We claim that momentum is conserved, yet most mov/ip 6u4skt 8l.(icqzjing objects eventually slow down and stopkp(/juiqi6 8l4 s.ct z. Explain.

When a person jumps from b* u2ygis:-v ga tree to the ground, what happens to the momentum of the person upon striking the ground :b*gvgiu sy2-?

When you release an inflated but untied balloon, why does it fl eh6j(dr27l hyy across the room?h72(6djh lyre

It is said that in ancient ti 9tecpojf+4y(yt3i d. mes a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. Whap(. tcjd3 9+4ey otyfit could he have done to save himself had he not been so miserly?

How can a rocket changekiq 9 , aup9rhbdob4). direction when it is far out in space and is essentially in a vacuum? 99br.hoq ipkda)b4,u

According to Eq. 7–5, the longer the impact time of an impulii 3uucl, xrg; syml65*z13xe se, the smaller the force can be for the same momentum change, and hence uy6xx si; ic3ll3*urzg51,emthe 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 rigid as possible to withstand collisions. T ,nin*vo c mz,fs-kw,qf49.8ln2i khmoday, though, csc k ,8lnnfiwo,q*f-,mz2 9.nhkv mi4ars are designed to have “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 tosn /nvx ayk;.hv ,izn /ec4fn,/sed in the air by t//ecx;4.vn/i, n,kz vnnyha fhe batter?

Is it possible for an object to receive a larger impulse from a small0jt0d .gol6.z o)dqs e force than from ad o0 qj.oslt)e06d. zg large force? Explain.

A light object and a heavy objec4i*l bja2p: xgt have the same kinetic energy. Which has the greater momentum? Expla:g bxl4ija p2*in.

Describe a collision in whi1 vwk0+r2*0kamqmlla pfw0:ich all kinetic energy is lost.

At a hydroelectric power plant, waterd,mefm qg *a5qb)*y i8 is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine b5 ,gm idq)a*8beqym*f lades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a 4tw y+1a95v pnh(iw0d. mwup 4h5 $^{\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 fr7y n w-o;q dnbc3kg0+kom a height h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Iwc nk;bk - o30gn7dq+ys the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in ye2 3ufm5n pge,our arms?

Why is the CM of a 1-m length of pipmei*m6ipf . c0e at its mid-point, whereas this is not true for youref0i i m.pc*m6 arm or leg?

Show on a diagram how your CM shifts 4f. kx p7dm0p8im,8-kwsdvhu when you change from a lying position to a sitting pivpdf0. x k p,smm4hk78du- w8osition.

If only an external force can change the momentum of the center of /(m4earkwp q7 mass of an object, how can the internal force of a /7e4rm wkaqp(n engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes into b b2 *rsq7n :kpoamjys/h1,v7many pieces. What can you say about the motion of/: 7 2qojnm*ha,pbsysv 7rk1b this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrowar(d ev,*ows nudvoav -+1m,7 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 f.39p r:a5nx za77mo cxfmgj/zuh, egof;9f 0o or 20 s. What is the skier’s change in velocity/ ofxjfo:oa0 .9 ux,g;77pr fmzm g3 enz9ca5h?    m/s

  A 0.145-kg baseball pitched at 39 m/s isr)k0 3 eqguf)o hit on a horizontal line drive straight back toward the g 0)kf roeq)u3pitcher 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 ou(k h;,fbmk66dmtz *y vt 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, anzmbkv6ty 6dh ( k*f,;md that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exern.7e i2zth tysx9li1 v:7c v0jted on a rocket, given that the propelling gases are expelled at av7y0.v ti :ish2 7tzx 1cenlj9 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 moving atwsx,c sjj2z7-ue1 f 9f $4.1 \; m/s$ 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 ale7y0) 9bdopaed vel 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 car0bd yda)9e7o p’s new speed?    m/s

  A 9300-kg boxcar travelinga t y ry(9cynv,,;fbg8euqy8 5pwc k80 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, winds can whip horizoxmgj:;g 5s5ti ntally 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 foi 55mtsj:;gxg rce 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 8.6mx/0n npae /,4e;fksvf /s on a level track. Snow vnk,p; x4f/a0sf/een 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 after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an ad.9gclkc8qc*5 m-dkvdy4 vn z2 c*j2u lpha 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 have when it is emitted? .c2 5*vd9ku4-k2vgqdzccd jy ncl* 8m   m/s

  A 23-g bullet traveling 230m/s pene;s .v (f/1lzg3b kpcuptrates 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 does it move after thel1;gpvc bfpuk3 s(z./ bullet emerges?    m/s

  A 975-kg two-stage rocket 6 ynvyr0yeyrrou:n0u0 s/ m2 :is 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 ; kwi, mks 0xfn(1k) bjx)pv+4ts9(o:fwtj lpin outer space with a velocity of 11ot(sv (mj4) l0bj9kxikwpnfs +)1 xkpt;,: fw5m/s To alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed oa+4c 8 ,fyygwoigv 2z1f 45m/s The golf club was in conifog+4y2a , wv8c g1yztact 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 8.5m/s and comes to rest in avqoc( cxiv ov8dwm0.z1wy1 +5 time interval of 8.0 ms. (a) What is the impulse o1wymdz(v ocw85+ .xqcv0 v i1given 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 speed v=25m/s strikes a wall at a 45xtw(ifw; e z8a*z )r76f*rjem $^{\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 craskrzyw)8 j*eg* hworthiness of new automobile models.kw) zr jgey*8* 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 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;xufk 89 gphlh8k1jp)ju d2,r at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due w8xpf)gd;p ukk 1l2ujj,9 hh8rest. 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 heht q*5a:or .3 ijcp10.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of timeji *53aore .1qth: cph. 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 person8 eatsc8u,jx1 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 (fo88c,1te ja uxsrce 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 dir e44wc2x8*/ulbv;jrr mk0 kvhection) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfecbhu 20v*4j4k;rvc/8wkrxeml tly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-on cj9(,0b jge dkvollision 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 repreev 0dbj gk(j,9sent 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 perfectj5nfxx- *g(t gly 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 bgg fx n-j(5tx*e their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speen0 98 du8/bhs3 qpx5o 7nzkghoar:s6:l z9p nkd 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 perfecrao68 bs 7 :ohk:sd0p8uhkngql/59n p z9n 3zxtly 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 tymd,jb(9r zce: a0s q3hat is moving with a speed of 8.5m/s collides head-on and elastically with another ball inirs(bz,jqm dec3 9 y:0atially 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 ono ytvn nw*2(h3to+f(ae 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 moving at 3.7m/s calc vw+an(h*nt t(fo3 2oyulate
(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 secon0d rx:co. icnx4qey)k5 2blg4d ball initially at rest. The second ball moves off with half :x5)g yqk4beccr2x4 0 o ld.nithe 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 frictionl l/cb q*tywj ajd++:u)ess incline as shown in Fig. 7–35, and elastically strikes another cube at th*+cdbq w yauj/jl+ :t)e 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)bb+vpq;d+e 1xk 4yne( bpo7o 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 exp sxn45z6k+fnf eriment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A s 6 n4nx5+kfsfzecond projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itselo a4ztl37us9v f in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.v4u39a7to vz lsertical$\approx$    m horizontal =    m

(a) Derive a formula forw0)ehu-7 6 h7u,ctppe 3rysdv the fraction of 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 at rest, inte d 3x,o0ewb8do 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 partic8xed,3obe w0d le. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a jf;qsw a:(; (7u rnjw4 dgogn d3zz01p2300-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 0.80q0ad7;w szzrg(1; d(nfjpog nw 4u:3j, 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 o 9s))wbyv:p+k-no:nb jrq j;j f 1.50 m and rebounds to a height of 1.20 m. Approximately how ma: jjbp;rqvj k)s)w nn:bo-+ 9yny rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a hea :)krm. :m4qvsxhkpw9d-on collision of two objects is the coefficie)kwpk vm sq: .rhm:x49nt of restitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cu)x(zaw/5 ffj io)k+ f slb0es2t into two pieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apa2xoasbjle)s ) fi5kf(0w/ f z+rt. 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 colq:yuy6- np0.2xww; ezr of8tclides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each massf n-wrzy26;.yt08ecq: wox up 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 sv n 8 cx)(h+eatrbc s+j:xph:1econd nucleus, an electron, and a neutrino. The electron and neutrino are emitted)r eacvb +8:h1x(:pnjs c+xt h 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 ; yo3xo 7sv/dehh7ak:$m_\mathrm{A}=0.400$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 equp /zatx,6)ov9 z4y7, ntnzv.zn m8zuxal mass, each having initial speed the two move off together with speed v/3 What was the angle between 7znnxva u zp6nz4y 8,xztt/ ov .mz,9)their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at2fg jnymf )a5,scj1y-- li*9lmjuj,l 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 e nj,fujism c2 1y9f*)-aj y, lg-mj5lllastic, 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 d8*c tc8lt5q(sqwh1bcollision with another atom at rest. After the impact, the neon atom travels away at a 55.6 s581 hq*btc(t8ld cwq$^{\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 collisio7m(w:j 5)ydk: nz+qza-d p xdkn with another atom at rest. After the impact, the neon ad mwj)k::y 7qdpxa+ (z5 k-ndztom 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-mass system shos*l ni*1odkjftz, 6* cijr :i/wn in Fig. 7–38. Specify relative to thtjd*16cf r/*ojz i:liin s k,*e left-hand 1.00-kg mass.    m

  The distance between a carb.4bkafv4ebaj4 -6 y qq7raw u(a kc:/yon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of the car. Ho fhbu9 9i2fmcg )+e(dbw 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 p)9h+ imbb92egf( dfu ceople sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used al5bx;z uzc10-1xjmsbs a ferryboat. If thr x cb51szzuj1b-m;x l0ee cars, 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 side ca;,xtc3m kp (*izt*qs $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of tobcyz* 244q zv:jwrumn5 -jc9b 6z:cwp mato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so *q4u cbcrb 69z-4nj w:cv: 2jwzpym5zthat the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cut pg-cu1egyr q5 u*ur(0out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fi q y1 *rggu-0ec5ruu(pg. 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 ascm2 1chuh p8ed*, uch*p3bxo . those in Table 7–1, and calculate the3u8*u*1 .hpb co h, cmpdx2ehc mass of one of your legs.    kg

  Determine the CM of an outst nw/1gpmn2y2 ousf4g++q4 b muretched 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 t(w/xu1g -ytvao o3x k:he CM of an arm bent at a right angle. Assume tk(vwy xoga/3u:t1ox- hat 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 are hang 7nn.26 yv(zvb gad- 8zm7aekdwv6+k ping vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will znw27k7d av(vagbem pdv-6 kyz6n+.8be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon a2ilcfa:qurz8ys- 9 p7re $5.98\times10^{24}$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 fmhse:bj(i7 -man stand 10.0 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 massrm+ye 4sw4g id6i ;3ixk,:pzw 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 ma6e +m 4pz 3 sidri:i;wkxy,4wgllet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylingtlll ql3j o h5nd hm 52+v:+e+qz)s7wdrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far abo+ m7vllw:hz)5o t3+ll2q5gsjd he +nq ve the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fs-j2 ejvif +1.ai:lby 1km6qw ig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, ofh- zny (ts5kc1 mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the5ys ntzc-(kh1 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 str u:n)e 46xkkkfikes a bat and is popped straight up to a height of 55.6 m. If the cone6nukkf):k 4xtact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m trajn0p(k1no (rf,hjy 7qveling 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 th* * syat(n( md:dta:e8z(o cqve corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give detaovm(8ztd c( eda(**s::aqnyt ils.

  A 140-kg astronaut (including space suit) acquires a spetafli1( fqkgw/wf (5m :4oem+ed of 2.5m/s by pushing off with his legs fr 41iwe(l t+ ffk5mg(/mfw o:aqom an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 k6ml1;t hqjzmpi(v9x b go(6c a+v(y7qg 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 astrop c zqh (7tya9q16jvlox;gmb+6im(v(naut has moved 12 m?    m

  A ball of mass m makes a head-on elastic cougp 6u79 b3ypum04q t tx57,phzc) npvllision with a second ball (at rest) and rebounds in the opum7,qcppp5ty0 thupzx 37)u6v 4nb9 gposite direction with a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case invoyv rww o+l l.i13b5 1bw7c+dhslving 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 s3hi wyd7b+cl.5v + o ww1rlb1before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of ayz syprq,nc67n 8m :3b flight of concrete steps of total vertical height 4.00 m. T bpr,n7qyn:y68s zm3c he ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the 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 directly a6lrwo9n,eic *bove it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high wil we *il69ro,ncl the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becz 7l vpujx;0n)xhh6xy.2abx0omes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block abj hp u0a7xl ynx vz.xxh0)26; 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 apgcju+lv7v68 f 2gy4nc x:ct: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 j6v 2g+ugpf7vxl:ncyct4c :8been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abotmr gesrhg) a/zz9530 ut $ 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 sudsol2g+w 7ovf.o qg r5-denly broken apart into two fragments by an explosion. One fragment acquires twiceg+g 2 q5 roow.v7osl-f the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formul ynbxx )sd/3tsg9:0pf+z to3la 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 massescr (v5e-r)5tndwcu , x $m_A$ = 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 radioactiveh /7dumk kkv)4ly into an alpha particle and a smaller nucleus. What will be the speed of this recoilinh)uv7kd /k4 mkg 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 an angle o vzta5io +t2 /7m7siuef 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 sncki pd, 4*ia8nq(qoc: ;h 7oglides 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 m if it is to rebo(p)ze0g i0 egnr/x6 viund from M, slide up the incline, stop, slide down the inci/n0 g6zg0p vxe()eirline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Satqqm1cxn:9;c*+k g1 w sac-aez)9cl tz urn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass xgclq*awc9t;m-qcn ka c) 11esz :z9+ 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