We claim that momentum is conserved, yet most movi3 uq(3ta jexa+ukg u9qft2-y9ng objects eventually slow down andauut( au kq x9-2g3yetj 93+qf stop. Explain.

When a person jumps from a tree3de(cxa* npt11ysg9ps /yik8 to the ground, what happens to the momentum of the pe s911t8adcsp p g/nyeix ky(*3rson upon striking the ground?

When you release an inflated but untied balloon, why does it fly acroshhe7 i 2bcvj8/s the roomhcevj8 2 b7/hi?

It is said that in ancienu luyswj.5kzh 21l7 9xt times a rich man with a bag of gold coins froze to death while stral7w.5x 2j9 1hlzuyksu nded 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 chang. dz3 -wdjy-zge direction when it is far out in space and is essentially inzd zy dg3-j-.w a vacuum?

According to Eq. 7–5, the longer the impact time of 6 4 g:pqzqa2hcan 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 acts. On thih:p zqcg42qa 6s 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 collisions. T 6ol+.c5lq3rz- qsgoyoday, though, cars are designed to have “crumple zqo l yqocr6-5+g3 lsz.ones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tosms-cb4b h vin5x3.1y5u sex l8sed in the air by eb3i8h. c y5v n ub-4lx5mss1xthe batter?

Is it possible for an obje.jj/8me7xhc 5s vq7 wsct to receive a larger impulse from a small force than from a large forcjse7 jq.mw/s xh 8v57ce? Explain.

A light object and a heavyxn .n0o f8r5jt object have the same kinetic energy. Which has the greatefnt0jn5 8 xr.or momentum? Explain.

Describe a collision in which all kinetic energy is los-k;a/b0a.y 0js )d e/xxnsyk at.

At a hydroelectric poweue+cb 8q)i k5-wj4hm kzwu8 /ur plant, water is directed at high speed against turbine blades on an axle that t uw84/wq 85)uh -uj mkzbki+ecurns 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 rebounds?

A squash ball hits a wl 01,bmom*czzall at a 45 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h ontlr1k*oc k*mw. d6 i5eio a hard steel plate (fixed to the Earth), from whichmc lo.1k*5dwkii*6 re 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 that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying aq)y3hdcf 2 fmh4.sn 3j heavy load in your arms?

Why is the CM of a 1-m length of pipe a)j.ysh4,tzz zfck1i0t its mid-point, whereas this is not true for your arm or )cs.i tkzy,0 zhzf4j1leg?

Show on a diagram how your CM shitbtbj)goo9hc5ylx8 o)-;k8u fts when you change from a lying position to a sittin)b hgbouok98)j ty;olct8 5x- g position.

If only an external force can change the mom jdc+* oqaqwq o7p;f 2s/frh9+entum of the center of mass of an object, how cans q*9aqqr/27oojc f+p +fdhw; the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodeses (ae eid;ql3ky f.;- into many piq3 (;s- e; eedaykf.ileces. What can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speedo(6 r8o g-q pov;)rycv of 8.4 ov(gpr cq8;6o -)vory m/s    $kg\;m/s$

  A constant friction force of 25wss7u f54ugy5 N acts on a 65-kg skier for 20 s. What is the skier’s yssfu575wu4 g change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is8-, y-els,pgdwty0 eb hit on a horizontal line drive straight back toward,p- d ty 0elebg-sw8,y 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 my4y2i fbem1ds+9 7qwujz;5s a 6.40-kg package 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 ks if9 s1z mwd+qyb5; 7ujm2y4eg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exertedfqmjgd:,f1p)lz oe +0vh9tekh+ ss/ 2 on a rocket, given that the propelling gases are expelled at a rate of 1500kg/s with a spee 1f+ k,zhmdhosv:2sqlf ej9)+ep/t 0g d of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an apparent breakaway for a touchdo s ho;g :8v8fbx0*ifdswn is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual speed immediately after the tackl gb:vxdsi8*ho;sf 8f0e?    m/s

  A 12,600-kg railroad car travels alone on alevel fric:a4uz,m z (b :cyasvs )siue*9tionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will b)zuby4(:u ci9esa, vzms *:s ae the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikezo iz ;s+/oqcw dc58e7o upt,0x+) hads a second boxcar at rest. The two stick together and move off with a spee0p5dzxc dh zoe,;o/a q+i+ot cw7) 8sud of 6m/s What is the mass of the second car?    m/s

  During a Chicago stormpg(w -vu(xi 8k/k) vca, winds can whip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per squ/(pu x8-kva)kcw g( viare 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 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 sjovdb4 wf;pb*y 8eg3i/ 7;ru qpeed 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 friction with the tracks, what u; 8w3pobrvdi ;f 4j/ey* bgq7is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 429m sd3 gx7(k.afgbd4q0m/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 origigd7s bgq(km3a9 d4f. xnal 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)39er) cgxutr jg9e 8sc/. dje emerges cleanly at 170m/s If the block is stationary on a frictionless surface whene d csu jcg)rer8j ./3x9e9tg) hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rockncvcy9 )s (2qeet 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 t)t r7dz;yy .j; wxnvc gak4z-;raveling in outer space with a velocity of 115m/s To alter its cour 7 ;wx4k.- rac;;)dvyygntj zzse 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 speez+ hey 9qsg7)ed of 45m/s The golf club+eyez9g7h )s q was 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 velocity of 8.ey6/gr1bzww9z 6x v5u5m/s and comes to rest in a time interval of 8.0 ms. (a) What iv 6ug9z w1yr xbe6z5w/s 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=2v/).domgi4 1cks ic1 r4lnfa;5m/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 enginee+frcrr 0 tqd6/i2s-k( swgr2sr in charge of the crashworthiness of new automobile models. Cars are tested by smashing them iq2gt ir(rr0rf/ cs sds -k6+2wnto 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 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 yo1-*z3 zkz6bh+ad i6qzj ea+and is stopped in 0.75 s by a head-on tackle by a tackler running dz6az6hzoqbk d3+ yaz*+j1 ie-ue 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) pnj1,;il8 i fxpoints in the +x direction and ixf 1jii,;pl 8ns given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can v8vsn9khbl/pfb ,;1sp u ) dq8oz/df0 a 75-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seatelvb pbksdnf98 o,8)h ;1zfs / 0vpqdu/d 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 eastv/-6acvobxmn),0sle a9 1 krc (+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?Let A xeb6ocnvs90m/,aa l1-k rv)c 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 snvk v6: rnfm+(cdga n76p+ o4qpeed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object +rnq:cm(p6av n7vgd46n k o+f 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-onx;obvnqbu )8 4 collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direc;)4nxb q vo8ubtion, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a spzj -y ncu9r2j; iisk1syh,x*5eed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of ea,s5cj y iizr1k *y2js9;u- nhxch 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 collide. af o21q0pvfjs head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a s0.fqj pf1aov2peed 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 ridepj i 001tjrw9o collide elastically as one approaches the other directly from 0tjp9ri0j1ow 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 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 emyi1k kzt -oaf86l.b3-k)zw+ 8q fks tlastic head-on collision with a second ball initially aotq83t).zs-+ykzk w6f-1 a8m ikklb ft rest. The 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 wlqvtm1o5r- m 3go u/ +(o7athshown 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 of(t1 w-ohtg 7 vm+lq 3ra5u/moof 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 e7 fz- okxym+68lt/wpof 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 in a maximfzlw/+2vl w u2um height h of the pendulum equal to 2.6 cm. A secoflw+l 2/wvz2u nd 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;m;;5mx4 aynq 3n 2sbwgq gi5u in a 3.6-kg pendulum hanging on a 2.8-m-long sws; q 3m2;by 5;54 unqxgaigmntring, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formulax4.:ea 4 lzeyq for the fraction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into two pieces, 2*cxadm/f9 a 7 sp*oqgfr fo2e*+w1 hsd0tm8mone of which ha /mt0+8 7op1*dfwsgs2*aa ec mqmfxod9 *frh 2s 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 particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into th:dn w1r ykxn2j7w b6c:e 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 y7wn: dxjrbnk:621w c. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a heighigz:5 g(efz5 .shq 0fht of 1.20 m. Approximately how many rebounds will the ball make beforezg0fs:hhqz g(5 .fie5 losing 90% of its energy?   

A measure of inelasticity in a head-on collision of twva :lcmrt.6 (io objects is the coefficient of restitution, e, de rmil v(:tca.6fined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the mass of the oth+mc bk(pm +j4yer. 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 the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio obm cpj+k+ y4(mf 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 hehuu(7nh/sx mw-lg2 rlo jg.9 4r0ytp8 ad-on with a 10.0-kg object moving in wlo98 rm(2t .j/lsupxgy4nh0ghr u 7- the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at relle yqkwt8;+ 75s)yvrst decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right aywly k8sr) e+l7;v5qt ngles 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 ackm20ma f ,q,-bgev:$m_\mathrm{A}=0.400$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 collisioigk*ixop)-. k*, w0jh9)y2aq gcaondn between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initii)yxo,og j.g- a n2h wkpkq9ai0*)*cdal directions?    $^{\circ} $

  Two billiard balls of yk +y8 jg;qnuo1d/f ,s p+p/ ,u/kwqwaequal 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 ouqqy,/jk 1oafgd;u 8 npy,pw/w++s/ kf 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 collc 4ja qlrh6:a-u64mxxision with another atom at rest. After the impact, the neon atom travels away at a 5h l 4xa 6-a4x:rmqcj6u5.6 $^{\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 eaod wbowv4 75b4 m4 d;2bf+una perfectly elastic collision with another atom at rest. After 4 +5m w;o447bbu debadw2 fvnothe impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass sy* lu 2q)cczeth3)m r7vstem shown in Fig. 7–38. Specify relative to the left-hand 1.07)uvr23thcmcqz* le ) 0-kg mass.    m

  The distance between a j41(uqrz b;c fcarbon 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 beuy (fndnl2l/,dnx; jk2p25w wspzk/ t uy6j5-hind 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 the byp(pj,6fd;tjd2xwun5 k w unk/ z5y/2lls-2nack 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 8bh m74gyc u;bkg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboacg78bh u4y b;mt.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides n*a1ssknx)75:il ;drl re aauoc- 2 p1$l_0$,$2l_0$, 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 casedr*32 k4m ;l*vu+/juxwzilmg s of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so t; +*mwz 4i/xjvgluldmru*32 khat the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius d6b3(iok0+qcgi3 +navtv0d l2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position o0v+bq06o g3i t (+dndavi 3lkcf the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as t9(ui0 zba yha r2,bi:whose in Table 7–1, and calculate the mass of one of yourab2b0wyi:9hru a z(,i legs.    kg

  Determine the CM of an outstretched arm using pt6/eznze:cr 35m d8c Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an np7om 2etln gka7oh fai1+1 - /qkfi5-arm bent at a right angle. A2-o- nf/ p aoi1 alt7k n7h+qie5fkm1gssume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position zb;7wblo,5 vg such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far b5gbob ;z7vw ,lelow the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moovor5nwb4 .a /fn 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)w ud7 5tyv,a6ekqq v+ 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 ofab eu1az8ph*: a uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this 18 ehpuabz *a:mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a ih66wfvfm . mj/v:33at+y.+ yqybmaf 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 ph v wmf6avqj+f. /ma3 fbyy.t6y+3 i:marabolic trajectory?    d    d

  (a) Suppose that in Exa t*c,w ctidft g4l0tr3rut7, 8mple 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 in the air and stationary wit *k8;q sm6tb1d fe,.i1mmwkamh respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speedk 8met6*1b fm.asqw 1dm;m,i k measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally /4oa(v.kuyl:mnp(81 zxvif sat strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4n(y.kvli: /mo vxf4sz (pau 81 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m twkwvi;y*hi :*d/f ,ukyl4; .x+fded kraveling 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 cor3sn.(i mjeiq-v1 p+an)h ask9ner pocket shot 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 also fa+3ihsek9 1 jvia).anm nsq p-(ll into a pocket? Give details.

  A 140-kg astronaut (inkqn4,6nz37vrrfcin0 t-ec 2r ft st 0:cluding space suit) acquires a speed of 2.5m/s by pushing off with his legs f2ttnf:7rr-3r tcc,q 4k0s v6n efiz 0nrom 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 initially at rest*03 un)3gsn iar9 umgb in obg39sn3*ing ur )mu 0auter space. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collisiosrz .dumq (d0+n with a second ball (at rest) and rebounds in the opposite srm .uq+d0( dzdirection with a speed equal 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 casr 9hldd*l0gy56m* v /lh8hgg me 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 rh/l5gh0 9hmllv6d* mgyd8g* of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a fligzrb db7o n*9 ,,nvb7ob* t0l)svyc7v kzd*ad5ht 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 different step 1.0 m lower. If all collisions are perfectly elastic, wh0*bkv 7)7,7*zd5vnryld ,bocbsn *z9vbadtoat is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg bloc; qx9xl 9s)oc 0yd78nfsjy q*vh+i5tgk 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 the bullet becomes embedded in i+8jhvf s9o7 cl*sd5;9ixq0 qxytg)ny t?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block oa+21ue)az3as 8 aj8iw d wibg,f wood placed on a horizontal sura2b1u igz8i+,8aja)w ed s3awface 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, 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 i 8rk 3 tfq)qny:hx7v h.2qf,ow2rzh7un a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposit r,7 822u .qtnwhqh3fr7qhfk vyxo:)z e 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 azo a(onquz/dy98taq(hy 5k,/ bout $ 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 eg.z7ciakzq4otm-z pto57 6*a xplosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of the5magt-*4 z q p.oo ki6ca77ztzir masses?   

  The force on a bullet is given by g, qd q57*i nx/syhxu8the 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 05(qfjj sm8dujr hy30$m_A$ = 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 radioactivebe)is /smwmqr(;t13mg2ge4zly into an alpha particle and a smaller nucleus;se 13ezm wsgtm)g42b(/ miqr . What will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angle of 30wnkt se5+* i83lj:je s $^{\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 30i0+ ncscuf4 jli;l,. py*ets4.0 $^{\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 wpp2vx8plr . gwm /o9m9pf;+x upper limit on mass m if it is to rebound from M, slide up the inclwfl pxmgr .;ppvx9mp8o /2w9 +ine, 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 the planet*1-y;w k ln.tj fy;tvc) qo,qt Saturn moving in the negative x dtl 1)two f-njq;.t ,yqv*kc;yirection 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