We claim that momentum is conserved, yet most moving objects eventualf lo)43:blzkd4 6qysly2y c7 aly slow down anb4:a 4yly)c 3l7d6yqzo2l fks d stop. Explain.

When a person jumps from a tree to the ground, what happen m+w;).p;8lks wrc ne4qfn /wzs to the momentum of the person upon striking the gro nw qfw/w)4z; snl;k8m e+r.cpund?

When you release an inflated but untied balloon, why does it flyk68esu2-heqw:e( o hown mj( 0 across the room? h6wk(hus0wo ejq e-o:2em8n(

It is said that in ancient times a rich man with a b7fq 3h 5dpx4m.f;ec tdag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push hc7em4 ; t 5dqf3dhxf.pimself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change dic/(es*c;sbx w** z6zkhjsd+qk4 l t.nrection when it is far out in space and is essentially in sk zbw/e*x(+cszlth;* c*snkj4q.6 da vacuum?

According to Eq. 7–5, the longer the impact time of an imanfda4, k sc+:pulse, the smaller the force cand: ksa +ac4,fn 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 possibility of fracture or death.

Cars used to be built asnn1v 6dq9gswp dhf pvfp :7(rr*/hy, 6 rigid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that colf:16h* ,p drw6 nd(vqfrps/ 7hyngv9p lapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in the air buv4q6zuy rjo69,mk 3 xy thejurm, 63 zqk6uo9xy4v batter?

Is it possible for an object to receive a larger impulse from a small 5ng3m6;viemoforce than from a lareim63 ;vm ng5oge force? Explain.

A light object and a heavy object have the same kinetic energy. wpgi40w+3ds; f k-sufWhich has the greater momentum? Ewd+ps03wg-fsk; if4 uxplain.

Describe a collision h8gyiww4j;qgw g qh7/igj89 6in which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against turbingd0g ;lqw j.5fe 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 dg5f l j0;dg.qwead stop, or so that the water rebounds?

A squash ball hits a wall at a 4b eqz a znt740+x2qilt35h8 xz5 $^{\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 ontb 5facf+.t8dq hd5.a eo a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answc bf8aqaddf5e 5.h. t+er part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in 5) cjv8hi7x4 qk21ycasm;xnr your arms?

Why is the CM of a 1-m lenglhenlpq -2lu)teeg3,o ; (u v+th of pipe at its mid-point, whereas this is not true for your arm ou3(2uqlv)leh-eep+ l ,gt ;n or leg?

Show on a diagram how your CM sh(9h+f :dj o, mmbixp9tifts when you change from a lying position to a sittingb o hdifm+ x,9pj9t:(m position.

If only an external force can change the momentum of the center of mass of ackq 69 uvfa1o9n object, how can the interucof9qka916 vnal force of an engine accelerate a car?

A rocket following a parabolic)7buu881u ww9bjudo n path through the air suddenly explodes into many pieces. What can you un ouwb8uw9 8)u7j1dbsay about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a sjk s3 (ghpo*u+m vv1w/peed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction fa6y x 11a02f br/ jcj(8uxct2zc 1flbaorce of 25 N acts on a 65-kg skier for 20 s. What is the skiyb1( 1jc0 1xc/226 x8atfzcba rljfuaer’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hffjkm42 /vmb/ it on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time bet//ff 2j mbvk4mween 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 outtmwt7 8rdy..z 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 tdrzy.twt m8. 7he 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 exerted on ar )ya k1fnu.i+ny4/b87i u 8djbof y.n rocket, given that the propelling gases are expelled 8uk yoa1ny n.4.bb8ii+7 /)ffny jdruat a rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movik + wpa(g0 cf-9jl lqjnj;-k+fng at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless m/b+g; r uyrw ab7lq)3track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will w)mb; ab7/gurq3r +ylbe the car’s new speed?    m/s

  A 9300-kg boxcar traveling at j3na d f89c;n2qvpsv8$15 \; m/s$ 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 horizontalljo4 ak)*j8r kfy at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is) *ko4j8ajr kf 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 speed of 8.6m0lc31q4glo ej.zx y)y/s on a levgy)0 1 l4. czoy3lejqxel 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 at 420mj s xoau0kvco-2bhtf55 mc/)ob z n8mf)eu/7:/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 35:)2/t v cbb kj8s5 x-/oncuffm 0zm5)ao euo7h0m/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 bl1zz mgr: ua9ie+.q, ffock of wood and emerges cleanly at 17gie z9,: m1.far+fuqz 0m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveecu (g5ogj )3aling 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 velocity otxm3i bv095bca ) dx;1 ak.odl.mmm 9sf 115m/s To alter its cours3mb . ai mkc sdx9ax5)o0l;td b.vm19me 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 at5alk+n hm9gps9qp b3y gy/b)d i ,/.sw a speed of 45m/s The golf club was in contact with the ball fogydka/mh 9qg).yw +53,bs lnibp p9 s/r $3.5\times10^{-3}$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 nailvckc:hv+w 8f ec/vh/yeg /h. / at a velocity of 8.5m/s and comes to rest in a time inter +c//ev8w /f ch/:cvvg.y ehhkval of 8.0 ms. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and 4. ptuix0;m auspeed 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 tzy-oaa p 0f.7 6fzq rejn-zi/7he crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50k zyz -rj0qafzo 6pi7 e-/f7na.m/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 eascio( wdo2sz.9: b5 cmwt and is stopped in 0.75 s by a head-on tackle by a tackler runnin. s w:5z9bi2ow(dom ccg 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 +x xt(8 wpj-2xqp direction and is given by the graph of Figp(w2j tqxxp8- . 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 ex074q wpl/pe3vy1 sg -rw0iq can 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 seated position (that is, in breaking the fall). Assume the breaking strength (force 3se-r1lpx7eqi0w 4yv/wgp0 q 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 movingfxu8./uo3e. m znc6 oq 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?Let A represent t/omf. c3uouzq .en6x 8he 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 3 o886pkq xcp h8cnoe3(m/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 afterx p(k6e8ch8 pq o8ocn3 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-onh 84w)ms+e 50r5xmv2ims x son collision. If one ball’s initial s254n 0mvi8 )+x5rexhwsmmss o peed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B 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 2tw 2l1f q;ahhzma,r+6.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tet;f +w16m zhh2,lraqannis 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 thamyx.+ay90 aaqfd1z0 it is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming s0xzy0f9 a+iq.ma a1y doftball 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 amusemi;o5o-l p1 ho29a 4xqjac)ysaent park ride collide elastically as one approaches the other directly from the 2aoah)x-;yqj4 l95pao1 c soirear (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 elastic head-on collisri)11srpo o /dion with a second ball initially at rest. The seo1sd/o pirr1)cond 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 asx, /9 zcu 0wih;sdd49 cah4mkv 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, wherzk h,ac90iw hxm/s uv4c ;4dd9e 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 ,fekjrer :-c /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 ressc5+q ggo ; mfvr1u/i8ults in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the tcios1+m ;vfrq gug8 /5he pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg pendul+zx 6u,jhd a /o:bwzyj5mjzb 3*s3*uf um hanging on a 2.8-m-long string, which makes the pendulum swing /zj us* h3m*ux j5jw3doy f6zaz:+,bbupward 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 kinetic energy lost, s s/d.qm4l4qf$(\Delta\mathrm{KE/KE})$ 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,f;bkcq 9b3ihi9 dy(g uh)+ dasa/+ hh5 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 ) +cbih95 3(kbdh+qds /faiyahh9;gu 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 cola .xvf ebi9;7tiau1x(lides 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 frictiona xa9fibuixe7t.v ;( 1 between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebhjk 4-e: iy z0*9uqzs v-cm)icounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its -c0s4 -9zzhj)qveki*i um : ycenergy?   

A measure of inelasticity in a head-on cohk5hkogm4 mmc; 5 i,ag9yb /:yllision of two objects is the coefficient of restituti a,ybkomc; kg m45 hg/m:9hiy5on, 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 5fcqv+bbyetdu jl ;fv1w (83vx1 se7.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 the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. f5 jebf1;8vvetsb.qc37yv lwx 1+d( u 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 collp-j;cf zql/.e ides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the fip/ .-zclj eq;fnal 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 nucleus, an electron, h:1ahzum 6q6p and a neutrino. The electron and neutrino are ea6p1:m uqhhz6 mitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of mass 6z:89 xa bnnvcn6c l.el2zd6d$m_\mathrm{A}=0.400$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 bk gwza ) cbx,x8eytm2wfbr z 6+h/z*),etween two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial directions?zty2 +k68)c/)wgmr*x a,zf ,ewbzhbx    $^{\circ} $

  Two billiard balls of equal mass move at right angles and 0tc:zaesv jjc+( ap5: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:z5as+(0 v jcep:tac j. 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 corol ;sj(n6 3hxo/5jr9bwv p2g llision with another atom at rest. 63 l bj(w/h9rsp 5ov2ngoj;rxAfter the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic cs , mo,js6a-arollision with another atom at rest. After the impa6 -,sa jorms,act, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system rc;5 v3y zjb3rshown in Fig. 7–38. Specify relative to the yr5cvzb;3j r3left-hand 1.00-kg mass.    m

  The distance between a carb-v ,x.brt0 klpon 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 beh g mnnsqiw37l68d3 d;rind 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 back seat 3.90 m from the front? Assume that each person has a wd8 nql373gidnr ;6sm mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a ferryboax2q4p6 b 7bl7w9 gmbnvt. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine themv 477xb69b2 gwpnq bl CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides nlvk/g0 i yp/igp(7dyc(e+m2$l_0$,$2l_0$, 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 hk,6 s7bk-t jns)d1nwh as a load of identical cases 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 that the crank sk b,n1w)t67nd -hsje 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 holenwudmd d-6sq**m4ffy* it 46al)tlh; of radius R cut out of it.hi) m t4 ;dqf-6m**fswnll *tu4ay6d d The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calcxojsqdw/9)a /++b bgxdw yh6dl4 o26sulate the mass of one of d 6bo+ xs wlbx/a/wg4ohd)+6q9 ys2jdyour legs.    kg

  Determine the CM of an outstretche1o7t6 c adyzl-2yyeids4.w xvv 18yb6 d arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an are x45lr)m y0ardt*lk, m bent at a right anglel k04,5lxdr)*my ater. Assume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his a0jtz nsfrxs8eqv. -e(u 5z:v2rms and legs are hanging vertically, and his trunk and head are horizontal, calcu(z0.xsur 8e t vesvqf5z:j-n2late how far below 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 s;d2zjstbfq(m6 fb :,Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on frictk t4c-3zr uzi9a 5mmp g2yp70an-)o lrionless 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 ofdcm2a98ii n06kx1 8ym+jn dgp 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 mallet is tossed, spinning, into g8d82d mn9i cian1j0 pm6+x kythe 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 diamete28clmc.lr, .kk x n,e 6rr6zwjr 0.0800 m mounted on a uniform cylindrical handle of masl, .66c k8 zr nck2jmr,lw.rexs 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 parabolic trajectory?    d    d

  (a) Suppose that in Exqx(x; dh uhhv5.q0b 2pa ((sfxample 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 stati( 95kdhmken w(k9tma 5onary 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 whkk(kn 5a mtwdm 9(h9e5at speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is p f a7ovuc*c22xopped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average forceu*f7cv x2cao2 on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with s lf0p-dt ry3 + uem6wjg4; nmw7z7(fbspeed $v_0$ 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. k)s+ 2huj1z ewg 0j.cp7–43. Relative dimensions are also shown. Should the player be worried abou. s 1)jpc+wujh0kegz2t this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by pushingi3k- ec2c. y3w1hx j;xmm g f6z1,comg off with his legs from an 1800-kg spac. - zj3 cxghmky21f6xm;cec,om 31w gie 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 xqt-gyuojj; w.x x1)7 60 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the x ) o17yux.-;jgt xqwjlighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with 7g/95ljf9 xlb k /kd+gxnh4yza second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourd97bhk/xng4+g fl jk5 lx /zy9th 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 involvi;y39qi 0uub3l0dl bh ing an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels b9ll i ;uid3uh0 byq03and 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+qy4b-vss( vr9a2 j mm the top of a flight of concrete steps of total vertical height 4a+vys smr vb-2j(q4 m9.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg bhv4wyt x;1i:f/jvpo+gpv t 54 lock 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 risejw i45vp/y:4x ;p t+1gfvtvho after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block ofm9f n xnxx 9gbe653 . yfyf4y80umks8n wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between893nfy9xy xysx05fk4u . mgm ne8fn6b 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 in a rowbofeqed o/:k.c*.un h+c 0nt3kfat of mass 80 kg. With the boat initially at rest, the two people, who have been schf* n:du.nk0 /+e.tkfe o3cqitting 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 is:0nmy8 oufxh1n/ 9y 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 suddenly broken apart ieyk .dt3mrf 10ma7 (ixnto two fragments by an explosion. One fragment acquires twice the kinetic energy of the other(. fa0x1im r t7d3ykme. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 580-uen ih ut7-eyl4 49hy+m f0ua0( $1.8 \times10^{ 5}$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 fnijva7w6r : 7$m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively intof6(k/m -jn8r3p 4nbwqgscw*,ohw5 4p il) lnz an alpha particle and a smaller nucleus. What will be the speed of th nmqncoj4( /wp*5r h,gi6wlfw8s)-n bp43kzlis 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 ang.( 5xytnn )crgle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a *;j vu-mluc b130.0 $^{\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 i/is zd/*kya zah/c5:tf it is to rebound from M, slide up the incline, stop, slide down the i:aish*ykz5z//ta d/c ncline, 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 Saqj6 si 4b+3xqwturn moving in the negative x di xqq46jis+3bwrection 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