We claim that momentu.nlvg x6bn//tm is conserved, yet most moving objects eventually slow down and sto t.nx/6 /bnvglp. Explain.

When a person jumps from a tree to the ground, what mgnv dta g(;o-7 lb5*ghappens to the momentum of the person upon ;ltdnbvag*o 7gmg-( 5 striking the ground?

When you release an inflated but untied ballo7d5b v 70qsnel:*i xlln6asd3on, why does it fly across the room7lv7ssn0el n53d:d*bl 6q xia ?

It is said that in ancient times a rich man with a bg5jncgk6vhmv+mud l)j1w0 3 -ag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. Wljw m-u hn6mc j v51ggdv+k03)hat 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 essentiagfoa o: bvsr zu*1n951lly in aang 15:f 1rsbz*ov 9uo vacuum?

According to Eq. 7–5, the le)e0, qooeiu9m0c5ns 7zo,x/ vb j0jzonger the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended tj5 ibej0xece0vs/,o 9u o ,7)q0nzzomo inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible02yo5um oxhi0kk(s 8x to withstand collisions. Today, though, cars a0ky5s x2u0mx(oh k i8ore 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(0j1ixl erm6a than a ball tossed in the air by the batter?ea rxi10 6m(lj

Is it possible for an object to receive a larger impulse from a small force th20ttrb7hv ; no,k)x syan from a lto;n s ,xh27br0t)vy karge force? Explain.

A light object and a heavy object havfx2i zwh y7ke:prw(xe5 j)o15e the same kinetic energy. Which has the greater momentum? Ex 2j5 ) 51ek7rfo( wpxeiyhwxz:plain.

Describe a collision inqcfl m1 d3)g( x5rlrw3 which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against turbinemf-n2 18auhd 5ufi hv5 blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water ren8 h 2mfa51fu ivuh5-dbounds?

A squash ball hits a wall at a wu- r:+njebb cq52hh78glp*t;; vkla 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 na;u+ -abgmw:0tc* 2b elwqr*plate (fixed to the Earth), from which it rebounds at very nearly its ganq -ebw2*uclaw+ t*0:b;m roriginal 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 loayftcz3zhki s1:p 1 5p-d in your arms?

Why is the CM of a 1-m length x /o,d9qa 13pkb1 i*tlc(yyghof pipe at its mid-point, whereas this is not true for youbdgpc(ahl3o, 9*1k /x1i yqtyr arm or leg?

Show on a diagram how your CM shifts when you change x c9ie; x2 *k u-3ry+cojykxp7from a lying position to a sitting yp; 3ek9x7ri2 *-o kcy+jxcx uposition.

If only an external force can change the momentum of the center m8du16 xy) lgw)0)ni8sg myli of mass of an object, how can the internal force of an engxd8u mi)n0mg8l w)lygi 61ys)ine accelerate a car?

A rocket following a parabolic path through the air suddenlwzjmn1v;(z5 i m4)sa 11w scbgy explodes into many pieces. What can you say about the motion of this system of s jm1)z ng5 vs;1mibc1a (ww4zpieces?

  What is the magnitude of the momel*+g+juhgg7df ; o4oi s,(andntum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 ag:)w5j -jarxqpv+pv.1 mtb4 N acts on a 65-kg skier for 20 s. What is the skier’s change in v ra.: x1vqb )4 j5aj+vtmpgwp-elocity?    m/s

  A 0.145-kg baseball pitched at b6 eu(xwybzvm-/ked+; 8o tg- 39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the conk8;-6w-(gyx t/vue bzbedom+tact 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(05*cr 0byef y:n,xldtz 8xly of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the chilcl :5lnz*ye8 x(xyfy t,0drb 0d 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, given thd -m+ aia2vkw1at the propelling gases are expelled at a2 am1w dik-va+ 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 moving at n jq+npz- n2)yx4, zfv$4.1 \; m/s$ 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 frictionlesidwm05va )dxa,ca8lvo701x e s track 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 av7)0edoa i8vc5l10m x d wxa,new speed?    m/s

  A 9300-kg boxcar tra2kmdmx6;w 8o7 ,v* ab4 lykknwveling 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 horizontally at speeds p9)gw,l 1 a4bljy y 9m4ndcr9a;qh/bhof 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind onlm bqryn9d,)4gah/yh9p 9 c4j;1 a lbw 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 al :spj 8keos6.jong with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with6s pje:8sjo k. the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initiallg3sb4fgj 0cn4f89r )jupo6l dy moving at 420m/s emits an alpha particle in the directiond)n l fr os9c0jgg346u fb4jp8 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 when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and emergmz /(,6l w sf;g8njrgbes cleanly at 170m/s If the8gl ws,6rb;m/zn g( jf 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 traveling at a in+bik*17t 8kiwc,zz;pw5 tespeed 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 sl wm10 jr:td(ts2dff ye-9r-with a velocity of 115m/s To alter its course by 35.0j-ef:1w(9lrd -m f0rtytds2 s $^{\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 4)yeij8 itp7q0.045 kg is hit off the tee at a speed of 45m/s The golf clubyqipi7j8 4t) e was in contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5xsotbu4d . 68hm/s and comes to rest in a time interval of 8.0 ms. (a) What is.d48bhx6 sotu the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes a wall at a 45ywek/i iq8:vn l:jxza*c 6;s) $^{\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 chauw812sm -w yugoq mnd;*ix54wrge of the crashworthiness of new automobile models. Cars are tested by sms-oqwd4*21ux ;5uy8 inm wmgwashing 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 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 and89 ( dwv ijt1pxeyg+9k is stopped in 0.75 s by a head-o+g9pjvx1kw y ei(98 dtn 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) points in thea u)zxsz , 9p+eapa0sx+h w49l +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphica sua+9x 49apshea ,zx0pzw +l)l 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 breakij0/x7c 3ruo 4bejlbj:ng 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 fauejb7 bj l:43 o0xj/rcll). 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 5l-il crwj- yj*tywid g2s*93t*i)eua 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 c*ew95- u tdi)j3ly-ii*j* rst2ywlg 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 easthfa 5r5zb9tbfh 066z b with a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-h0ftr abzz6 6h55b b9fkg 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 collis/llb *g8cmzax(3.7 be*huvwg ion. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite directi7*g8ba hvxmw(*l cglze /3u.b on, 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 s-rtd )b3j wpbpri-6 l+peed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elbrd -pr)-36wti b+jl pastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.7dmqu .m3 4vsx6wf +acty.df 6220 kg 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 b ysa6uctvq 67+f4d. fmm wd.3xounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide e ;4 wdve:4mcjvy2oj v 2nud*8ilastically as one approaches the other directly from the rear (Fig. *4iycnvoud;m2 4ve w vjd8:j27–34). 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 an5il 1 4le.qmnw elastic head-on collision with a second ball initially at rest. The second ball moves off with half the ol1q5nwe.l m i4riginal 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 cua pu:y,c,1s uabe slides down a frictionless 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?c pa:u1,ua s,y [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of mass u50 i,rqmamj;vdy c3;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 uhxo on( -xv8l2 w7+qn*fxc*7ri*f dp1 results in a maximum height h of the pendulum equa27*rf+pv-*n( oqx7in 8ldx fcxh wuo*l to 2.6 cm. 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 b+n+-(+v,, u dw6f*ingnn ipt u(lzb smuries 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 and horizontal components of the pendulum’sg n(mi -l+u(npnv,nid+b6,u fs*zw +t displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fractioklb*9s8 n)dj in 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, intie9qpw,uz 92vi9e n j;o two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B re;ipew n9z,e99u j2ivq present 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 at dz/g-x xax4-ki g.(i1ruy1 cna red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports ca k1/.xa1 -iic4 xgdy -xnrz(ugr, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and reboulhb ix3- bk0lg-x 45o-s.ujvynds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its e5bl4u0 .kx- hxvyl soj-g3b-inergy?   

A measure of inelasticity in a head-on collision of two 2e-errjavls2nj hic3mv6g *) ;a *k w(objects is the coefficient of restitution, e,wn *e362ca-*l( 2svei rmjr;hkv gj)a 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 ma054 4beyd4f,qe5l0lwx voeqi ss of the other. A depression iel40l4ixq5 q f ed,540 ovewybs made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object movinn9ipg7gu7b0 q .yx bo;g in the +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the finalygbb gp9n7q u .oix0;7 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 k t3f0gy, 4ajz+lgxf-loy p9y9q,*w t9k7hbxat rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momefjoha+,4bf3g-q 0g yp9 yy7twk9k*l9zxx, ltnta 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 mqdzpx3 2:h 5c a,o7cyuass $m_\mathrm{A}=0.400$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 obe3cjz b 1qu44 rfgi*-jjects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial dir*czj 4 jg-eur 4q3fib1ections?    $^{\circ} $

  Two billiard balls of equal mass move8/1br nrsk te09jiv.h at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of bal0brk/hsvt. i jnr8e 19l 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) auv- s jl)10ywc( 9dusmakes a perfectly elastic collision with another atom at rest. After the impact, the neon atom tras-uuls a0j (wycd1v) 9vels 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 perfe:so ,: z kn9rc/snoitj2k)3ra ctly elastic collision with another atom at rest. After the impact, the neon atom traveoc)nr:s z ar jis/2ko:,k9tn3ls 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 shown in Fig. 7–38. Specifyhn 0,v1 uyg tvm8fbx( sw(3n-o relativsb0gm n1 h(ufyo(3xnt8,v-wv e to the left-hand 1.00-kg mass.    m

  The distance between a carbonrxalz/5 + af t:he.ezml v642k atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind thazkk72*a tpfi s:rs4bkukqg. u 1:z/2e front of the car. How far from the front of the car will the CM be when two people sit in theqzkk:k14bpz irgf7u:2 s* 2a. ksuta/ front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is usejx 9p:gz h00ild as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboatlpxj :0igh09z.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidelc n a;*k wih/b-kb/c:s $l_0$,$2l_0$, 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 identicatsu )w srp0pftvxm j ah--4g) a7li)+*l 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 crsjx- h agit-spp*)vl7fa)wm4t+r )u0ane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular5mef2 vmf4/ jk2* snzg hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the centfk 4j /2sm 2m5*nfvezger 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 7–1iz /juib. k+u., and calculate the masiz/ijb.u .+uks of one of your legs.    kg

  Determine the CM of an outstretched arm ukpmlqw8(5s7y urz arq 3om kkz4 j7r6dq-2c/3sing Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculak1 kqu5gnv x b1pvc)bvww )-. u)3dh2nte the position of the CM of an arm bent at a right angle. Assume that the person i1 qu 3kn. cg w5)vvu)b)xd2pwk-h v1nbs 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and ((ocnh7hv zxarr* 9mvo lt./(legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torsoa7rcn/rh(m(vl (hv*9zto. xo’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon ar)6fbobk ps8 m 1x2c im6:yqze4e $5.98\times10^{24}$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 apo spwz 0(z-2kunm/2:gmwx no 2art 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 cyli/eopvbx ./, qlndrical 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 show b. lp,x/oq/ven 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 andiy)1vjf 38u q6 xe4uau a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in 8ju63fe x4 u1yv qiu)aFig. 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 Example 7–14 (Fig. 7–29),vgan*4ot:xu/ $m_{II}$=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 stat 0wxv;+jxyo :fionary 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 bal f0xvxo j+y;:wloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is popyttq:y)+ p)bnu * fby9ped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate 9by*y + )):qnyptbt futhe average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with s ev.vw55xx: xrpeed $v_0$ 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 wib+i;i7bfatz0 *y w hc+th the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worriby7w a zi;t+0ch*+bifed about 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 z5opf d( ec78p+*cgg 7b*wdxf2.5m/s by pushing off with his legs from dxg pzf*+dp7fb5*wc g7oc (8e an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other f+ votht03e5b 80 kg, are initially at rest in outer space. They then push each other apart.5b vttho0f+e3 How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes 8*wnj x ;x. 9o/7glff jk(03dn)noql6swthq wa head-on elastic collision 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 wo lxkwo ) gqjt 7qfwl(f093n.;8hxnj*n d 6/smass 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 invol ),ra m eoqw6xv*iwz(ta2tm/7ving 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 btz(x o* q7a2/wmaiv6r)m t,ewrakes 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 the top of a flight of concrete steps of total verti1yumn0m r(ihr6w 9rab.h1ko +ad+(q ccal height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a dim ow0ruq(k+6 d1ahm9ai1nc .yr+h b(rfferent 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 ogjxwym+f szy+8isnq):6ib 06f3wto 2f wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet be stw 2)6my f0+8 jqw3ziygin+s 6o:xfbcomes embedded in it?    m

  A 25-g bullet strikes and becomes z6bc6 y5n;sm(zhje s- embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction betwee (6sy zmncbj 5;zsh6-en 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 othefn uq+ub- paz wo(*.:dr of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, wh duzfu+o.-b(a* wp q:no have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was yl svil4)p m9qcs)/xfhd7:w ;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 z-g a)f* *pc)ya jctvi5 qj:v1fragments by an explosion. One fragment acquires twice the kinetic energy of the other. a5jvj c)fc pt1az* igyv-:)*q What is the ratio of their masses?   

  The force on a bullet is given by nl8nd/4dz +pb15f yba the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses ble.h ygu s u+7sd /(t/w*giz.)n yoa67( elnp$m_A$ = 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 alpyot -+82 ez;o4ys6por)dc s whha particle and a smaller nucleus. What will be the speed of this recoiling nucleup te-o z+ 2ys4)ro6ywsc;d8hos 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 50rdn1t f7j f)/qwrvkfired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a m itc x 13f2m54;msao,:vqsac 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 upper1)lcj6feko 4x limit on mass m if it is to rebound from M, slide up the incline, stop, slide down theo)k lx 6fe41cj incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshotuv z: ob yk:rjv..15tu effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Satu:kb 5ruo.vv:t. 1zu yjrn 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