We claim that momentum is conserved, yet most moving objects eventue(*vidroha n* -2g.spally slow dows(2hr*ve.* oiagd n- pn and stop. Explain.

When a person jumps from a tree to the ground, what happe;5ncwl qt5b3/ 8ovvb ans to the momentum of the person upon striking the groqn8b wt5/5abl o;vcv3und?

When you release an inflated but untied balloon, wop1idn,i in n.; v2;rchy does it fly across the room?d p;2,nni1o .ci inv;r

It is said that in ancient times a rich man with a bag of gol:h4/zdi,u2 novj j.n) w*lsodd coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself thzod )s,n j*duon:./l4 2ji wvo 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)jd 9 rgdkp1r, and is essentially in a va d1)d,krgrp9j cuum?

According to Eq. 7–5, the lpq*oyq)rj(8 g7 ihuz zq u96w9onger 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 which the force 8zu (7)*6iq9g houwy9rp qjqz acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand cpjvx+; tgh;g;3 h6j:4me qchnollisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What i3 qjj 4pvghg xn;;+6c:t;ehm hs the advantage of this new design?

Why can a batter hit a p aweq7vwx2 2a8itched baseball further than a ball tossed in the air by the bqa2a vxe2ww8 7atter?

Is it possible for an object to receive a larger impul)ni86i:z 1ztv t/ ljwsse from a small force than from a large force? l vz1 tst6jn/)zii 8w:Explain.

A light object and a bhgv4 vxd7e5. heavy object have the same kinetic energy. Which has the greater 4v57hg .xd vebmomentum? Explain.

Describe a collision in which all kinetic energy is lo,a+yhf u(uuw.rtb2z 4x j5m6ost.

At a hydroelectric power plant, water is directed at high speed agaj2*gmmh ) y 5n.: g5uxo8mbt;hjsheo) inst 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 tha2o; xg.mtjym5)n5)jhoehb us*:8 m h gt the water rebounds?

A squash ball hits a walw:3tl ds czrphz7 0myz7p9;d9l 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 h akce pxx5./f*n 2qf v2s*zi8seight h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty tsxni5ps8/*qea2c.k 2vz x*f fhat falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in5gph(k 2m4 br1x i;wui0d/k ck your arms?

Why is the CM of a 1-m length6 de)b h,xuze: of pipe at its mid-point, whereas this is not true for your arm or leg?dzh e:6ex, )bu

Show on a diagram how your CM shifts when you change from a lying position tf e). +c.ryxayo a sitting posi..y yxfe)ar +ction.

If only an external force ctz.:(o 8,(vtxqzlbh xan change the momentum of the center of mass of an object, how can the internal force of an engine acceleralbtht8zz:.(,ov x(x qte a car?

A rocket following a parabolic path through the air suddenly explu m0e km8o(ac2odes into many pieces. What can you say about the motion of this system of pakce8m(m2u o0 ieces?

  What is the magnitude of the momentum of a 28-g sparrow f5f l jdwv7s;d-pu*-7teem* ablying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for o k5juyo2o nf8:( t.xw2itq l)20 s. What is the skier’s change in velocik f8o)uqltwi o.j(25y2xtno: ty?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on *u1xznclsh2t jp+kdm1 1(r .i a horizontal line drive straight back toward the pitcher at 52m/s If the contact time jx1 1scnzil+tk dp.u r1*(2mhbetween 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 pac ;jgy(6d2 nuoqkage out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ig6 yg;qujon( d2nore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propellip z f4 a/.tfzjsc2:p:sng gases are expelled at a ratt.j:a sszpcz fp2f/ 4:e 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 movin fgkh2 .l8ow*d8 ven.tg at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless trac(ss4xe*oib6ofrj *4 snh0 v)4 zk,tjl-dgc w7k with a constant speed of 18m/s A 5350-kg load,initially at resw4**ltgjbo-0r)skj4s4x6s hnf e(dvi,o cz7 t, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelap4u +ae 6h m3xx-ch4ting at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of 100kex17q8uvie*+8 n (rpm.nc izq m/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 (mzn8i xuev*78cqrnp1q. e+i 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 of 8.6m/s onypsln 1dc4 : 5wc;jd)r a level track. Snow berjn: c)c ;5sly d4d1pwgins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in the d o)o3yna/hn. z ;*+)qtkha vosirection of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a h y )szta/*)q;a+oho3v.nn komass 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 blocka2 d4ki vmi0o8 of wood and emerges cleanly at 170m/s m0dv2k4i oai8If the 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 ro( .zbzl 6 ht2fj7p6dfzcket is traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outwy;5b w(e gw7fer space with a velocity of 115m;wy7(eb wfw5g/s To alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed of 4.z8 zzyxmu*y s*fd ybx0;c 2(q5m/s The golf club y*sd0 *xzq8(xy2;ymc bzfz .uwas in contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a vvzm. 2 ;nv vc-ha1lh*celocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What vv-.1cv2anmz;*lh hc 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 speed v=25m9ej34fww hx t+ a6wq,v/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 crashwortw2 y;rvno/ci 9hiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h ( /wv;n29oricy 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 and is stopped in 0.75 s by df5 )hot8t6kpl+xwu;a head-on tackle by a tackler running due west. Calctf8+)k 6;tu5lopdwhx ulate
(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 bal-3w;1mj,loqjyzqt(v l (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 asq,3v1qjt -;(z mjl ywo a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking thevj)nuz/ fx (b k2-f,gl 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 s2)bf, k/ ( -flugzvjxneated 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) wi g(qzno w4q6p5th a 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 each ball after the collision?Let A represent the 0.44n6 pgo54zqqw( 0-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 collisiovl)av , s46b msxz;sx4n 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.l,v 4x)sa46;zsmx v bs900-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 perfec )cp6p2vyf *yypex0: xtly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the 2p yyx) pe0cx:* f6pvypositive 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, 8 qg8 gejet4l5q5tfg;moving with a speed 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 Assumingge 4jgtt ;le5588qfq g 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 0.2xs/m5-fm73kd0x * vq pbueq +m20 kg that is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculat m-73/pd5qx0x +ubqskfem* mv e
(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 amux 1eex kyf;(d;sement park ride 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 A approaches at 4.5m/s and car B iexd;ek y1x ;f(s 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 collision with a se-xjj g3 zq g7x)efh0 qlfnk19;cond ball initially at rest. T eq h3j-;l1x0jqg9z xfknf g)7he second ball 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. 7–3q 1izsz)*03gf sh j,qo5, and elastically strikes another cube at the bottom that is only one-half its masszh0 qj o)i3,qs1f*g sz. 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 massq;x6 uqu0;vpc-o -rw f 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 experime/7yakx5 a h8u*ys)p pent, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm.p/uy8p57 ae)kas x*hy 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 haqdb)uzj6 .bg +nging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determi6.b +j)u bzqdgne the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fractioxy** u 1jx. ow5rnx8c0thbqnzk1go 8*n 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 ab jvs mo07y7a2n object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic e2y s7o7m 0bajvnergy 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 n ;p5t.enz: lp3)n vdfstopped 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, kno : 5nfnpep)ntdvz.;l 3wing 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 cvx7f /4*ma 6puaqfqs3bfws;3c.xb5 height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many reboundxwxp3qbv ;a7 f4a3 fu/ 5cqmscs. *b6fs will the ball make before losing 90% of its energy?   

A measure of inelasticijasz3 l7gy7 u9z*y2py7jj6i yty in a head-on collision of two objects is the coefficient of restitutyljzy2 jup7ay 7s9g *7 yjzi63ion, 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 f98b h6o mz1yyik; u:dof the other. A depression is made in both faces of the cut, so that a firecracker can be placdhz8f 9 o1imk:y yub6;ed 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 o2 hez6/aajc0a.mn)ba 10.0-kg object moving in the -x direction at 4m/s Find the final aaj.02c baomn z/he6 )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 i k0xvk 8vc,3nqnto a second nucleus, an electron, and a neutrino. The electron and neutrino are emittedqcxk0k3vv,8 n 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 mas;mc9z3x(irw0 ersz *gs $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equal mass, eachuaws a /znp.v/y5tm uj+-a )c) having initial speed the two move off together with speed v/3 What was the angle between their initial psv )-an ac+/jyuwm/zt)u. a5 directions?    $^{\circ} $

  Two billiard balls of equh75 zlf51x.u9vfn;/i gl pn mral mass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A an zxl/vn5 7fu5rmh;nip l91. gfd 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 perfoubuf,-5xr jzx s- ;g l9b*s)kectly elastic collision with another atom at rest. r*5okxzfxb) j-su sbgu,l9-; 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

  A neon atom (m=20u) makes akm43 evb 6eoh/ perfectly elastic collision with another atom at rest. After the impact, the neon atom travels awbeeho v/k634 may 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 showna95(nm(uk gzr in Fig. 7–38. Specify relative to the lef nu9(5(arz kgmt-hand 1.00-kg mass.    m

  The distance between a carbon atom (n,z nbo)v 0)gm$m_{\mathrm{C}}=12\mathrm{u}$) 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 iew u8 wynz:krz6z/ *8z+3wnyrs 2.50 m behind the front 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 people sit in *w rue: ny/ynwz83r6zkz +w z8the 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 ab 7779 zw9phc; cjzvbh ferryboat. If three cars, each of7 hw7j zbcc9h;p9zvb7 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 sidesvx883 1m(9gf iasrtu9z /klzc $l_0$,$2l_0$, 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 tomato paste (see Fig k/ bv0pcs(o 2paka2*o. 7–40), each of which is ko20/ (s*avcbaokpp2 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 radius R cut out oybco z6d5 /2a6 ldh,hzf it. The center of the smaller circle is a d b od6d5z,/za2h6ylhcistance 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 subtraction.]   R

  Assume that your proportions areriy-l8mt: yj8 the same as those in Table 7–1, and calculate ty-: lj8 rty8imhe mass of one of your legs.    kg

  Determine the CM of an outstretched ss,dl0ak1,. q xpakl +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 oc3;ekcu w 1 if,9qn6a o6b5hythe position of the CM of an arm bent at a right angle. Assume that the person is 155 cm ta;bn,wye6q5h ouk oc319acf i 6ll. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such th i 8nowj+i obxrx;q.:k8 ojs-4at his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be jo8+i- xxjiook;q4sn b:.r8woutside the body? Use Table 7–1.

The masses of the Earmkul(7t *v9),nrxom:m+ p )md ylq1xhth and 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 onxs i(bg nflab l1(87h; 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 ui4ofa. ooi89ebtfcg8at3 3utl+ 7h t+niform 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 handle is the point that will follow a paraettg 3t8lt9 oioafa.+ f3 7 o+84hubcibolic trajectory?    cm

  A mallet consists of a uniform cylindric n* :5ts-rtunwuf2/sc si+pk(al 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 handle is the point tha c/r2k wusfn5ipttns-: + (u*st will follow a parabolic trajectory?    d    d

  (a) Suppose that in o/(;fmu+8byo12wo nlg a8 )o-i u efnbExample 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 t/7m-*kdr*v i 4txxgk+s1 xr wf0jfi5in 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 to Earth) does ttdfvsg*/t 1wkrf57 ixkx+0i j- xr4* mhe balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a; ;8m(mewq /frubjd.e 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 the ball during fdu; jr.;e(/qw mmb8ethe contact.    $^{\circ} $

  A rocket of mass m trm++ wgf0dvhwi6 (tqx5aveling 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 shown in Fig. 7nz8k vq 9u/onx qz *7v)6re9ei–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also f* n)q9neivo q/z6 7rvuz x9k8eall into a pocket? Give details.

  A 140-kg astronaut (incl*a:xp e9ufdtp4 3sp2muding space suit) acquires a speed of 2.5m/s by pushing opa2:s p3 t9 p*4xdmuefff with his legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are i oypqb njf9*r3qafoy5;6j.k7 nitially at rest in outer space. They then push each other apart. How far apart are they when the lighter6nq 9* .5kf;3fya oj pbj7orqy astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a secoi vi:qr9s1a8 wnd ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its originaqii9v1wr 8 :sal speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an8 f tgxz+p;f(m 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 kine 8fg(fmz+xtp ;tic 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 of total vertical hyhpu ) 5lfld78d/)xs qeight 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourthy5 fh8xdqs/7p)lu d)l bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically vd7.8:yaxu +yzu gbl 3into a 1.40-kg 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 will the block rise after ug8 3uzydba7l v.+:yx the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.x g+08, ehah 1 n47iev2nrfriq35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of r4qvh 8fan2rge 0+,n7iex1hi 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 in a rowboat of76* k(pw*n t:qq;muv,p bwpdj 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 whdpw6 (tnb:up*m; *j7qvw, pkqat 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 wa ht8ni19bq3foy hmg .4s 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 into two fragments by an em e)m33 +j1azrh2,qx cu:9 yayh2,av kpuv7w kxplosion. One fragmen2ph92)hm:m13kawu, xv7 ,+ye3a qc ukjya rzvt acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 53qyntnxrhr- tyj*i v*9dd69 .80-( $1.8 \times10^{ 5}$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 massesdyn)xy 3 y 9 sf(6w lido,o6jyr/so-;m $m_A$ = 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 alph36a v),p:1kbv)z.d1p fbbeot, zw jfxa particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alp6f.f 3w,zjxe z b a1pb:))kbvdv1 opt,ha 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 i o1 edh3n 5g,8(tiqmfangle 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 35kpzi+t r :0zghv,k :u0.0 $^{\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),gy 847 .3rh6 abyjeofcwf n4);ufgs9j what is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, abye. 4gfj8fc3fa; 7j94 )ur snohygw 6nd collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn movinluv+mrpw9lbc/,9 y(-*- mwr 5 sqz tweg in the negative x direction at its orbital speed (with respect to the Sun) of 9.wt* (vp l+ m my/z99-wsq,rrw-cu5ble6km/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