We claim that momentum is conserved, yet most moving objects eventually ;f eu;i mg/u)vk 8y1eqslow down and stop. Eei/f;) ygukm;uq1ev 8xplain.

When a person jumps from a tree to the ground, what tzcp*a 3(e.qxz 6 f;iphappens to the momentum of the person eac3tf.(z6x q;*pzpi upon striking the ground?

When you release an inflated but untied mjpb, ,yx 0+ziballoon, why does it fly across the room,mj z0,bx+ pyi?

It is said that in ancient times a rich man j0 e8m38vi9,r v ycnh)*dzg9j- ehr mtwith a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictj3i ey -dcm8mh r80e9g j ),vrvzt9nh*ionless, 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 when it is far out in space and is essex25yt: 4ur+kgcary2uxg a2h. ntially in a vacuum?+22 4u urt2arxyy5ch. xag:kg

According to Eq. 7–5, the longer ;u pjl7 a6yxc*vo7wf8+/tt; gkiny6ithe impact time of an impulse, the smaller the force can be for the same momentum change, and hence the sv6i7yat kpnw6u7 ;clfjgt/xy i;o* 8 +maller 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 possible to withstand collisions. 2 n.x5 bi,4(t 3dx nbewkf:btdToday, though, cars are designed to have “crumple zones” that bnbbx5 .w :d2fd ten3(x4,kti collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a bal(2 y x8c lc4kona/rvdnvg8va1tx*, q5l tossed in the air by the b5(41 8nq,va/vxt8 c* nvxro2cylg kadatter?

Is it possible for an object to receive a larger impulse from :-6uksl v s aa5mv7kj-a small force than frmv l:k6av 5-uaskj s7-om a large force? Explain.

A light object and a heavy object haveu:co, ayay1yz .+aw.(18ib ) oxumza q the same kinetic energy. Which has the greater momentum? Exp:.8 z,u(ywmaico).zbuo y+a1aq 1 xya lain.

Describe a collision in which all kinks) dawr+qnj,c ob4;0yq v9j1etic energy is lost.

At a hydroelectric power plant, water is directed at r1fvtqm+ 8ul* jen,)hhigh speed against turbine blades on an axle that turns an electric qjn, l8ftr*1 )v+emuh 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 walll-7)m: mw efpf 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 stej6 :njox.;hn*mn o5m kel plate (fixed to the Earth), from which it *h nk;no.xjnjm5o:m 6 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 a heavy load in your arms d3 a35mntl3f9i 3dfhv?

Why is the CM of a 1-m length of pipe at its mid-po/iqlg o 15udu.br+s2 lint, whereas this is not true for.luq2l51disro+u gb/ your arm or leg?

Show on a diagram how uw3ua e;moy/iw1:1 atyour CM shifts when you change from a lying position to a sitting position.3o w eyaa;i1utum 1w:/

If only an external force can change the moment1f((cx mb5yeyfnt 0;oum of the center of mass of an object, how can the internal forncbe ymo( yf; 05f(tx1ce of an engine accelerate a car?

A rocket following a parabolic path through the air suddenlytr 00hovec2d d 6;a7fh explodes into many pieces. What can you say about the motion of thicho72drh ;t06ad fve0s system of pieces?

  What is the magnitudectrk+2*a , qxx of the momentum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts,l p0pk.g i+nq on a 65-kg skier for 20 s. What is the skier’s change in+qlp i,p.gnk0 velocity?    m/s

  A 0.145-kg baseball pitch vrb-z3txnwn0q * zc)5ed at 39 m/s is hit on a horizontal line drive straight back toward 3w b*r 5tz0nqxn-zc) vthe 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 thrqz (q.x6 zgjadip f)* yha8q4nv6n4f3ows 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 thed. y 3ganzji(6pzqq x64 q*v f4h)anf8 boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, g*;xs;egzm (*dqtan 7given that the propelling gases are expelled qg*t(z xa;n;m7 dsge* at 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 movhts5k vv+g7( bing 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 7hd eyhwb0s s:9l9 ;jozn: zu3track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed? ; 9:s 3oy97us: eblndzwhzhj0   m/s

  A 9300-kg boxcar travea5vzde -:rg* 8uo m7ycling at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horij)cw d;uyoc))zontally 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, e; dj)ywo )ccu)stimate 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 l2;a0w +vn6dwy sru/nfa-td w ph:,0 sspeed of 8.6m/s on a level track. Snow beginf, wa wsnd60+luh;vtny-0wd :/ra p2 ss 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 initiallny 9a,*g(g)c9hu xeec y moving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have wh,neuy c9 h)xa( 9g*gceen it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates 5q2l 1 + 6fawk5mjaowla 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it woaf+qw15ll2aj k5 m 6move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speed o 0iy,riczifw, (*myd)iq.r3 yf $5.80\times10^3\mathrm{~m/s}$ 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 kgs e,3g3kut gx-n;1h:dcbn:d h is traveling in outer space with a velocity of 115m/s To alte,;3u-sbdctn :hd gkhx1ne :g 3r its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off t g7 wx imtrj2 +mw-nn30o0nat1he tee at a speed of 45m/s The golf club was in contact with the ball forxw7+j in-gr 32mmnatw1o0t0n $3.5\times10^{-3}$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.l myqritp(- bf b;3::n:(lrlbr* xkr;5m/s and comes to rest in a time in: br ;lf*k r3-:mqb;rlln(ryx:(pt biterval 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 sp3jz2 ir hph6fw+v1 b 3tdt,na788uuc2z(dzfmeed 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 chnj3 7nup onk;(5d7uixarge of the crashworthiness 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 from the time of impact until it is brought to rest. (a) Calculate the average force exerted 57;(iunnonjxpu 7 3kd 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 a)pzjd;2e6pb8ryefp m,7i 1ts nd is stopped in 0.75 s by a head-on p)sb8im ;y,6 f2p1zetper7j d tackle by 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) j4whn6(-1 5 6qghpjdqgl c2e9osse03h8 cuzspoints in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Usp9c -2jwn6seg3 6huh zg j0se41dq5c8ohl sq (e graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without bx e(pdbn)h;6 1/ u r -zhh,oi:sdft7smreaking 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 br- hmfzdp(siuohxn )e6s:h1; b/,rdt7eaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) wilko2l o ,x3vf:th a speed of collides head-on with a 0.22x ok,:olf3l2 v0-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-on c7,0zb5ssb q e-n j4 fmjb-bet/ollision with a 0.900-kg puck initially at rest. Assuming 4qbeb0-/mn,z57jstjes-bbf a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-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 ezns/. r8 svx4u89ogiklastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at4 noxzg.k us98s vir/8 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 collideui g1nag4u p12s 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 t14n 2u1gipaguhe 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 kgs8uq0yu9xp x50 v0xwd22 laxa h: ieb9 that is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speep2xx: b00 sd2ix0lhax9 wv8u uqy9a5ed 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 elastically as o/db)xa*a, z ghne 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 calcula, aadg) bxhz/*te
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision withfbva7,5u g7h h a second ball initially at rest. Tfabv,7hu5g 7 hhe 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 frictionn:s-r 8agr q7ztio 2** lopjzcr:e70 dless incline 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 90 cm off the floor, where does each cube land? [Hint: Both leave the incgn:j8 *d0r os 72t p*:azrz7 riel-qcoline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case w3) yz5w+gqfnof an object of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results inla4r79aof: mb a maximum height h of the pendulum equal to 2.6 cm9oa:balfr7 m4 . A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in 5t7c 5wl4k psra 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and kw 55 rs4lpt7chorizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for thr fo:,1z dg fwz)je77fe 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,u( eatx9+0gqz4m.gu m one of which has 1.5 times the mass of the other. If 7500 J were released in the.0za(g +eqmux4tm 9gu 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 the a1.xzjmy d wp 1b1-q(dt 4lvu9rear end of a 2300-kg SUV stopped at a red light. The bumz pwj-v4ddtbm(u l x1q19 a.y1pers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was 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 height of 1.2jto h()jz 6:i9vf0n tu0 m. Approximately how many rebounds will the ball make 0tuj nij6 zfth( )9:ovbefore losing 90% of its energy?   

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

  A wooden block is cut into two pieces, one with three times the massa psxpa3 ydr0lp+4g: , 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 explodg+pax ppa ,30rsy4ld:es, 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 direc*ce z)s8k/g dr s3 r)w8nvc2hition at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of /wez) k)n c2d8rcsh*8srig3v 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,e q*ja1zmkt,hod/ k9 second nucleus, an electron, and a neutrin, q1jea/td,9*hz m okko. The electron and neutrino are emitted 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 mj+ kkzo( yww*9ass $m_\mathrm{A}=0.400$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 coll,z*dkb c e 1e:5 9rngt jq:njn7wkt9v)ision between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle b1 dnze vn57q9e:r: t9cw,jnk jt kg*)between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the or5ib1xk 3 8 l:dam;appcigin of an xy coordinate system 1mca38pp k:bxd;l5ai. 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? 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 collisiorva mb ,09g1 kd;k9v61whge qrn with another atom at rest. After the impact, the neon atom ;,1gre 9vb0kvr qkw1 hd g9m6atravels 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 collision with another atom g l/0mk1( +fmhzg:6t6kn egw wat rest. After the impact, the neon atom t: h+mn k/gz1wg6e (tm k60lgfwravels 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 m.n xd(8 b+b7xnzjhz2oxk*, i0t ymisg: )ay t5ass of the three-mass system shown in Fig. 7–38. Specify relative to+btt z ,kj y xyb7(h8.z g: 2xnnds5oi0ia)m*x the left-hand 1.00-kg mass.    m

  The distance between a carbon exyo;x - lkeqw8m23s5 xn)8anatom ($m_{\mathrm{C}}=12\mathrm{u}$) 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*da l+epylg mhgpl b*.)89ep8 the car. How far from the front of the car will the CM be when t8eldg8 pm lph)+*l. y*p9a egbwo 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 me;: /h jeofq h/de3r06800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM j eef:dq0 r;m/h/he3 oof the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sideoqsoyjwwz 0- 4 3* 2ryym+m4ins $l_0$,$2l_0$, 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 hais,w2;2h.q rl7g jc*xm: i vtzs a load of identical cases of tomato paste (see Fig. 7–40), each of *m, 7q2l cjihsix:v.wg2; rtz which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius d tl-va reg7w1bn3qh34 /rzxxpr)( q72R 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 of the center of mass of the plate? [rvhp 7q/az t714dl(werb)r3x3 ng-xqHint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and ca54;et e*bdnfi lculate the mass of one of your l *4ebdi;tf5n eegs.    kg

  Determine the CM of an outstretched arm using Tableu6xpzam k5io :-b*g2gjfk6q8 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the posit5gg*lin7 k;i cp.*bgr ion of the CM of an arm bent at a right angle5.l 7ikg*ggbn *cirp; . 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 arms and letkr94b- mc -h5rhucy.g0 p;n egs are hanging vertically, and his trunk and head arn eu;rc 0cgy4h-.k tph9-b5mre horizontal, calculate 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 andi feqyg::)v d; 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 manrv eb6j.*w *un 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 czy cg j l;09fcha4n*-wylindrical 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 o09*czh a-4lycn;gfjwf the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 zpgw8)k6b ,vgw4wh 1b 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 tvb8gwp4 w6zw, 1 b)gkhhe bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29)vgt0c8c0w 0 m;jpbxh;+b xol(, $m_{II}$=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 stafimkr-3vjbds; vv7w: -nxgq 4cf683v tionary 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 Eav :cq4 vjgkb6n7xs3r3f-imw8 v dv;f -rth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitchedp- ns, pe8yotd1uf0j) horizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact t8u0y ed),1- jpspof tnime is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speedio*s*ne5py do*n n 4+j8eyw-p;epqs5 e ,7rao $v_0$ 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 shq, *:heatqv 1kown 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 fall into a p1kq t*,hv :eqaocket? Give details.

  A 140-kg astronaut (including space vvob 125uwu.p7la m4xsuit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-k5au2wupmb14x v.vlo 7g 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, arev or r6*qo*/wa initially at rest in outer space. They then push each other apart. How far apart are they wh* q 6o*avro/wren the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic colru/j uvt n34kuf3*ox; lision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the masxn vor/*j4uutu3f3 k;s 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 i-y 8**jpjus4yp.u kdbilcj6 7nvolving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of massj 8u*cy6d ypj4-p.kub7 *lijs 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 off/8e wa.wklnq) 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 different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaen) wa.8w ql/kches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood a* (l n cczv;n5p4pwn+ht 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 become *4n+clnc5;p(w hnpvzs embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.jsc5gzn4* ar +35-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, what was 4a *cr+szjng 5the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg andw:w/5ecxbmc * the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchan:eb/ mxcw*w5 cge 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 p)bwn0c+v gyo w2/ga9was 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 brokenx/mmd596mj b ,cix twt1/ufa jh9- w*e apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of th bjcei,5*9 whxu6xtmf /9mt /jadw1m- e other. What is the ratio of their masses?   

  The force on a bullet is given by the formdc0w fj5eax*- irj 44dula 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 p7/ .md ytpo u nlu:.nl;n)4ww$m_A$ = 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 de) ggrjl5q3 19 lfg(c-h5 gqtxocays radioactively into an alpha particle and a smaller nucleus. What will be the speed of this reco3hxqlj- r9fo)gg1 lqt5 c g5(giling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at a iy0)mfb pd;)in 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=2.4 bt:guca9 d3e2kg slides 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– xs 2lg:.vuv9 4kj9ce(lqjtd5ci+q+h 46), what is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide witqls+cchklvjut 259qgi+ .v:x4d 9(ejh M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effc i1qrf1mrm,8ect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun cfq,r8i m11mr) 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