We claim that momentum is cons*y2a-xvv9ikqi uz 1ijg*z z;jy3fo9.erved, yet most moving objects eventually slow down 3zoyvj;*zq9z1i *x 2-j y9g.fvuki ai and stop. Explain.

When a person jumps from a tree to the gr( b9(x6 p5jpenvyy0d eound, what happens to the momentum of the person j6(9 e v(dpe 0y5pnyxbupon striking the ground?

When you release an inqv.ijm6 7x*(/kvv 0:nz nrlgeflated but untied balloon, why does it fly across the roomlkv06q*:i7 xm . vjz(/gr nvne?

It is said that in ancb8b1 -8qle nfoi:q (euient times a rich man with a bag of gold coins froze to death while stranded on a frozelee(n 8o b1bq8-if:u qn lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is pdozkgeg0c; )8j6rn+ far out in space and is essentiallyg+dpn8 c0 ); zrk6jego in a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller v/mrjxqtu4b ,,y;uc (the force can be for the same momentum chaq,bm; ju, c4u /t(xvrynge, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid ax sovd6 cmm7ht s)z (+/z4g:mbs possible to withstand collisions. Today, though, ca z g/o+m4dm )7ssm6(v :xthzcbrs are designed to have “crumple zones” that collapse 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 airap*ep/ tg0-yk q/s2ds zne9e 4 by the batte ye9ne/t24sg kde *a/zpps0-q r?

Is it possible for an object to receive a larger impulse from a smas1 jxdqvb:s hhllt 67c2 :81c1 w:jn*jv0jqrl ll force than from a large force? Expla7jc6s0 *j::bhds11v1 q 8 w2l :lvqlxrthjcjnin.

A light object and a heavy zf992rbb k)og gbnpf ,p8i0w -object have the same kinetic energy. Which has the greater momp-rwzf i90gb9n8 bg ),kfo b2pentum? Explain.

Describe a collision 3;) kjqoad8kfd zx9 9uin which all kinetic energy is lost.

At a hydroelectric poknpl z g3g1x;6wer plant, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generatiknl1x;3gg6zp on, 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 wall at .e mq1qa6.i)+ fts0y4+tph mdviv6 oja 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixev 1: h)h- ssh*x bd2t9( djbpco eo(at*-qlx6sd 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, durb cexp 6ddh-9 ( btsl(ta*)sx :21s-hovq*johing 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?w wn4e d8bfr20

Why is the CM of a 1-m length of pipe at its mid-point, whereas this isbpvraq x v6m- *m7*fw4 not true for your arm v w7vr m *xq6b4f-*apmor leg?

Show on a diagram how your CM shifts when you change from a lying pob,cvqy:pqn8 9a,5ib rltl*n )sition to a sitting position)* a 8lnbqqvl :cb,9,5rty pin.

If only an external force can change the momenr;fv su blw7+itr.gm)v 1-px- tum of the center of mass of an object, how w im) sv 7bt;p-+1-xflr.urgvcan the internal force of an engine accelerate a car?

A rocket following a parabt4vyqao. b)q0olic path through the air suddenly explodes into many pieces. What catqay bv0). 4qon you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g vq( ; 4.c:red3rnt fposparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N j /p: 0ncnx*xwzm13h:fa wtu,acts on a 65-kg skier for 20 s. What is the skier’:x1a m : np wxw,zhn30/jtcu*fs change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive straighggc*olr) :4wvkky 0d- ep ((nvsjj/ 3gt back toward theov*)vn-gkr4l:y3s jd0wp( / jeggkc( pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a speed oyt h1 m6tx36niay)2nkafisf (c 6 cb0kapx,( /f 10 m/s Fig. below Calculate the velocity of the boat immediately after, /(,nkpif axnktsiy1a)x0a(6mfcy 3 ch662t b assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, giv6oaz5o;;i7nc;kea e ven that the propelling gases are expelled at a rate ;5aekev;noz;c76a oi 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 movin7uy,byp7z3s rx e ,v3cg 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 71txin 04iklc6) gkw8.n v.jle4edal track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. Whtae6)81li 0w ig.4l cn4vknx.kej 7l dat will be the car’s new speed?    m/s

  A 9300-kg boxcar travelingbs0 2jszs2z j) r .u.,+niqsdp 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 hor7j4d z5pe zi6tizontally at speeds of 100km/h If the air strikes a pdt6e7j pi4 5zzerson at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical 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 8.6m/s onlo 4 wu+262;jjkriztx a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignorinjo22k; l4tuxi6r jzw+g friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving atcb8; nv*w-4 2itofo94jlil ur 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha p-u t4 92i 8rlblfi*4oncvow ;jarticle 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 278l jsxzw0r koqbs d)c:x::i,.fmr 5 b30m/s penetrates a 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 move bl)cmjdsksx o:,bx.7: i f: r8wq 0z5rafter the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speed of9w )dkrz3 lru8p(-6zw lzd8no g6joy ( $5.80\times10^3\mathrm{~m/s}$ 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 velocitycpxtwg.,pu( * wnyr4 1z9*ffg of 115mwn , pwxcffu(gry 4z*p. *t19g/s To alter 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 o0j-rzo1ir + ob-xbw(wla6 8o xff the tee at a speed of 45m/s The golf club was in contact with the ball a6jiwwz18o ob(r--olb0x+xr for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes to rev0ddpfdvh( c 6 ee/b:9st in a time interval of 8.0 ms. (a) What is the impulse bde pfv9v60/h(e: cddgiven 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 an1 w+dv2grrdj,))osq- 1a cfzdqr88 kud speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashf2skz pvn)fxf,3qe)o( m fv x4i,o(-cworthiness 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 rest2) q v-) xncoofsz4xk (e( pm,3v,ifff. (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/sidcg(0mw 9/oo oy.+b e to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Calcul w+g m 0od(ycooeib./9ate
(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 0os 0si33unwnlg 4bp3z sa/3 b4.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time.43pg/b as so03 34unsb3inl zw Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking the lo9 yp8h1pfa8ym wer leg bone of either leg? Ignore air resistance and assume the CM of the person moves a dis818a yyfmp p9htance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of collides heyq 9knu np0 k 2(5vpex61j2bfdad-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 the 0.440budfq22x5 en (6kvp pn0j9k1y-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 speed9z(:shvr e4 mh 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 objec:(s9h vmrhez 4t 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-on collisiix wsqn3dj58cs5(9y uweal.v5mi ;i4 on. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be w vqis i3yci;8 5xjw4u(n5 5sd. l9eamtheir 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 2.5m/s collides head-on wi/ h8sgvrtz.k *th 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 t s/.*kh 8zgvr0.060-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/m9wed.vg)8 i rs collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a dv8wmr)gi 9.e speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ri o v3va3q7*-k d3r atali+m.csde collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is3ca+ovmlvr*tk siada37q - .3 moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a se*4 my)b1;ka-om wppn pcond ball initially at rest. The second ball moves off with half the ykpa-p o41w pbm)n* ;moriginal 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 slides5w47 guamv pwod)83vt down a frictionless incline as shown in Fig. 7–35, and elastically strikes anotw vtm43 5aw guvd)op78her cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object)zr +h74scmx g f*av.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 experimenyqj 55e1 198jukr8 lnts 8kyznt, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swk88yetksl1z1yj 95njq8 n5u ring 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 b(pvm pxo k1*h m(+qd(2ugmtj, h3zt )fymu d:5uries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical andh (xh,+5 m(tup )dum3dyv(g1:j2f q m*ptzokm horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for3 sq+oast1k7fduulg(1a+ 1b u 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 bre;o mijlmo pxufgc98j qf1b-,5 ta7(4faks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the he4pj;o(8ft7g, xf m-u1mbf acq ol5j9 iavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped at3g; ;:-2ub (h 9cnuzwfog;xja)idpee 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 cw e 2z iune9fg-phg(x;c3o :u;jd; ab)ar 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 k,*v o) actamp, 90vvyheight of 1.20 m. Approximately how many rebounds will the ball make before losing 90% oft0 ma 9a,vkvo*y)pv,c its energy?   

A measure of inelasticity in a head-on col6:r (kb8rp vbpjb.c 9flision of two objects is the coefficiep8pbf cv .j(:bb6rr9 knt of 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,lg7l*dtn ,j: ojbdm*z) h. swxg5h s35 one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rousddgg.*)mhx7* o55wtb:jljz hsn ,3l gh-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on with a t+m ov y7 182ryrzifz110.0-kg object moving in the -x direction atyt+z7yzo1r r m21i v8f 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decaysh+-q1: c 9po i(nazluv into a second nucleus, an electron, and a neutrino. The electron an19ia + nu lvq-o:hczp(d 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 mas :*v8s e2gd8p gy+wdfgs $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equal mei:/ 4kiby0f pass, each having initial speed the two move off together with4yii f:e/0kpb speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles andwri) gp xx4.fx*9vs;z 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 witvsxpfxx.w *;4z 9 )righ 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 collision with anothw5 5w +qfsjar3er atom at rest. After the impact, the neon atom travels away at a 5qrf+5ww5 3sa j5.6 $^{\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) m, b wrhc7z5a-rakes a perfectly elastic collision with another atom at rest. After the impact, the neon atom travels awh7bz5- rr,a wcay 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 masw6 w go4onjjkbj9 35(as of the three-mass system shown in Fig. 7–38. Specify relative to the left-han3(jkownojw6 b5 ja4 9gd 1.00-kg mass.    m

  The distance between a carbon atom8dmz;(jo i.e) g2dlxp6dwmd- ($m_{\mathrm{C}}=12\mathrm{u}$) 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 car0q.48b/mibdlr2c/kul 4lt/ e )ho ux i is 2.50 m behind the front of the car. How far from the front of the car will the CM be when two peil2//o um4.di ub)he rl8c tk0lqb /4xople 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)e4 (r.y*hda02k obvf eozq)z m by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, detehvodkb aerofz. q)(0yz* 4)2 ermine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesl;e1j ux6jis 0n 5vf6n $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of tomato paste (see Fig. ilz ytkn 66,g4take y7j7o8kfp13s(l 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick 1llyk g j( kk,nszoe atf784it63y6p7 up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R paw0 3db) 4klecut out of it p) w4bld30kea. 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 thobstm ,7c3 w+7au2b ww b3* yvm,tf8sjbse in Table 7–1, and calculate th7m,,s3tw+b* v 8jma3u7yb2 b cbfw wste mass of one of your legs.    kg

  Determine the CM of an outstretched arm using Table 7–1. ; ,p6+jjqix:az(ln i7f4ad lo  % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent e2m.i4abl (taii0; wfat a right angle. Assume that the person is 155.maw2ifi (e0;t 4 abil cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs aj p qutjw+-y87v2a-bw re hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? U-jju ww2yv 7tq+8 pa-bse Table 7–1.

The masses of the Earth and Moon ar n1 x8dzxm4so a.ubw.1e $5.98\times10^{24}$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 anp;pylllcc7 a55n(g)j9 (ggso 80-kg man stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of massk6) jqzziac7)q 7y2 gs 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0 )a77gjizqsz)2y 6cqk.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?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diameter 0kw g ) p8v-8;uusrfa)y.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 poryvsf8 - 8);upga)u wkint that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Exam3 xzy +wpl,gr8wg (l(lple 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, l:bffbb ,t4w its gondola, of mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to f ,4fbbwtl:,b 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 horiz4r -* zveu-nlbip2o4vn.uc1zontally at strikes a bat and is popped straight up to a height of 55.6 m.lvzi 4-u2ncb*e-nu4o.zrp 1 v If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with .dfziv20fy muz oq*25speed $v_0$ 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 facedv:yy;-5 *h d pwh0hnsy with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worriedw;-: yhdy5ns*p hvhy0 about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (inc q8r a)rnysa3upnvt;8zv:j 04d n: q;dluding space suit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-kg spaceydnj u)n drs4 v0a p3 q;arnt:q8v;8z: 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 th;mb3e pd7-h4u mdk,gy e other 80 kg, are initially at rest in ombhm,3 pd7;-yg ek 4uduter 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 rgnq3wd:s m0-elastic collision with a second ball (at rest) and rebounds in the opposite direction with a speed e rgsmwn0dq-3: qual to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case inv5g okejl)g6qoh: m/v,lwzb . (olving 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 and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed lwb:)vk lg/,g6hlq.m 5 (joeoz imit before applying the brakes.    mi/h

A golf ball rolls off the top of a 5 :xh+/ w0)fqvz nzfacflight of concrete steps of total vertical height 4.00 m. The ball hits four times oqnwh / zf+0x:5afvc)zn 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 block of wood at rest cmk* 8rtv,;ru8k -8+qc2 yfbzs0n y )laj:ugydirectly above it. If - kuacgr8 j8:u8y* fv l )0nq; sm2cz,btrky+ythe 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 it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of:uwf3hous+u- ,o*p (vcbc: rz wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between tvzusof3b occ -r*,w (h::u +puhe 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 qy8vehb eh7 6v45d5bb-g/m ss 75 kg and 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 sit6qm / vsheh45gb5sybv 7-8e bdting 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 wa-zqze+ rup beieq dv;6n i-1s;7pv:;ms about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments by ann9(0 a,sp4i go+ancuy+m;j sb explosion. One fragment acquires twice the kinetic energy of the oios,b jn na9u ;(4g+ca+mp0sy ther. What is the ratio of their masses?   

  The force on a bullet is given by the formula :txz29b:e7lb+a y f otF = 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 amg 9/gr 9+ndpxug4g25tzh1o$m_A$ = 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 into an alp d0ziqpxahuaj).v )::ha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particlij)d0.a:v zu :ap)hxq e 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 of3cca lz/+ds, enw1w+a 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=2.2kmn2zgbe;it 7qgp *j49g 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. 7–46), what is the uppz fjr-ysm-,6xjan t6)er limit on mass m if it is to rebound fromt 6y-,z n s6amr-jfjx) M, slide up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 showdh1j4bdc;o mu4rh .o6s the planet Saturn moving in the negative x direction at its orbital speed (with respect to th416 dd comb.ho;u jh4re 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