkrought to a dead stop, or so that the water rebounds?

A squash ball hits a whcz1(c1/w7(lkl hl e4zc1 kaoall at 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 aji9/t4c zzkd ivp,( k+ height h onto a hard steel 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) f4kpi jdiv 9(/kzczt+,or a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in your arm:d:1 8bih6 mob63frliawb; bus?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is not02; wglf k)yvs true forsw20;kvlyf) g your arm or leg?

Show on a diagram how your CM shifts when you change from a lying posijk rcf :8rr5jvgdg-j5s ao de(a9g0j2 0o0 m4ation to a sitting r4okrjm2cg0jg9 :(jo-gdjr 50e0a5dva fs a 8position.

If only an external fojc,og1fsf(sr 7(c ve7rce can change the momentum of the center of mass of an object, how can the inter7g(c(ssf1 fo7 vcr je,nal force of an engine accelerate a car?

A rocket following a parabolic g4;q-gd j /amfpath through the air suddenly explodes into many pieces. What can you sam fg/adqg-;4jy about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-9n97 mr z+(dc0 akoop bgta;sx*g*p) rg sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What bb a)x(lvpz( rq3f ,-qis the skier’s change in verfqp,(-b(xq)vzla b 3locity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizj4v g*boq2 1y 4misp+bontal line drive straight back toward the pitcher a ybpm42s*41 jiqvb+og t 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 pa jrp5q9j3dt y0 -cwbl 1yb23ul rh7n5fckage out 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 45.521- 39u nj7 phjd tyqbc3f0rllwry5b0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases ar/dyn9nwnl jzo+p8+1 t e expelled at +1 olj9n8z/ tnw+ypnda rate 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 movingozbum,)ltz kt72 kuq;76l 1np at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless track with a conskz tts(/phvf7 rkij0 i1 b-: c-jj2f1wtant speed of 18m/s A 5350-kg load,initiallc1zi1k7 r-j fi j(p/s2tjfkbt- vwh 0:y at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelihgf*ty6n e*xksx lih m1:6( lz6r7-qj ng at $15 \; m/s$ 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,/7pt+vhmgc ui:*i pp 69etz,t winds 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 69 i,pt 7h+t/ei*gpvct mupz: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 railroa/kkf ,di7e4mh d car coasts along 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 the car a k/k4 efh7imd,fter 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha p pul 03fzum:*jur 4yocql89a2 article 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 andz :l3*4 om0uy9uja8 f url2qpc 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 travelf ir/ k51k.*zh ;dlvb8etb mz:ing 230m/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast doekf; mh:z51r d l.e*v8/bk ibtzs it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is t eipza4 k47b 0,fs9pxnraveling 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 spay+g.nqcc ed44 ce with a velocity of 115m/s To aedcy.q 44n cg+lter 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 + ip,h7md e.w uz (o-zf(xa(kitee at a speed of 45m/s The golf club was in contact with the zpe+dxf(-(,w oz7(ihi mka .uball 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 c26aisg46,v )o.2tg a eibieujdx69wn omes to rest in a time interval of 8.0 ms. (a) What is the imp9,)t6ge4a.av j6 uiinwx ebi6dg s22o ulse 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 c i4eumac;c7h dr9q xw +0bqrk498ae/.06kg and speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in ch*nxc3p (o7i6ra cmv. sarge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calcul.napi6c7 o3*(m s xcrvate 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 in bg )k.t 7g. aki4vuksq-hax;7kyn)i .0.75 s by a head-on tackle by a tackk inkv).iu-gayht7gk.s;x ab7qk .4) 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 tennisr:w j9t;e ec6g ball (mass 0.060 kg) points in the +x direction6;wc 9 gje:ret and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump wix. ) gfafutfw64wr66- rgh)mjthout 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). Assumt6ghw)gr 6mf 4) -j axf6rw.fue 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 sy3 8kv63w pihpwl:f 6vpeed of collides 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 t3v:l 83ykphwpviwf66 he 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,fn;q zr+;gq x+ moving 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 objectq qrn+;zg+x;f after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastic head-on collihh(,t3j: .ysf p9hmnwo qf,r; sion. 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 therpn h hf(s,.;:39jwhy, m oqtf ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s coll :4wzho7-e zuiides head-on with a 0.090-kg ball initially moving away froe:w-o 7z zui4hm 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 bg eljlwhd3,*,x av.c qk6s6*moving with a speed of 8.5m/s collides head-on and elastically with another ball initias6alw *, q6lx ,evcjdg hbk*.3lly 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 amusement park ride collide elastically as one approachzn3 y b-zmd1wj:-c4ices 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 wm-z1b z4y3i:cn j-dc 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 anlf/c3+w hu/8nyg7h y e elastic head-on collision with a second ball initially at rest. The second ball mf7l hwcy3+uegh 8y// noves 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 inclinp7;cdtj(x g /we as shown in Fig. 7–35, and elastically strikes anc(gdp7wx;/jt other 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 object opnjo3hxc*9 b pgwu295f 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 heighd* 8e,qlihi1qt h of the pendulum equal to 2.6 cm. A second projectile causes the the pendud1 i lh*,iqeq8lum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg pendulum)/ks1a ;0 xyi-t buelx hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal comp/ak si)eul0 ty x-;1xbonents of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction ju,v9wt/zer 5cdel/b4 5+6unsscim 0of 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 breaks an object, initially atz5uiens6na pr )*13d p 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 piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) Kapp 6uderzn )*in3 15sE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear e.t5 .yck,-oj.lh3:h y)pnv, bfd bdb znd 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 t: t5y bh-phy.3,dbjk,b ..dlfz)o cnvhat 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 ah*2r. jehm*by zf8zo6( s ,sak height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of itsy8z.6*z j shofrs e ba,hk(2m* energy?   

A measure of inelasticity ing 0tcbgjz sg:bj81; 0u a head-on collision of two objects is the coefficient of restitution, e, defined s0zg: ;b1jc 0ggjtb8uas$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
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, 64 utaa2tc3wxone with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels?u6act4wat 2 3x ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/b 1bd(:6sbn 9odt8lt:.f fplfs collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Fin pdlfotb6lfs.9bd f:1( :8tbnd 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 seconkhthpx9 (fg +s1.cf9ud nucleus, an electron, and a neutrino. Th xg 9+ uh9ffh1skp(tc.e electron 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 mass xl s7f;, cf0h:eg9x s7m(d 6nkp;m6vc/p cdwt $m_\mathrm{A}=0.400$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 ehd(-8/u+ v56 k s9rkwqr wiu qwaqm0x+g,2weequal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial directions?q drwv xumw(q052heu+k,ai6w qrw-+esk /8 g9    $^{\circ} $

  Two billiard balls ofhk0v5 ce.x3e j equal 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 Ac5e0 3kxvehj. fter the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with;j 1ve9sw dk7f another atom at rest. After the impact, the neon atom travels j;w7e df1skv9 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 perfectlytqv(i .qt i05s elastic collision with another atom at rest. After the impact, the neon atom travels away at a 55.6 (qti0tiqv.5s $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. Specify()5bntm ux6nxi -;sn q relative to the l; qsnn -tixubnx)5(m6eft-hand 1.00-kg mass.    m

  The distance between a ci lj1skv*-5 viarbon 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-v)em m36yw,ar b. 2berkg car is 2.50 m behind the front of the car. How far from the front of the car will the CM be when two people s arb3bv)yer,. me6m2wit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of maaf5-m q k vl-ly.dfm37( 7)coedpmmp8 ss 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine q- mdlma5 fdm k-(e.p)8ym pv3 f7olc7the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides ms;/arao2k7oo 1gce 6 $l_0$,$2l_0$, 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 9q, el 3*ut7sy-smmg sa load of identical cases of tomato paste (see Fig. 7–40), each of which 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.*yuse g,9lst -ms3m7q$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a 3,9bs1o:ey 4tydxhetcircular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the h3tt41:so, dbeey 9xy 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 ca4 ncfopso1a0wc5 c+e (t7 i9dzlculate the mass of one of o+5n9 tc zi1s4cwe fco(d 07payour legs.    kg

  Determine the CM of an ou- v 67y80xi k kwbtc/ds8tn4altstretched 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 gz:y m00+ sjzql zlp;o(rew,s5btg(7an arm bent at a right angle. Assume that thjz(rb0, mtz0( slezsyp+l 7g :w;oqg5e person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his aknfbou-(;9t hrms and legs are 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 bn (;th-ufbk9oe outside the body? Use Table 7–1.

The masses of the Earth andc8,e, ypn nud0 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 8 p(edw:o/hi p-k dq*di/4kmw m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.nfw5 0:l+s0q memeatd1 a0;h s00 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 m:el0 amatfdenq+50; 0s swh1is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical hei j 7 xa8*zinhnc*4i,xad of mass 2.00 kg and a diameter 0.0800 m mounted on inn *87x a*,ixhc4jiz a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–2 a9j,ou8 kyke7cf6b*d 9), $m_{II}$=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 andsjdz 5+h /jsuxebj8+/-fo(roorw+ r, stationary with respwux or+o,s se rz(5oj/++ j/ hjfdr-b8ect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is poppe :k: . byfmo6dawls67rd straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force onwskld:r.fy6a m 6b: 7o the ball during the contact.    $^{\circ} $

  A rocket of mass m travelinocw*8 vg.s4 zrg 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 kc*y m2ti7o:y the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Shoutki:27m y*cyo ld the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (inttk qfl7w..5r q, unt:cluding space suit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800rtn:q7,fwtt lk. . u5q-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 d+ey.w(+qx4 lnqhm 2f kg, are initially at rest in outer space. They then push each 2 dnfyh(+qwem q .lx4+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 wi.jqo :h;cwwi,h cg+kuqq *m6 8th a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its originw*h6:.ogwq ;, kqcim cq hj+8ual speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court caseww mpa/i(lj)1 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 exceeding the 55-mph (90km/h) speed limit befolawm(1ijwp ) /re applying the brakes.    mi/h

A golf ball rolls off the top of a flight of conb6 ep+ oaw*nn*7o0jg 44 nqovkcrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each tim a o4w j+*o7kn0gen v4*nqo6pbe 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--fj sj*alhz3 block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a szj* -a-l3jhfspeed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedde2nivyy8n 2 1,ysy jwz0d in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic fric 1ynvyns2,w2i y08jzytion between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other o gts95pg+g w*wf 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?5 w+w* g9tgpsg The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was aboz93,xw a 0elh5rs79x 4 taeiklut $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments by an exploxb x a bs2np*+qd5;0wvsion. One fragment acquires twice the k5;wdpv*xxb +s0a2 n bqinetic energy of the other. What is the ratio of their masses?   

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

  Two balls, of massesq jn. 8ytkkxny42(x9 1xa.p bq $m_A$ = 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 decfh msh((jc6o412 hwc gays radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the spehj1hwc 4c26mhogf((s ed 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 an angle of 309k *(hyxszs8i $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.r3d2 n tsv5m*a0 $^{\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 if it is to , ;vqp-droq6vy jh3 .jrebound from M, slide up the incline, stop, slide down the incline, and collide wi qvhj jvd3ry6p ;oq,.-th M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the pnbv)p;j a: gv1;gn 3pvlanet Saturn moving in the negative x direg3pn1: ;vjang)p; vb vction 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