We claim that momentum is conserved, yet most d)hrx7 .c6qfy moving objects eventually slow down and st.xyhf rc76)dqop. Explain.

When a person jumps from a tree to the ground, what hachr4tl)9zgc 1y1y41sye be * gppens to the momentum of the person upon striking the ground?9cy 1*1 e14)terhcb4 ggzlsyy

When you release an inflated but untied balloon, why does it fly across th8u lduhp e(f+1e room?h( u8 u1plfed+

It is said that in ancient times a rich man with a bag of gopdxv4 jz28unp/i .5 iild coins froze to death5pxu2z .jni/iv8ip 4 d while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction whenv 0;smdi4(o+afk 7hhj+ftrvkm z(y. 4 it is far out in space and is essentially in a vacuuvk4oy4 msmta fivhrj7h k;. (f(0zd++m?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller tjf9(e42euzt vhe force can be for the same momentumve(t 24zeu9fj 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 possibility of fracture or death.

Cars used to be built as rigid as pkcl :99m, - vml;eafhr+rob+jossible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. Whr:m,l b9-+9or ;+ljhm fvecak at is the advantage of this new design?

Why can a batter hit a pitched baseball furti)58oex xq.ejyhn 9- iher than a ball tossed in the air by the b 9y in58xhqxo -ej.ei)atter?

Is it possible for an object to receive a larger impulse from a small forcemvk6t0fy7z: f-ow 3habsx ::q than from a large force?q h0a- :ys f:6of7bxvkzmt:3 w Explain.

A light object and a heavy (jy .(usboy f(object have the same kinetic energy. Which has the greater momentum? Ex.j (u( (oyfysbplain.

Describe a collision in which all kineticybyy h53-yzm t 1jp36i energy is lost.

At a hydroelectric podh(:tpcac+ l 0) jcdyq /.j ke5zm3xx)wer plant, water is 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 so that the water is brought to a dead stop, or so that the water rebx :jk leca(05/3ctqh.+c djx) pmdy)zounds?

A squash ball hits a,/w uxx j5g /bl3e.-uj7u bkgh wall 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 (fixebwaqq sj5x87zez;mmn16 2i7d d to the Earth), from which it rebounds at very nearly its ordx1ab2 nmij8s z6z;qem7qw5 7 iginal 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 heavzs34/ bc v(paqy load in your arms?

Why is the CM of a 1-m length of pipe 8 9yf.rfjvsdc2 (sd,d tq4: owat its mid-point, whereas this is not true for your arm d,4td8fv(qs2wcs fo.j y9rd : or leg?

Show on a diagram how. b(owult.8md .is1ubid. m;b your CM shifts when you change from a lying position to a sitt8.sd bm;u(.bi o1diwb uml.t. ing position.

If only an external forcng73 l7n(otcw e can change the momentum of the center of mass of an object, how can the internlt 3on7 (nc7wgal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes mv0.k,mtavs 31 )rhe,bzu .tninto many pieces. What can you say about the motion of this system of piecervmt z 0.abe,k)tm,3.vu nhs1 s?

  What is the magnituduav;+f1qr64zuc de i6 e of the momentum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction f2r rp(da4da6b orce of 25 N acts on a 65-kg skier for 20 s. What is the skier’s change in velo6d2pda 4abr (rcity?    m/s

  A 0.145-kg baseball prjb15,am ze, fitched at 39 m/s is hit on a horizontal line drive straight b b,mer,51af jzack 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 package out horizontally with a sp48pp d:5 fj,t lttzn54 lnj+cgeed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assumi:j fz ,g8 tt5ljtn4d54 ncl+ppng 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 exerttv0e,: uzf s9yed on a rocket, given that the propelling gases are expelled at a rate of 0sf vyue9tz :,$1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving at4m;ypvff qm6j*x8x ozg p2f,6 $4.1 \; m/s$ 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 ,+.d iqhf;yw son alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is drow.f,d+y ;qshi pped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling ew4gyfelonfvqi(/ldh/ uz;0 2f4 m:7at $15 \; m/s$ 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 whipmrfb)y /shp,5 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 maxim/h , fsr5byp)mum 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 iu, /t(iq s0d.-eoa pmalong with a constant speed of 8.6m/s on a le0 tm.soi(ud,ap /eqi-vel track. Snow begins 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, 8 aupoz2+os)cqxwf ; at 420m/s emits an alpha particle in the direction of its velocity, and the remaininz;o ,xaus8+q)fpw2o cg 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 when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and emerges ci;r ts tr(nzqwd.-4u:uq. dj8leanly at 170m/s If the block is stationary on a fri8id.r qqut;j zrun(s:-d t.4wctionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is trqenwo k2t89,vaveling 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 mabtli8/ az0j7 lc2x +ufjh ci;)ss 3180 kg is traveling in outer space with a velocity of 115m/s To alter i 20/8lja7 zi+)hbj xti;ucc flts 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 x8en plkyo3 sss80*r9speed of 45m/s The golf club was in contact with the ball fo*0ses y8sk pr x3l8n9or $3.5\times10^{-3}$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 in8otw4y7juf d1 a time interval of 8.0 ms. (a) What is the impulse given to the nail? y tw dj4f87o1u   kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed hc9 r x3ob ql4d,4(lkqv=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 crashworthj -(),hyu t:mk 6sszgriness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s frr j,g) -ust6k ys(mzh:om 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 and3vy2s8v dqr8 f7k)1f.bpky rq is stopped in 0.75 s by a head-on tackle by2rsfyvk 7 )pq kr.vf813db8 yq a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points in the:rr k-l6e/dj p+hl 9y3eevax i7-hfa6 +x direction and is given by the graph of Fig3+ 6y prae va/96i ej-rh-hdkle fl7:x. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can f gteef2w-;o1h6qd n6a 75-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person fwg6hot6d2n fee1 ; -qmoves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direct e*:z4 :qp 54lihustmkion) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be4kpi54u: h*tm:qz s le 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 spd) ezbmifrcfm)wxi: 3 378 nj*eed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, whw8m )i7c3efbx*mn3r:)iz f djat 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-o kpc1c8.pv vj-l6tda;n 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 speej ck dpa;lvv 8-c16t.pds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides head-on with vqs xr- y i39(*9kxjjba 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly-*yqixjb9ksr (9xv 3j elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s collides h50hzhy +p3 gidead-on and elastically with another ball initially at rest. Afterward the incoming softb+ zg50 hdhyip3all bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastica*c*3kz wcj1oe lly 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 is moving at 3.7m/s caoc*z e1 *wcj3klculate
(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 bakgh-2; qw(vx kll makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original speedq2hx g -;wk(vk 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 inc m+(yyy4zyfns++houv-j19eyi k6 gv7line as 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 y (fvhvniuoy-k9+4g yzy+1e7 jsmy+ 690 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 t.yfj,.k , *x j0mf k,2d;mmqtett +ueof 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 expl15m;s2 xum ymeriment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the smy u;25xmm l1pendulum 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 travelingbpx /k o6fr2jj/ vq1)f 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 t /rf/qb16kpv jjf2ox) he vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetici5:i)0 3 oju bpt,sgaa 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 wr39v9w rmhzm9 7d7(l;rptfi breaks an 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 energy did each piece acquire? (Let A represent the heavier pa939tfdvhr(pizm m79w w r 7rl;rticle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into thi4j5 c)l uq y/ikd 9h6tc6y5vae 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 impki45juc a5dviq y 96)cth6y/lact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from z 3tfxt8 /bp*0wtqisp-7w/z ia height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make befobwp3*wf x z7 zitp08t/sti- /qre losing 90% of its energy?   

A measure of inelasticity in a head-on cd2 5bipt4h6arkis *.vollision of two objects is the coefficient of restbks d* a.i24ri5h 6vtpitution, 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 piec0r x g*5nii ey,sty 54-ffq)azes, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and 5*y 0i f)fn 54ezi-,rxys aqtgthe 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-txe :1)sr1vz3 2hxswl yi1z*d on with a 10.0-kg object moving in the -x directi:s12h)slz1rtz 1y x*idvw3e x on at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleuse( p p8paolt+9, an electron, and a neutrino. The electron and neutrino are emitted ato+ptp 9eap l8( 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 mass x(z+(af i:.r; ) hljcnekfqmrwid56: $m_\mathrm{A}=0.400$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 equrkvw 3(5mnu (ial mass, each having initial speed the two move off toge3wk5v(ui( r mnther with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and;cl0q9y8 w ie7iafo 8a 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 and what are their two speeds? direcayf;oe07wc i 8lq98 aition of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with anothyid5 ; eeh0ju6w;y (mier atom at rest. After thwy06ueeimyj 5;( hid; e 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 a pe+z7b 3tuop:g irfectly elastic collision with another atom at rest. After the impact, the neon atom pbt7og+ iu3:z 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 threedx(g8ncjqw/v6fa+egmy ;0t 8j rhac j0(x6y ;-mass system shown in Fig. 7–38. Specify relative to the left-hand 1.00m d;r qy/(hw6;gnx8 8yajec60tfcgjx aj+v(0-kg mass.    m

  The distance between a cd ppf.;bb4tdeymvi( fp0eid06l3kvj 1p ; e .8arbon 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 th7zxcl94-5utrnyju ( wz;)b ok e car. How far from the front of x kz un)r (wu jzc9y75to;bl-4the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a fz s0ud. kjb/0tkibn84erryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of.u0 80zd 4bjtk/skn bi the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesh *;bjhuh52vj $l_0$,$2l_0$, 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. 724un7my xrvtk 8 me+j7 sr-.aa–40), each of which is a cube of length l. Find the center of graa28m-r ru k.xa7ms7tynje v+4vity 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 circud kiso5e9.:ufto3 c)v lar hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the posis 9u ikoo)v5:3edct.ftion of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those0txf +y y aik-*7rl7ca in Table 7–1, and calculate the mass of one of y+yxykrfc*7-i70 aa tl our legs.    kg

  Determine the CM of an outstretched arm using Table 7–1tmx cd. y96z0z9y9xm*ofh2 wk .   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of thei-g sys /;ez.3voxd0 b CM of an arm bent at a right angle. Assume that the pers-v.db3o 0eszx /;iyg son is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his armn6nnow4dy 0 (bp+3qd7m/bc2fqwj+ trs and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the+7 dn y ww(mnj34p t+2b60qbdc/qn rfo CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moonvg2pshhn s3s;a u(0:y 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 mand4b+ gd.v 5o t7o4u6i3cqaz -w 5iitgv stand 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 hea 7wuq7(swo::/lrb v twd 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 handlts7l7 uqbw:(rw: w/ ove is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylc1 ,oev 1;ec0jous-ko indrical 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 parabolice 1vocok;e, 1 j0o-suc trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. lca8 9:yf,xa+ 0at;t4 ozwyck7–29), $m_{II}$=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 My ,crzl.uq+dhd( n4ukb*p7 k z9r;s-m, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon the7.qzhnryk l4du 9* b+upm( ;z-dkscr ,n move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat, eaj9kl(5fktd*w fu 6 and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculaktf9kj5*e6fd , la(uw te the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m treb57ue z qw:.waveling 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 s:eg t3 ybisw*c/ h8a/oc+y :slhot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will ala gh+3yy/: ste sci/ obw8c:l*so fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of,r1dt-u d*4 rt 1hoi lhk2z5pj 2.5m/s by pushing off w ttdk1rhz5io ,4 djr 1lhpu2*-ith 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 tz5 kpgi2 2eyat80kp7ghe other 80 kg, are initially at rest in outer space. They then push eacya2pz5 g8pi27gkekt 0h other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a )31wyzo h*.y 2jktahj*vxz. d head-on elastic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth i hza3k2hd*.ovy.1j w jzxy*)tts 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 e ,rrfc12pkn cqb4.yi 7xpert witness in a court case involving an automobile accident. The accident involved cay.cnqrb1 pkfrci 4,72r A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic 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 off93 0scdkw as3b4k bs,lbkih-, the top of a flight of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a di i ask3 lbsdh0wk,9b3ks b,4c-fferent 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 ve+7tgof*fu iq9 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 high willqi+g*ftfo9 7u the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35 -x2n1 pr.h2hls3x hgv7r4 +ondl8qd e-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 9.5 m before it comes to rest, wha d n3.q l1xr2 por7+e2x s-ndgh84hvlht was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg anx73et xd i+l7-jrkmy 7d the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, i7 k 3 +trd7mylxj-ex7the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will 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 jp7;xdx/jm*jk8o y d)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 frah 1k-j12pexlb:tw-)kh un7b : nsc8 vdgments by an explosion. One fragment acquires twice the kinetic energy of the other. Whck1d18hsn bj vk-)2b: l wpn-7ut hxe:at is the ratio of their masses?   

  The force on a bullet is given by the formula F = 580:f+tc3akqj7 0uzy7 r,n qa pl8-( $1.8 \times10^{ 5}$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 oblreo*uw8sfqx; h .f6g5-t9b7 q9 r k$m_A$ = 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 decaybjs* 3g4lpk yt)eth(, s radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha pa,s blt(k*e4t p) g3yhjrticle 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 fi:pi3-m. y1/z;jgmb fscu l-qj( coq0z red at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg sf4dr3 smx)fs69 on h0jlides 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 the3xndxl/u v- ti65xzt+ jmf4x(v cfp*. upper limit on mass m if it is to rebound from M, slide up the incline, stop,/xv 5d+* z.(f-jtl vt4px cxx3mniu6f 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 shopk;k4oz 3 bjy7vtw,d m,yb, 0dws the planet Saturn moving in the ;bb y 7,dp4voyw 30ztj kdk,,mnegative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s