We claim that momentum is corjp* mc3j)z7x d -)3yldbe-qjnserved, yet most moving objects eventually slow dow)jr )ejjz3d p*qdm-x -b7cly 3n and stop. Explain.

When a person jumps from a tree to the grou ebfowf 6(+5d)e upof2nd, what happens to the momentum of thf)2eopd eo6 5+bwuf(f e person upon striking the ground?

When you release an im,4qpf -z-k+-oia/ x4dw buja nflated but untied balloon, why does it fly across the room?od +4z4-maf-p abx -qi,wuj k/

It is said that in ancient times a rich man with a bag of gold co8k3/msd2 ona ;lz ag vz zf7dw+y1,uk7ins froze to death while stranded on a frozen lake. Because the ice was frisdu7 2/3,7z;kfvng 8+wzdlkyoa1azmctionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is essentia/saufs*. )po4f) lzrxlly inlz4)s.f*pa) fsurx o/ a vacuum?

According to Eq. 7–5, the longer the impact time of an impultp+)zfkjfsk *h4ga)xvg /x;+se, 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 automobx fztpa4gx+ )hs fk;kg*v)j+/ile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Todaq+v )anc2rbv( pd/l 3py, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage oc rv/a)l p2(nbv3dqp+f this new design?

Why can a batter hit a pitched basebalda2 r-qskna, *xw. ny,b;8stll further than a ball tossed in the air by thelw,*8 ,aqr-a;nyknsd. x s2 bt batter?

Is it possible for an object to rs, 6al1y,niyheceive a larger impulse from a small force than from nls1i6ya,yh , a large force? Explain.

A light object and a heavy object have the same kinetic e-y5cvj hnf n,1eb mf+1nergy. Which has the greater momef, b fe1njhy1vmn5c+-ntum? Explain.

Describe a collision in which al 8219yn; zb;ninv rjvbl kinetic energy is lost.

At a hydroelectric power plant, water is direh.ralsh2z;a.8 mth: 1 4 opmjected at high speed against turbine blades on an axle that turns an electric generator. .;hmtaso hmh:4jplar z 81.2e For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall afb1wh8i(bl q0blszp ur7 *( i:t a 45 $^{\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 a0bd+,koiw 3f s height h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momf0 oswk+3b i,dentum 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 carryi4b1da )p pak7 cfl.)deng a heavy load in your arms?

Why is the CM of a 1-m lezt4q bq3ej n* vbzjnh8k-65b4n ;hoi1ngth of pipe at its mid-point, whereas this is not trueobhnq16*znz44v3 5kj jni-hqtb8b e; for your arm or leg?

Show on a diagram how your8pnsd:rg:*ez n0ptiy* w 0zr; CM shifts when you change from a lying position to a sittini*g0*tdy n pes w;:08:n rrpzzg position.

If only an external force can change the momentum of the center suks n fry)lx l13x1;m5m -1gvof mass of an object, how can the internal force of a nkg3rlfxylsx5v1)m;s1mu- 1n engine accelerate a car?

A rocket following a parabolic path through the air rjylbvs8 jx;; 5pvyj1l75bn(suddenly explodes into many pieces. What can you say about the motion of this system n7bj v5ljl vy ;rpj8yxb;s( 51of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying withmu 5(+i;yadrwu(ttv (a 5j)np a speed of 8.4 m/s 5()(u arj+5vutwi t ;(ymd pan   $kg\;m/s$

  A constant friction force of 2a6al3mz (0cuz 5 N acts on a 65-kg skier for 20 s. What is the skier’s change in velocity? 0 6az3 cz(lmau   m/s

  A 0.145-kg baseball pitched at 5 ezrhpq+j3m7u/k 9xrm3 obz 439 m/s is hit on a horizontal line drive straight back toward the pitcher at 3jxk o45r97mrbqz z +u/hmp3e52m/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 packalit(extts/g2nu3+ c ,ge 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, a tn eucgt/i(ts,+x 3l2nd that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerteda)m4lgt 0t-8 qva f;ei on a rocket, given that the propelling gases are expelled at a rate of 1500kg/s with ai)latfgv mt 0 ;-q84ea speed of $ 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 breakaway for a touchdown iswu8ok745v .n f btta)r tackled from behind. When he was k.nfa7w5r )v tt uo4b8tackled by an 85-kg cornerback 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 car travels alone on alevel friihgs jsyr 4 +g)wt6o36vaf*t; ctionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto thsit3rg;fsj6+ v6hw 4otg) * yae car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s stg90.syrox :as rikes a second boxcar at rest. The two stick together and move off with a speed of 6m/s What is the masrxg. o:y0s9sa s of the second car?    m/s

  During a Chicago stostr3yk7v,g kc fsr328 rm, winds can whip horizontally at speeds of 100km/h If the air k37ytsfg, c3 rs v2kr8strikes 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 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 f.rs(l yfx03w 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 ws3lf(f.0y rx 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 42nfaz 3mii1 2(y0m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle2ifyz i3 1anm( have when it is emitted?    m/s

  A 23-g bullet traveling 230m/rft/,vlc m07p s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is sta,t l pmv7/0rcftionary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speiijn ( lsrtu9g7z*rj2,jszy1- ,fzo7ed 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 9l .xuk w hiur1l o:f:sr1+7oft) bj)sspace with a velocity of 115m/s To alter its course by )lxwut:b7lf.u+ir s)r19o:o j1 sfkh35.0 $^{\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 of gzcz y h769si645m/s The golf club was in contact wisi67gzyzc h9 6th 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 ati74 yi,;mdxph a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) Wh;iim 47,pxy dhat is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speebvb9 x 3; wq31*hxmkpdd v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthinei/)evpi zdyv*f /a)l ;ss 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 vavyii;)//dp)zfel *brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in 0.75 s 6m,hyq8;*h, tljp bxk 58y b3rz(khytby a head-on tackle by k mky 3tyz yp6h(jr; , x5hbtqbh8l,*8a 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 (maq (k7ygnut;5 zm7 bg5ess 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estqe5 ;7gzn5tg 7mbu( kyimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without break paieyx:n7r+3 ing 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 sera :yen p73ix+ated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving easjrqmnnbf+,s9o9s3 a2 t (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what wil2rsnsn 9 93, obmqj+fal 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+,.ec.0im .zc )pkp sj2g pouo has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. u+cjp0 .. eoszp )ci.omp2k,gv'$_A$ =    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 cola : fvx* 37 m5j yachji,:toi.k+,rb:n7eaupm lision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposit7 5m hvxak 3:,bic:a,oa7f im ej+yp*r:t.n uje direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, m6js1u: ij-r2oggde k ;oving with a speed of 2.5m/s collides head-on with a 0.090-kg ball g- is6grukdj e:2o 1;jinitially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/2 )2ff9p *j2mb mq4dbqxxf -rfs collides head-on and elastically with another ball initially at rxjf2d b-m4bf2)fqmxpqrf29* est. 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 ridep).4c4 i hfimo collide elastically as one approaches thf.pi44o ic m)he 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 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 md;7 1xpkaz29e ofvb q*akes an elastic head-on collision with a second ball initially at rest. The second bx9bv* eoqd2 kf; a1p7zall moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as shown in Fig. wv: d drjxvij6fh0s1fy8f5777–35, and elastically strikes another cube at the bottom that is only one-half its mass. If w5f:hjr1xsf76 jydv807i fdv 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 of mas(,sm zif+j7id1ziw (hs 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 experimena( y+ 2g-gqyf3qb)q -ppgy.r7 umtv)nt, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projeptv-)n7.pry y q+)u mg3q 2q(gygfba-ctile 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 itself in a 3.6-kg pendulum hgef:n od0*+tbanging 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 displacemenndto bg+*ef0:t.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic enedaoq 9, yrhc968ahxn/rgy 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 anmo7 -ml8b n :r7nd1gaj object, initially at rest, into two pieces, one of which has 1.5 tm mj7 grbno-1n7al d8:imes 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. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-;r.vgh5 v kkji.t*c m-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before g-tjcr..v*5vmi;khk stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a heu2)9 hc cbb,hw.oj6 rcight of 1.20 m. Approximately how many reboundsu cb2 6,. )wccjhhbro9 will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects i4zzac. ez yx()s the coefficient of restitution, e, defined asz)yzz4c a(.ex $e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
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 witfravnxbp8 ch.*7qy8xtr3,elx 3t(c6 h three times the mass of the other. A depression is made in both faces of the cut, so tn( ht8epy6l,c br fax.rxx3 *c7v3tq8 hat 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? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s c *+kavuea o;d1)dtmxm+ ,2eoqollides head-on with a 10.0-kg object moving indqa1vt;exmdm2 ,u e+*oako)+ the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an 3kk xe6hmi(i x9te*;nwtv 4,t s5u3mvelectron, and a neutrino.3s3 69ewvhmt5,mx;ti (t4x vi k *kuen The 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 ma( eqgc ai2l.1z v+yhg6 ju84nbss $m_\mathrm{A}=0.400$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 objejid1z wr6/,i itw1wvc 5g usbd0k9; :gcts of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial directio 6;wuzcivwsj ,d0:i1ggt51 krwbid/ 9ns?    $^{\circ} $

  Two billiard balls of equal mass mo +q7*om 4mu 9khh6pdoyve at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B iqho m+6 *om7 u9dpyhk4s 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 ano(5/a z20j:jfxou rs vuther atom at rest. After the impas0xao 2u(j5r :f z/vjuct, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision with an5hf,weq sb**g other atom at rest. After the impact, the neon atom t hbsg5* *feq,wravels 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 shown in Fichi48r/ .dgcs1kof0p i20a byg. 7–38. Specify relative to the left-hand 1.00 4ch1sdi.82rac0kg foby /i0p-kg mass.    m

  The distance between a carbon atompc o--spk8ur p2 7vl+6 mrpnz0 ($m_{\mathrm{C}}=12\mathrm{u}$) 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 q(+lft(cyrl :is 2.50 m behind the front of the car. How far from the front of the t c(l (:lfyrq+car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used q18)erh g)/it-qzj;dc,c tms as a ferryboat. If threegrh-t ,ic cj 1e)md 8zqs/tq;) 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 sidex laglo)61dk .s $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of tog;ky7rpp5 .mhmato 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 tipk.pg5hmr7y ;p ping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular holeev((zej 2i, b fsd,.b nesw-4g 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, ie-f(e4zsd(v s2n. ,egwjbb: Try subtraction.]   R

  Assume that your proportions are the same as ts jaas,+p v7yd44p9z3g w3x ychose in Table 7–1, and calculate the mass of onca47wdyjs4g p 3v +a3 p,s9yxze of your legs.    kg

  Determine the CM of an outsk+e zq ;wxf2p(tretched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent at a right angldv.rp(- btb1w e. Assume that 1r bb(.-v wtdpthe person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms an1 k krc9hdn9/xsdn+(wd legs are hanging vertically, and his trunk and head are horizontal, calculate how far below thecn d1dh(9sk/ 9xnwk+ r torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth andr2n t *hfjy7v3 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 fricz;tkz.x60 0mkbh r1yxt y5ww(tionless 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 t/:ets:bk:ijc)7-llt w g .nwmass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the hantwtb)wnl/eki:j.c- g:sl7t: dle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a . (( cg5cru.uv9xeeofu,nbp,n/jh l(uniform cylindrical 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 .l (n,jgu.xe v r5(/(upob9enfh c, ucthis 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 E d 0roma;yx(0uxample 7–14 (Fig. 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, of mass M, are in the air and stoq24)e5/i *diks qnctw/l)b iationary with respect to the ground. A passenger, of mass m, then climbs out and slidesotdqk2q5*il/c i4n/bi wse )) 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 horizontalltvm1r;4sb ki,5f qrf2,bdjc - y at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on-12jrk cd,5r4it f b vsqm;f,b the ball during the contact.    $^{\circ} $

  A rocket of mass m t/i r 7ndrlje gob2k;hj903q l1raveling with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot sho68n42r ho iux67dtf8t ojyg:kwn in Fig. 7–43. Relative dimensions r6 gtj7tuiofxnkd84:hy86o 2 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 details.

  A 140-kg astronaut (including space sui;)cp p,x(v6hp:v vgut + pfpe0t) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-kgvv+g:(px vu0tpf ph p,p6ec); 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 ((rgmf1m- hc8rq2 wkykg and the other 80 kg, are initially at rest in outer space.1r ( my8-gf whmcrk2q( They 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 ba3w(j qp26frk xll (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed.f2(k 3 wjpqrx6 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 invg;c6a d, kzz-rolving 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 sli;rkz-cza,g6d d 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 gthabby0)6 b) 0u*rys concrete steps of total vertical height 4.00 m. The ball hits fybb0ugb*hr6y a))st0 our 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-kg5 uasrzi*77 3 0h)wp-llnafd w mje+d9 block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high wim7-0dhaf 5ud*i79+s rzlnlw )pw3eajll the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes a9jtebahc x26pr/liy*s(2 /tz9xr 7 ln nd becomes 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 blo*(nl/l/x 6h2 tzrb2i799paces yt rjxck 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 maslhu/1a0- im el07al1y n emsq1s 75 kg and the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of /0-ls eeyl01ul n 17aaiqhm1m 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 ab4rf sd o v-49cqz :ux6y8dgus0out $ 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 brml/(l2 pbp9g g meg*l:oken apart into two fragments by an explosion. One fragment acl (l */ m9ppgl2g:ebmgquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is givet+ / nwrg:qd/vn by the 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 masses tf/lpgauijt56 0ox cn-p k,6*$m_A$ = 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 into a24 g /a8dyyo ethc/;vxn alpha particle and a smaller nucleus. What will be the speed of this reco a8d yxcvh;t4gy /e2o/iling 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) hen 0)qx zn8wd w.z-.sis fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.0 ;sj q3 hurkf os6km:,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 rebou 1x,n:or4q w6angkau axvv34+a 7 aamc:iyl*.nd from M, slide up tho *nu,m 6anka:q1c4i xr 3.aawv:x+ ylvag a74e incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planelsgelwuz5ba(g6d,y 0+wftc 2 +-t km,t Saturn moving in the negative x directiow ug5+-tzbgdc m2 wels,,yaf0 ktl+ 6(n 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