We claim that moment8)(eoig jbth (um is conserved, yet most moving objects eventually slow down and)o (8h(jiegbt stop. Explain.

When a person jumps from a tree to the ground, what hapkmddl4wzi c 9ol /() frd+am29pens to the momentum of the o4mmfz (k9/crdil d+ 29ld aw)person upon striking the ground?

When you release an inflafvetb81z7 kf(ted but untied balloon, why does it fly across the room?(8kfe v b1ftz7

It is said that in ancient times a rich man with a bag of gold coins froze to de;l;z3 indd l;gath while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done toldz3 i;ld ;;gn save himself had he not been so miserly?

How can a rocket change direction when itiezx)-wv377duso (sdx. l q 9.e1wus g is far out in space and is essentially in a vz3w v.o.ge s(dws- d7q7i 9u)su1lx exacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller the bs:+ b gbmlb7mduynu12zb969force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibilitsg 6ym mlnb:bb1b d7b uu+z929y of fracture or death.

Cars used to be built as rigid as possiby m 5d85o6faxtle to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. 6foxt my8 5d5aWhat is the advantage of this new design?

Why can a batter hit a pitched baseball further 7b2xzm2 nzmp6c: a4z9cq8 v-hl3p nazthan a ball tossed in the air by the batter?z7 9 cpb: qap8ac-mmxzzz2hv34nln2 6

Is it possible for an object to receive a larger impulse from a small force ln usvnpk1 :0+6lw dr o,-sum-than from a larg ,s-mkd 1uusplw6 ro-n0:nv+l e force? Explain.

A light object and a heavy object have the same kinetic en pc3wng4 jo31cd4 zi-fergy. Which has the greater momentum? E4cg 1zn dfpc w4i33o-jxplain.

Describe a collision/t+p0qr:zjrnohr 6 l : in which all kinetic energy is lost.

At a hydroelectric power plant, water a 1mc.-yma5acis directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed 5 .c mam-ya1caso that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a m+i y1bj pnvx)s)h x2t2bj 64rwall 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 4mjf 53 +rtey8bqi :/swna+ ibsteel plate (fixed to the Earth), from which it rebounds at very nearly its orir 5samt+w:+ey ib/fiqj34n8 bginal 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 backwawin h51;47fzpu 0bnr ird when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is not p:krvtol 1(. wtrue for your arm or let(.wv rpk1 :olg?

Show on a diagram how your CM shifts when you change from a lyings1fzv rct513p *r z.ji position to a sic1zf is5rr.3ztv 1 pj*tting position.

If only an external force can change the momentum of th0ofxmq(o jiusy n 28m2d-9xd u .qwv7)e center of mass of an object, how can the internalqv)ouw . nx7m0uo(9s 2d2yxfqm8di -j force of an engine accelerate a car?

A rocket following a parabolic path throp3r3x5t be0g+ tfk5:jl :lh,nlvqa3tugh the air suddenly explodes into many pix5+ lt v3tlqnp:0terb3 ljf5k:hg3, aeces. What can you say about the motion of this system of pieces?

  What is the magnitude of thfua9wc8 2op *xe momentum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What is 7kxflsx(r1 .w the skier’s change in velxf slr7xk1w(. ocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive strfibtazt) 430,h ot(elaight baol,0(af3 tetitb)zh4 ck toward the pitcher 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 )8h1 5kfaodjquare* 3 package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immedia)au3 5 1f8k odrjhaq*etely 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 magnitude of the velocity of the boat is    m/s

  Calculate the force e odyswg1z2f ;lp7/t3l yo( ;uwxerted on a rocket, given that the propelling gases are expelled at a rate ld;ywu;w2 /st zo(logy 73f1 pof $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving ato 7,gesdgeo))t kt8-pm0v;i d $4.1 \; m/s$ 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 r.hiw xlb4s/55 wwzn dvt4,8jtrack with a constant speed of 18m/sj z4 w8tb/lh,wx4 5n5rdvi.ws A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar trac3l cabu1-m4bveling 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 fu4q0+6 nfvv xhorizontally 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 0vffx+u0nqv6 4.50 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 c0h p+ fhf01wk 1uyx,b/z ha:qtar coasts along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring frikhfh/0ta+w u, 1y pb:hxfqz10ction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially o+3iq r 6)sn g65kthxj-bvyk2moving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have whriko5sh2)6 t-y3+xgknjqv6 b en it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and emerges clet8xjb8*4g o9eh mk1r xanly at 170m/s If the block is stationary on a frictionless surface when hit,1 xr4*8xejg8tkhb o9 m how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is qnqru7lh- i n jz28a5,--iry1ak9 vtttraveling 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 veloci)9nqgzlr z; 6jty of 115m/s To alter its course by 35.0g r;lz)jq 6z9n $^{\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 45m/s The golx(na *aib3f4:dtajp,clj 1iz m oq (.*f club was ibdi* *c, j jt1p4xiaz(q(nf:3aaml .o n 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 velocity of 8.5m/s and comes to rest in a t;*rqg*5 pzs+ bsroygaadl x t./.la04ime interval of 8.0 ms. (a) What is the impulse given to thes/a *r.x+rbgl d.ylo*a t4p;0qgsz5a nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg anvgw(m4ey;ifc9bpd3x: a k0.jd 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 new auk k-w3zyv+jo0 k dk):itomobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the kizdj yv-wo3)k+k:0 kcar 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 g*xl3bti hm72 zaya: -in 0.75 s by a head-on tackle by a tackler running due west. Calcbtlgaiy z h32a-7m x*: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 ball (mass.hp:fl5dq noha ;qs-a1w giaj ax.0)+ 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a functio)dqa- 0x p:q.;na haa1g.slji oh+5 fwn 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 br4o s/l z9bc:sgeaking 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 brs9b4:scz gl/ oeaking 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 movina4v7 ib*0ryz bez, g.clq*y: zg east (+x direction) with 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?Letlbzv:.zcrai q0z *g e,74 by*y 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 col jpy,s,ic-; hplision 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.i, ,jphs-py; c450-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-on collision.8bsky5a,i 8tu 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 pos8,is5b utkay8itive 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 c8p dy ek+-qld)ollides 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 ball after the collisikl8pe-dq)y +don?(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 vt m f8 +694q-rluu /n*hlboqsmoving 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. 6l8o-h+n* 9vququr4lfbt /s m7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as one wht70+pj. l onw/cad1approaches 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 approacj w70+h1 wlconat/.d phes 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 collision with a second bal0 swinb5 bg w6gq0br-/vlp5r-+f.g f nl initially at rest. The second ball moves off with half the original speed of the first ball. fn/s ql wf.6rb0 ggibp5-50-+gnvrw b
(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 ans+va1 8 *hnlss shown in Fig. 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? [Hint: Both leave the incline+ 1nn 8*svhals moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case 0m vaeev7, rwqnsohx.x+;: -l of an object of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results i* og3q 7vscx4pi y nx,8-uo)dnn a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twic8ixsnv y-x o*7pd3 n u4qc)o,ge 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 230a45dwz; iztb)5l8u l ym/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the penzyb 5tzwd 8ila;5ul4)dulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of m/sng9v +z9 -4aq doeykinetic 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 two pieces, wnga9jsxmt la xif5.0a( -+8bone of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinet( b-8.m n st+l9f jaxa5xagiw0ic 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 coll 2kcm2xf.cku e4;3*fpe : rmxaides into the 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 coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was thate.xx2 umc;3 :fempka k*f42rc 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 r b(lyj1k)v(zr)b(mk er6 nqhby 93r7 cebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing h6ym)9 7(qr(y1 c lvbzn3kb( ) rkjbre90% of its energy?   

A measure of inelasticity in a head-on1wi k*wk.k4q*per)wcf f(,o ca4 -d rc collision of two objects is the coefficient of restitution,r fre-*a.), (dpcfi1q wwc*cok4kw 4k 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 tim1h 03kjvbbq. xes the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rj.0 v bqxk13bhough-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 th6vkp. i:uviczu62i:se +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass if: ukvz.iui66p :cv:s 2i
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second euz/ibmm kh8a *)n:c 4nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have mome)kcnhm4bam8 z*i :u/ enta 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:gor /l+tt2ves $m_\mathrm{A}=0.400$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 inx6istn+jibx w/;dj jl03m -l4elastic collision between two objects of equal mass, each having initial speed the two move off togethebwxn/4 j3ilt x;i jmdj+0 6sl-r with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the origin t4ce2pn/17 f;edfrvz*7ny f 0ljgxf, 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,e 2; lnefr 1dc* y/fz7j gxp4f,70nvft ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision w0 b r28e1fvdrkith another atom at rest. After the impact, the neon atombfkrvre 120d 8 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) makr* d2bs rtfll6v)m3s ,es a perfectly elastic collision with another atom at rest. After t2lf)3lr* 6sd ,rm bsvthe 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 thewqdw3 )5;1g1 nn quz+;oisbviv: ,h we three-mass system shown in Fig. 7–38. Specify relative to the left-hand 1.00-)h w: g1s;;nv5q3ew iwbz+u1ivd qo,nkg mass.    m

  The distance between a car. 7ih4idu 92hrzz/npwbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of the car. How fwwq 27/h8bnr far from the front of the car will the CM be when two people sit in the front sen8f7wr2qw/bh at 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 km;22j8tqv llk k /u7 +tftx9shg, is used as a ferryboat. If three cars, each of mass 1200 kg, oqh/ flt+8jul tv2;m 9ksx7k2t ccupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides 8/rwe fuj) b4sv4nas5 $l_0$,$2l_0$, 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 identi yj*3 wqds:1l-pn anaio/+y 8dcal cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in p /y:o* i1d3 ad8asq lwyj-+nnthe 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 o,(yc kv-*lb k gianjpt4 13lc;ut of it. The center of the smaller circle is a distance 0.80R from the center C of the ;4kbcjy-31tgi,l ( lc *vnapk 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 are the same as those in Table 7–1, anytrpqes9at+ c g;)1l4d calculate the mat9ca+sle )r1pt y4;gqss of one of your legs.    kg

  Determine the CM of an outstretched arm using uy 8(tj heo;;y+ty.i:e ehcrmr+i .4bTable 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm becaxs6hn*7yrv3rtld :6 e 1 ot3nt at a right angle. Assume that the perso36tho3vxr 1nes7 6l:ytr ac *dn is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hajgj;- ;qq ,yjnw jh50gnging vertically, and his trunk and head are horizontal, calculate how far belqggq-j;yj;h,5 jj0wn ow 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 rex257ge/f i.w oxid7s6 o gj6and 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 standiee v j p);1cr8 x29lc9pu(tgej:s9cz 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of ml lxfpe9z,f u3+74e2m j(cawbass 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 bottom3f e9pjxcf4(+z ue 7wab,ll2m of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindri,ok8:b/t *hwczf u28rymspo8 cal 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. I r28o kofb cu,*m/stz:y88p hwf 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),x1 5fzy s0f v2.xggi*b $m_{II}$=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 pss (gfz4+j2 b:8flka 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 ksfs:2+ jzl 4 (fbpag8and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched h h21rgy2hc sz4 7pc7eporizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, yhc4 7p2 1rsc hp2z7gecalculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with7a1 xfqrhoqc7xq( jbx8jv; ozny/ 197 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. vmyim/9t t6+a Relative dimensions are also shown. Should the player be worried about this v atmmi9 y+t6/being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (iz/q+-fc tsqxslyr06jl1;1th 22 yylh ncluding space suit) acquires a speed of 2.5m/s by pushing off with his legs from slyh h -;1xjc2qslzlt rt16/+y f20q yan 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,ox3z.yr 1)i;xd( uhcp are initially at rest in outer space. They then push each other apartcyxzi (h3 d up;)rxo.1. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elasr 2kigmju446*zjgml b2 0r7 cztic collision with a second ball (at rest) and rebounds in the opposite direction with a speed eql*jg6m7 cj2u rmb 04ri2 g4zzkual to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case)48 jvmdb01ztawmd tz+6f a5ro gvb3 : involving an automobile accident. The accident involved car A of mass 1900 kg which crashed6boat:b t5mzr aj f)841 vd+wd3vg0m z 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 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 offkcm.vy +j-0t es-p /vb the top of a flight of concrete steps of total vertical height 4.00 m. The ball hits four times 0y./ v-bvmsjkp-+te con the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vemgyegsc +pw-k15f; s )rtically into 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 hy w;me1f-gcsskp 5+)gigh 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 pgmjds6 d p83 6p/zr0 uwex70uwood placed on a horizontal surface just in from8 z67ex0ru 3pu wjdd0spp/g6nt 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 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 ;ccv*je c2g 11 mdz/sodmqar:e4(: de60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sittodezc( /v114:;rcjs* ed2d:ag meqcm ing at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass utbz50 r2wbvi h* nadj9g qt.o--g:v4 was 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 suddenphe,qo*no5 (0qa j6oz 23yhhw ly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the otherojoayo5 *z,h 6w3q(hn0pe hq2. What is the ratio of their masses?   

  The force on a bullet iw x7bnr q32mhxo0pf+kh6(np;s given by the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses hcyde.0 ;plf5um 0j. 72rmce e$m_A$ = 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 radioactiv jg*yg14 h 7ltz0r24(lqnqqsqely into an alpha particle and a smaller nucleus. What will*zhqs (24r t10ngqyq47qgj ll 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 a:ao01nza7 ol2 qlg mm)n angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a4jmbr/ ,w)0fs1n b/d9ya eef il4o9 z6la3r jq 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 r5 k3mqv,n v a43ir37vpxh7pig ebound pqmi3a4v3nikh,7r3vvg 7 5xp from M, slide up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows thex4h:2 - jx0 3aloid5aa udkss- planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) sla32ja xdu:sdi-o x5 k04ha -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