We claim that momentum is conserveq:jegj-hr s7bwvsw3/8 j ,8b xd, yet most moving objects eventually slow down and stop. Explaiw, h-7rwjs3 b/eb 8j:jg8svqxn.

When a person jumps from a tree to the ground, what hgpu;.s w hto mc--k; ,v9*smquappens to the momentum of the person upon strikin,wv 9m s.u-; *uohpkm; sqc-gtg the ground?

When you release an inflated but untied balloon, why does it fly acrydpmo b(5- vp* q(hwm+oss the room?wv*5+ m(q ph-p dby(om

It is said that in ancient times a rich man with a bag of gold coins fjc+2 a l o8*hu)-oph)baz mmhqwq+ f*5roze to death while stranded on a frozen lake. aa+h2m)-o+zjcl) p*8hum*bqh qo 5fwBecause the ice was frictionless, 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 directioa4bj4j0d+ x nz0 lh+ogn when it is far out in space and is essentially in a4ojd00 +l+xzh gnjb4 a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smalb nii,9+r p9k5lp wdw-ler 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 are9i+ bdw 5wkprp-nl,9i intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built a1(zne *jgrz e8k8 ,zwks rigid as possible to withstand collisions. Today, though, cars are designed to( r8ze*,g ezw 8zkkjn1 have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pxy1:ie . s1lqyi l-0gbitched baseball further than a ball tossed in the air by the bati 1lxigbs :leq-1y.y0 ter?

Is it possible for an object to receive a larger impulse from a small force taj3 gm9x h3myh4u-qrd ql.g/;han from a4 j.l /hu; qqmymh9dx rga3-g3 large force? Explain.

A light object and a heavy object have the same kineb0l.-soz sd 4ru14 kmlpa;l, wtic energy. Which has the greater momentum? Exprlw;k4zl0bo. u 4- dml 1sa,pslain.

Describe a collision6 6ebks4 b4a5u(kxdvkig,s 8 +ila g9i in which all kinetic energy is lost.

At a hydroelectric power plant, water is dirij b)x i0lds;;aqro(7 4meix5ected at high speed against turbine blades on an axle that turns an electric generator.i)4ir a7(o;q 0db;emx5xijs l 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 w w4hj*m.ywcr s-jy 1u7eq;bc;nc 6rw;all at 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 a height h o)ym4il 3oex7aln h/* *vht nj0nto 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 ih0i*jvn/7talol x 4 )emn h*3ys 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 vqf)h d p:7 uj6ut-.glheavy load in your arms?

Why is the CM of a 1-m ltft38 f qv89obength of pipe at its mid-point, whereas this is not true for your arm orb t8oq9fvf8t3 leg?

Show on a diagram how your CM shifts when you chau6l *2 uky*v2raoh2lkw0f u3znge from a lying position to a sivkh* 2 r*w 30 6zlo2ufly2kauutting position.

If only an external force can change the momentum of the center of l7g7i 3kmpc4e py(3zx mass of an object, how can the internal force of an engim(3gz pip3x74 7 ecklyne accelerate a car?

A rocket following a parabolic path through the air suddenly expl5 xgul y6yfet1)6pv2f odes into many pieces. What can you say about thef1u 6)2lp egyx6yvf5t motion of this system of pieces?

  What is the magnitude of g()h7uzi8v rf the momentum of a 28-g sparrow flying with a speed of 8.4 m/s( u rh)v7fz8gi    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for trjg2p3 y(ynd 56uhc( 20 s. What is the skier’s chang ( h3j2cuy6ypr(t ng5de in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a h 1zd1 p rs-7he(ls-ncs) 5hfqnorizontal line drive straight back toward the pie scdzsnqs)11-nrl57 h(f-h ptcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out ho/2us jh u ul7(dd*jq,lrizontally with a speed of 10 m/s Fig. below Calculaduu/d(, ush7 q2ljjl*te the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given mtqv ir77uz hob7e*w*y(5 r;fz rf*x (that the propelling gases are expelled at a rate of 1500kg/rvur(q5exbry(; t7 wf* *ioz*hzm7f 7s with a 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 is tawu)ky i8 b;czl-6 u*lyckled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutzl)cyb6 y 8ui-;ul *wkual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alon fz 1::c,j(mw /brwzwie on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be:zwmcr1,jfiw( /bw z : the car’s new speed?    m/s

  A 9300-kg boxcar travelarz-dy ,o ( wd*fyug vlk(a5(;ing at 15m/s strikes a second boxcar at rest. The two stick together and move off with a speed of 6m/s What is the mor*fgy y ,;z k-d d5uv(ala((wass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at cldu fdh: v/+7speeds 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 vd: fchl 7u/d+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 speed jqe pp5 dz r- n(m77swc48iex0of 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 th e(x0w5-neqd7p rp s jz8cm47ie speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in th6lvkbr cggno4cp7gl1gb4 (69 e 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 nucleug47pb(4 6rl6 glkvbcg n 9co1gs has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block u* 1mac6v) sjsof wood and emerges cleanly at 170m/s If the block is stationary on a fricti6s 1svmju ca)*onless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is tra;x yc yu+i(aava.4b. wr*uo5 sveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a velocity n6 u+fy.:tj+n ) wzwqjof 115m/s To alter its course by 35. nwtfzwyq+ ).:jjnu6+ 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 t t3 iukq:yh r-8v0xima2;*dphit off the tee at a speed of 45m/s The golf club was in contact with a dqrvt28u;xm tkh0ypi-i: *3 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 naqzrh:z n(doq lj51vxkh,- /eak (c.r0 il at a velocity of 8.5m/s and comes to rest in a time interval xzk:co e r 5/(dj-qv lh1z nak,0(h.qrof 8.0 ms. (a) What 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 .dna 2z00qhjn.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 charge of the crashworthiness of n ece ss e8-q4ikytjqx+8r/m9, ew automobile models. Cars are tested by smashing them into fixed, massive barri,e8eejsc9 r /k4m-qsx+iy8 qters 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 at 4m/s to the east a0wnrcf.qtrkbdw 3 1j34 ;(mrd nd is stopped in 0.75 s by a head-on tackle by a tackler running q jr3rmn(r;0wbd c1dtk3 4w.fdue 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 ten-2-emkpx6tkbme+3ua rn* o .nnis ball (mass 0.060 kg) points in the +x direction and it *ueak2k pe-n n+b6o. x-mmr3s 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 75c*r9:e0 9qeabvn)bw r -kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from n9 90w*ecbrr qeb )v:athe standing to the seated 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 east (+x direction) with a su(y4fhb.zziu s d.+-m/wuq;speed 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 eachu. szwhq b 4;siuu+z. /ydf(m- 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 collih 0cnsf5: r0,/op p2tcgel re,sion with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the 2 /eho ,t,nls5gc:pcerpf r00speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo ag wwi7zsa:o9tkgn 6xka e gjp;/0k;f1k et- )( perfectly elastic head-on collision. If one9gz6) awgw ept(7k1xk a;e;0:f-kktonsg ij/ 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 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 speed of 2.5m/s collides head-on with a 0 gidzr.a.(j l2.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B reprglrji.(2.az d esent 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/s collides head-t- xl8 )-f6mqblw n.edon and elastically with another ball initially at rest. Afterward the incoming softball bounces backwe-lt-wlbf .qn)6dxm 8ard 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 amus (dd- 1ceki nme8m6s0xement park ride collide elastically as one approaches the other directly from the rear im0 c8kx1n-sdd ee m6((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 makes an elasti5(ys s 8*wvf4hhob0q ic head-on collision with a second ball initially at rest. The second ball moves off who0iqy8h4*5( sbvfswith 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 i/tg 3i 2yd ;fna-lrcb+n Fig. 7–35, and elastic2cafri;/y b- tgdn+l3 ally strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of mass nm308gtt0qq u yd x71qm$_A$ 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, proj60h ( pug,nt zrj) +m1dx:dr p(/zboqiectile 1 results in a maximum height h of the penduqn6) prt0zbi ((o/dudg x:jzr,m p 1h+lum equal to 2.6 cm. A second 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 itself in a 3.6-kg pendulum hang g *s70kdjk ..ynccvq,e5yp3ling on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Deter,g*nkjlcp05 .s y qv7ck ey3.dmine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fractzm a f:n1+0x e:zyk(biion 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, into ,otaqm87cgw1 two pieces, one of which has 1.5 timcgo ma wt7,q81es 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-kg SUV stopped a p1ca 4vsp3 *eyhtgub,6+ud- ht a red light. The bumpers lock, the brakes are locked, and thv1g beyt6h3,sh-c d+a *4pupue two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height36/nvw3 br76fmkc l*v ej6rhk of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds wilvwr 6h*c l6bmr knke/73jfv6 3l the ball make before losing 90% of its energy?   

A measure of inelasticix ;7i /wyzhjh8ty in a head-on collision of two objects is the coefficient 8yi/x; hwjz7hof 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 cut into two piecmg1ef- l ed us.l+a/umgt4+new *bm* 3es, 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 reassemufu/ belg-*.nwetlms+* ade4m+13mg bled 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 cr -m 9z:xnn2ew5tpgdix) xu;8q2 ; vogollides head-on with a 10.0xqnnv9- ;dzmrex8tgx2i5 ) 2puwg;:o-kg object moving in the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a seconn pa)90zes 2wsd nucleus, an electron, and a neutrino. The electron and neutrino are emiazn p 0)ss9e2wtted 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 masq4kiu5: x6)ny uudg*z(edjtc,sp0 +ss $m_\mathrm{A}=0.400$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 inelip;x:p. p:l6g u-f adcastic collision between two objects of equal mass, each having initial speed the two move off together with speed v/3 Whpdp-gi:x .c:lp a6;u fat was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at ro.ynzz : mc*(u;s/mluight 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 is moving along the positive.nz*cs;o (/ :mzumlu y 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 perf0thzq5 a kq,63 kq8:4rm po0gaj(x nakectly elastic collision with another atom at rest. After the impact, the neon atom travelskq:rm nhaqak5az(0p,k ot3x6 gq0j 84 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 perfectly9 dl 4(dg*e-mpgtdz5e elastic collision with another atom at rest. After the impact, the neon atom travels awa5tgpgdze ld 9(4d-me*y 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 tgeaqo 4xw07(w(hb91jwpn4bu hree-mass system shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg e14ojh9anb qu( w bp7xw4g 0(wmass.    m

  The distance between a caroix6xg, n/+xkbon 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 i3r2 hecuv90o car. How far from the front of the car will the CM be when two people sit in the front seat 2e ov2i93r0ch u.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, i5z:n; bpn1ty+m +nxfhwk*z 5 hs used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboatx nbfn;m+yh p+ 5tz15k:n*zh w.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides qi cgl + ze*pg*8x+l6t$l_0$,$2l_0$, 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 t-k, 6jf 1i;g)pa .ysxu wk.jsjomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center o jj;ak-, . fs jxpiyw1.k)us6gf gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has ao,71z5h exmf n circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtrao e5hxzf7, m1nction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calculate tp/y,xcz b5m -;)vfn iybib+j( he m(xcjy;np bzbbim)i5 yv/-+ ,fass of one of your legs.    kg

  Determine the CM of an outstretched arm using Table 7trao y9lp euhm/n n 6nv5pvw0:l m);8;–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the posi1lp50t e mtc-stion of the CM of an arm bent at a right angle. Assume that the person is 155 cm tall.-c10tp ms5lte $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that hil5q, mmgum i7(s arms and legs are hanging vertically, and his trunk and head are horizontal, cmuim,q75(mg lalculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon are*m)cv0mzb l0s: mgj+ d $5.98\times10^{24}$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 frictionlesg* z.f6a / vajgsk4rbyeid7 8cgyuw.),z/c6es 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 j 4ldt 2* jx9g w0d8h,yfhd1zja 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 this mallet is tossed, spinning, into the air, how far above the bottom of the h8yjdw4jz* xhjf9dgh 2 0l,td1andle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of ma 2nej8x:;juefjzt j84 ss 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–ju8jfz2 t4 8xjne: ej;42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29), s 0.or6rtjdje bv8-4c$m_{II}$=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 rr(4eh.fqw8u *eur +y, of 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 the balloon. With what speed and direction (relative twyfu 4.erre rhu8+q*(o Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat anlo 33l0 r7huvs4tweem9d.lt2kh 18yh d is popped straight up to a height of 55.6 h18 m te4 thu.0h933 lso7le2vywr ldkm. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling withk 5tc ,7tuw-e.,r1 xi3/zffhb;pde bh speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown in Fig. 7–43. Re*y11 y mcsg+talative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in whichcasym1*t 1+ yg the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by nciq x.e860s :sc0kd epushing off with his legs from an 1800-kg space capsuc6s 8nd:cis.xq e0k0 ele.
(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 masft,ho- b2e(-pq-kz tks 60 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How -ko-z (ktq - h2feptb,far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes au,jzzdmsg*898:7omalebulq430 ppo head-on elastic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal udb l 9o m80zopl8s,mg3p q*j4uaz7:eto 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 )97a1dyxk whhl qoz9b v 9bl83an expert witness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic qb9xzv7h8dl9y )ahwl13ko9 bfriction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of totav 8licjdo* (.vl vertical height 4.00 m. The ball hits four times on the way down, each time striking the horcl*vdo (ji8. vizontal 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 a34i 2jehkfgs(n/ezss*e/ (f l t rest directly above it. If the bullet has a mass ( ( gj3s4enl /fse/ek*2zh sifof 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood pla(7e/mhqx pcc ue9r3- xced on a horizontal surface just in front xhc79 re(mc p/q3-x euof the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit inscux2 pzbqw7 ekcxd/30 t; 2w+ 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 thed3tczq;bpu0/7 xwxc+ kse 22 w boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was7 vcf)n2/z 9kf(lh9rgua t4 ma about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart +agi;)dqv g x/7qt:mtc 1(s. /ozsr(zza ibd)into two fragments by an explosion. One fragment acquires twice the kinetic ;1sqoi z.t (d )gd/mz izcstg+ /)q(vx:7aabrenergy of the other. What is the ratio of their masses?   

  The force on a bullet is given by th 8hbnv uhm1-v7 mxx;/p*ja(c se 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 cb4 * 4pe6pomg$m_A$ = 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 s+ ct-n:b1xt981x*lm.tsmdaeczml h,i0k 3v decays radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the al3vl-x,ehmt k:bx1m *d 8z+nmt t9 sl .i10sccapha 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 ta)ka / -yzoz:m1ugpu g3rget) is 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 slif ,fx9ol1pd 6ch:y.j ides 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), wrl6bj fmc0og(c4 k0x 6wd*sj 8be b5j9hat is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide withm0 j0escl f6jkb9bxrojg *wb8c6(4 d 5 M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows 1mtkr(q tk9mn5i kv06 the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Smn5t9tk( 6m1r 0vkkq iaturn 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