We claim that momentum is conserved, yet most moving o4uiigla zm672 bjects eventually slow down and stop. Explain.g m6i2ia 7u4lz

When a person jumps from a tree to the groundlv10xh m 9wp;i, what happens to the momentum of the person upon strikinglp19mhw i;x0 v the ground?

When you release an inflated bu5twr m)xtdw i/ v:l1e/pujh1fx akt2sl*h*/ )t untied balloon, why does it fly across the roommiha*df /u*wklt1t)w esp1vxh /l tj:5x/2r) ?

It is said that in ancient times a rich man with a bag of gold coi bk* xjtfll 32gd-6au5qy)a h(ns froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself tokl5btq(d -3 6)ajlyhfg a2*ux shore. What could he have done to save himself had he not been so miserly?

How can a rocket change directiot/ i1f.cug2zwt.5 )s4e nzulvn when it is far out in space and is essentially in5 uizul.2sf gczwn 41)etvt. / a vacuum?

According to Eq. 7–5i ( *vcr.fmjt:, the longer the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on whi.:m*t fvi(jrc ch 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 w2( n1mgh41 v z3 xvakdib3npc9af+ kx7ithstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the k93(b21x pnanz+gvhmi3x a4vd71cfk advantage of this new design?

Why can a batter hit a pitched baseball further than a ball toss9zm jd8qo* yy4ed in the air by 94y8q y*zmojd the batter?

Is it possible for an object to ri 14)sms8b 6 btnc.dumeceive a larger impulse from a small force than from a large force? Exp4i s 6mbms)dc81ntbu.lain.

A light object and a heavy object have the same kinetic energy. Which hajyb5d. a(k* 5 vprcvv.kv9d4es the greater momentum? Expl. dk9.v cv(ravd5pjek yb5*v4ain.

Describe a collision in which all ka c -7mj1c,)v f y3sqxu,tsf o6mnqr-3inetic energy is lost.

At a hydroelectric power plant, water is directed at high speed agai8tiktp 4+5k*1z(qt gdufwv/ l nst turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so tha +g8iwkzu(t 1tpk */4df l5tqvt the water rebounds?

A squash ball hits a walhjf;qsgv0 (a+x pv2n+l at a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixe -cslmyv.s 0m/d to the Earth), from which it reboun ss/lm-y c0m.vds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in your af f,lah0; fsvlx8(dy,rms?

Why is the CM of a 1-m length of pipe astocmc 1b1x5zsl+)b)k1j3 xq t its mid-point, whereas this is not true for yox513b zsb1j)mql )xokt +c1csur arm or leg?

Show on a diagram how your CM shifts when you change from a-h+-o: t bszw9hbis *z lying position to a sitting position :wbibh-to*sz9z +-sh.

If only an external force can change the momentum of the centevm z0tryt-jy93 dd;l)h *+z vtez u(i:r of mass of an object, how can te0-rv: t vm);z+3utydt*zz(9lhiyj dhe internal force of an engine accelerate a car?

A rocket following a parabolic path through the air sudden0mhr1f4 zzjfy q98w 09ch.yv vly explodes into many pieces. What can you say abou09ywcvz8jrfv0 9zh 4.ymf qh1t the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g 4wacp:4ri + hog7bvq.o4:ldosparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skiernd stoaezy)j0vy87+0 h9v ni9iak jqb(gg+;( for 20 s. What is the skier’s change ingz7 +jj (y0idk89(9b+ ;tha nog esv q0ay)nvi velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s ogca;hv u09jnx4 (e8i is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the cnvx9aogc4 ; h 80ieju(ontact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a speed of vwgq 8u(i) 8wn10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45)8qgww8u ni( v.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given thy cu32u2q7npcz wvlrw9e( j/m1z x77tat the propelling gases are expelled at a ramwrpzx9l7 e7 nt2v3yjc1 q/(w2ucu7z te 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 ai7npq oo e,d* p8)8ij1(mphmp t $4.1 \; m/s$ 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 ap.m:wju 9sc4i df7uaa lk* t)1level frictionless track with a constant speed of 18m/s A 5m:dufwti*a 4us9.71)ja kcp l350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelin41s6j 2bwre pmg 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 c/c2pv mg 8,zen d2hc/n8ca3b yan whip horizontally 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 maximum3ap,v2hzec g c/82dnmcy bn8 / 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 railr3t hav-b73nil noai*x x:k+)z bs.n w.oad car coasts along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and k)nl*3 7otxn ii. s:3bwahzx.v-anb +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 alpha par.6bka m1h1bwf y8n x(fticle in the direction of its velocity, and the remaining nucleus slonm (k1 y1w.ax b8bffh6ws 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?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and emerges clepr;hw iz*4;(b0clt w / pqjd pq,7yb.danly at 170m/s If the.q(p iz4yb;;*lrb, wqcptd0h dw /jp7 block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveli(g8h c:e6)vpyg ko p1v +s.kajng 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( b*jm(ybc cq atxib 2m/(1t-x outer space with a velocity of 115m/s To alter its coursm1bajmcibt yc((* bx2 q (-tx/e 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 jf/bdzi +lnej. i4;ou)e(t k40.045 kg is hit off the tee at a speed of 45m/s The golf club was in contact with the b4je/ebi tlfnk;.djou i(+4)zall 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 veloy ls;9z uu:aam n1)w(lcity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nailw9: l (yz 1lma)aunu;s?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=bl b un(;kw.u20.06kg 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 iny hdl uvnq+)(7 charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes+dh(uy q)7lnv 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 and is stopped in 0.75 i g2;c:kejjd5 u( q5fq8q2neis by a head-on tackle by a tn 5jej(2uf; idc:5qg8qie qk2ackler 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 act;:a jhjjw8.og8 y8dj xing on a tennis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. 8jjohj8;: 8 .xagwdyj Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jd 7 1eihade/:ep h+)3kozxza gkm;i 1+ump 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 strenak:;e+himz3eak/g)phzi xo7 11ed d + gth (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 speed of su1 (c6iwn x,p collides head-on with a 0.22nixu c swp1,(60-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent 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 spewa4b7 x+w 3ejubcfva+ ta28m/ ed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a pec 32a+mt/exw7u + 8jwbv baf4arfectly 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. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastic head aac1c (9:8xa 9kqrayh-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represenq hxa9cr :a8a1c ky(a9t 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 speegv 8 cdy 2/t:a3;l/ qgryqnxtj4f6oh7d 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 perfectly elastic collision, what are the speed and direction of each yl/qg3rtf48q 6 oxn/yt;ga7:vhd 2cj 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 speeog s50grpb;kcy2c978x j5b qf d of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with c52b ;f 9pqxjgcyo 570srkbg8 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 ri2hc3e l48p8 mjkb+co6asu q)ade collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car Apclqak6o4h3b mae 82u)jsc +8 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 elastic head-on collisix +b-*f4wz)/ p tperjzon with a second ball initially at rest. The second ball mov+w fj*e/rx)p4zpb - ztes 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 Fifuex9y5nm ;+ tyv*ua .g. 7–35, and elastically 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? y. + ueu5t;9fmy*n vax[Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of a/6k v(diib)-d (f5 vypfhm oq3n 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 experiment, projectile 1 res:-b*il/ lup vu2hi c(kults in a maximum height h of the pendulum equal to 2.6 cm. A second projectilebhi:/(i p2v c-lu*lku 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 travel99 gvbxb *v.kning 230m/s buries itself 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.vertiv*b. gnv b99kxcal$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic e*an(ayy *ium:z7 (mi knergy 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 bgh7p :sc.-n ex,cwt0nreaks an object, initially at rest, into two pieces, one of which has 1.5 timesse hn :c0 g.c7ptnx-w, 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 tgj 3:ft5l3egg he rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficienl :f5e33gg gjtt 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 height of 1.20 m. hi lj,mo7-k6hApproximately how many rebounds will t mh,o6- iljk7hhe ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of b8to joztc317rt7 fj *two objects is the coefficient 7j8b ct1*t7zfjtroo3 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 cut into two pieces, one with three times the mass of t:io vdwe ,*+ba p1e- rm+exlh0he other. A depression is made in bw -1+:0m ,hb le*v+oedaxepiroth faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on with a x oip y(4hh m itp mw*wz)4d:qo*53;:aovm. db10.0-kg object moving in the -xbiqy(top m*:5344iwh a*mxz:dowvho m. ; dp) 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 re t 484c+t): ohpntyhqost decays into a second nucleus, an electron, and a neutrino. The electron and)h4t4+y thoqn: opt8c 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 massv si;xea62;p u $m_\mathrm{A}=0.400$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 -9qpcg vbmm* (of equal mass, each having initial speed the two move off together with speed v/3 What was the angle cm qmp-*(bgv9between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass movldx6w 3e7n+o *pavwk,pv/qg.e 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 is moving along the positive y axis (Fig. 7–3dpqlok +6, v7 wva* pwgxn./e37). 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) mak/kkp d-ra/6a pes a perfectly elastic collision with another atom at rest. After the impact, the ne6 d/ka-p/prk aon 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 elast im,boye(p ,3iic collision with another atom at res,,boi3 epi(my t. After the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–3: q 7 prqrm,dn1yxe,)e8. Specify relative to the left-handr)qe p,7ne,rxd:yq 1m 1.00-kg mass.    m

  The distance between ,q (ev-za9mr;ggjlx) x8 4kms a carbon 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 fronuvnh 69irw 3/at of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three peoplew 3a/6nui9rvh 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 as a ferrzww d;cdr na +um 6.68+nec9sz ;pc+kryboat. If three cars, each of mass 1200 kgwknn mrs6z.r9c;zaed p;8c+cd+ w6u+ , occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side9rws gw2 69tz: naq0uhblx :7ts $l_0$,$2l_0$, 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;8-;uyar tvb ,ac9aa s cases of tomato paste (see Fig. 7vba8 cayu-a9,tr ;;a s–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of r3on:g ; 5bpamiadius 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 gn:3o i;5b mapof mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the sa -36 yzfx agx.8yl0 vu8r .t/it9sodepme as those in Table 7–1, and calculate the mass of one of your lg8 tdep8xy.ra-x i 3zuts/ 9l6o yf0.vegs.    kg

  Determine the CM of an o 42o1/tahr qm(y- llaeutstretched 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 80y 9-3t yvfnqb.lw8 iznpl5e arm bent at a right angle. Assv ielnyb89 8n pqzl.-0wt5 yf3ume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a paj 1 y,2tt8pfzpz;j7vosition such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far b1p2 pjav, j7zt;ft8yz elow 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 anku o0,on*r+szjca au+v38 t z,bs6x- hd 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 10.0i // 0(8r)z cinoktvqi m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg a8c aslegej r/:8ip :dqaf8pu53jou9 8nd a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follo8ada/l e:5:jq9ei pp8g8oj3fu ursc8w a parabolic trajectory?    cm

  A mallet consists of aem b ars/. vk+n/.endze1d;i7 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.eaims n7.d v1+/e;/rbdz.en k 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.a7leox/btyw*5 (p yh. 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 statiokuzfxa.s -rr7m 27js-2ys sa;nary 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 to Earth) does rssjm- x2-rks7sa2 f ;uayz.7 the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat 2bq:;+t .s02 rvl.up ywt jbvqand is popped straight up to a height of 55.6 m. If the contact time is 1.4 vqb0prwq:t+lv j u2;st2y.b .ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with spehvw-,nzvz 76a8 /gav yed $v_0$ 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 k 1y,e:z*l(gj r :neqgin Fig. 7–43. Relative dimensions are also shown. Should the player bej: k*gl1e ,yzrge( :qn 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 suit) acquirezm g r8b4 i731qjirxo(s a speed of 2.5m/s by pushing off with his legs from an 1800-kg space capsug4 qz81bj3mr (x oiir7le.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are initially at restaotl* x(x nga193,dq7u /zieu in outer space. They then push each other apart. How far apart are theyo/ i,nxtz7xud1ae (ulq* 93ag when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a npu*oik 1r r/l3e8.ky hrl9z+second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass+l8* oe.1lp r/hzkyn 3ikru9 r of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a tf7c y:x4aa4kcourt 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 k44xaa yf:ct7 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps ofk.j m*flr*5i-*r :yk) dbufpw total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 mr f. p ikj*:r d)ywkblm*f-*u5 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 dire9siho b.dg* u4rz ck,*ctly above it. If the bullet has a mass ofdcb *h4z ir.ogk*u,s9 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 blocz:37gu-9yyh/ udno5j)ows zhms 2/uvk of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic fricti7:z/u 3ozsju o) /wgyns9md v2h5y-uhon 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 othe8zke3 pi7)k+gwy*m en r of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction wiewepnmyk3) * g k7z8+ill 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 abou bxw w;b,/;oixt $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments by an explosi2v/aoe r 6rbzk2i7n)h20xh fdo.f .lx6 s: pbqon. One fragment acquires twice the xsne)ir2oa bx760of6.f q b/.hlzh:kdr2v p 2 kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = nk57t jfvy3 a,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 massesw6z;suc d v3g+prws6xslh+* y959y m b $m_A$ = 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 an alpha parti s3w5 od.)nrsecle and a smaller nucleus. What willd).wnseso5r 3 be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angle of8-;vxjkeilc6b5) 4zfhj mhi7 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 slideg6jnw6 h7v/yv s 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 reboun d rz/9:/y i(tbccldk.rq 2j4sd from M, slide up kc tib/rq /(.:cd9 2 l4yzsdrjthe 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 7–4 xwgg;xocs 5b41afio3x,fccv 0 *i+j +7 shows the planet Saturn moving in the negative x direction wf+j0x vio4+ b5,x;sga1*ic xfg3ccoat 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