We claim that momentum is conservedaf phu/,7qb *p, yet most moving objects eventually slow down and stop,b q7up ha*/fp. Explain.

When a person jumps from a tre qj2 ()oscpg 29wk0mqle to the ground, what happens to the momentum of the person upon striki 2mkp)l(0ow9sqjg cq2 ng the ground?

When you release an inflated but untied balloon, why does it fly across the roogp1.xne +h26zgk2 gn fm?xk 2gg ne62gfph.n+ z1

It is said that in an19 8iyashew;xct7+zgiz y1 b2cient times a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Beca y97g+8wtz i s1hib1ey; zc2xause 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 far o64 s /uaiz6nbos9t0ar ut in space and is essentially in az a o69nta s6s/4bur0i vacuum?

According to Eq. 7–5, the longer the impact ti /2el/m.ot ;hyj5niam me 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 to inflate during an automobile collisioe5otla.jnm2 yh i m;//n and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisiov hgc9d0jwotnqc9d/5b0a + bdz6 8ql7 ns. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the adv wbvbzolqad/9 70h5 g9c6c+tn 08 djqdantage of this new design?

Why can a batter hit a pitched baseball further than a bd;ojc-q ;y v7lall tossed in the air by o 7dy;q-jvl; cthe batter?

Is it possible for an object to receive a larger impulse from a small forcesra(2h t9n n7k(rh :wj than from a (kwrr9hhn2:sj7(t na large force? Explain.

A light object and a heavy object have the same kinetic energy. Which has th5l56 6awvp jphe greater momentumv6jal hw56p 5p? Explain.

Describe a collision in which all kinetic eneru ,3fp1l t7pilgy is lost.

At a hydroelectric power plant, water is dire omv mpid10lu) lnj4(*cted at high speed against turbine 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 rebounds?ln( m0o1mv dji4)p*u l

A squash ball hits a wall at ab7 1pwp)3pv mi 45 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixed to tg n6zu+6psmr 094ixgmhe Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of pu xgsm64 pmg9r0ni 6uz+tty that falls and sticks to the steel plate.

Why do you tend to lean backward when carp /ed)d95wq qa ie2/1n/btv*t8lno jvrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, wherea)th 7)stxcn3x 4uxo 8rv1fg u+nv+hp*6rk6j es this is not true for your ftrxu6usg he+)xkj36v )vn*ch nx1 4t 7op8r+ arm or leg?

Show on a diagram how your CM shifts when you change from a lyinw 4:axf9+xfpi dn 2wi0g position to a sitting positif d2fp9x:ni+4ai wxw 0on.

If only an external force can cha u 3p)/uj97xto 2segrcnge the momentum of the center of mass of an objecux r eu9)/3 7jt2cpsogt, how can the internal force of an engine accelerate a car?

A rocket following a parabolic path through the aipxj :3z -s lc --nmlqaggkzg-s( jg667r suddenly explodes into many pieces. What can you say about the mot6l-:gl- g6pgs-s7j(-k j 3ngm xzqz caion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparro3 cikct,)psq7w flying with a speed of 8.4 m/s q,) p3s itck7c    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for a( g;t7d *yh6kgd m9xi h9rek(kiz7+r 20 s. What is the skier’s change in velocityg6(7x+ i(7a krz 9km;t *rg edhdikh9y?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive stf0x:w nsrkah5 3 g q(,x2zb-qpraight back toward the pitchezh,25wq:s ag px-n0f(3bx rkq r 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 of q90ao/e4-zxpg4rq y i 10 m/s Fig. below Calculate the velocitr ei0/a4 -pq4 gqzo9xyy of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a r5g8gkvd-s :j:q o:s;tb r5 clnocket, given that the propelling gases are expelled at o ;8t5q:bjsdnkrc l5vg:g- s: a rate of 1500kg/s with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an apparentt6s 45yd1d nr/l7f w 1dn4ftbe breakaway for a touchdown is tackled from behind5dfrnnd1b46 47 ftw/lsy 1t de. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictionless track with a conj)ki 5 go 7pmsza6/3*dp:d2vox 9kdqb23tkws stant speed of 18m/s A 5350-kg load,ingqtobkzkavp om5323pds dj w xs /6)92k7*:i ditially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strike 0srud,1 gii9vs a second boxcar at rest. The two stick together and move off with a speed of 6m/s What is the iu irs0g1,dv9 mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speeds of 4 nvp0ixq m7ephgc60av: g.1xl.m; tw 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 on a person. Assume the person is 1.50 m high and 0. vha1 0x6m04ng:plpqi.7c.v gx;t ewm50 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 spl bo7 ,n+saqu (f2yc1xeed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the l cy(7n2+ ,qx bofaus1speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha par )ch:2yix2xc2ce v sj(ticle 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 scv jx2)2yxeci :hc2(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 emerges clc7f+fe wewkasw4: 4h*eanly at 170m/s If the block is stationary on a frictionless : w4*s+ecw7kf efwa4hsurface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling aaod+zok3 8/ oco huit.lf v *eh),b87qt a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a velocix 9 w)uiohy97 as-qt.lty of 11au)9i- t9 hwo.xyqs7 l5m/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 off the tee at a speed of 45m/s The gof2 rwpk28v 5qct6r/ yaopyvaz;(;i 6tlf club was in contact with the y8tw ry26 c vzqo;r;a(2 akf5/v ippt6ball 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 rest in a ti:r lso/c 4h9nlme interval of 8.0 ms. (a) What is the impul/:h9nl 4r locsse 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.l)gc 76*ctdr h06kg and 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 engineer6 ys*+bg) myckp3wkh5;lkn32 dh+ b3yf )wwsx in charge of the crashworthiness of new automobile mode+ 5ksnbkw3y2mp)c;h d+hyw b*)3xs 3 6fwkly gls. 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 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 4qweu7, -n g6 bnow-p-mm/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due west.6e7bqu o, p--mngn- ww 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 0p*;m2 ut,4q5 hh sqhsn.060 kg) points in the +x direction and is given by the graph of Fig. ps,h hu;5qsq*mt 4nh2 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg pers2y5e4 kq brs kf(6x(zaohfk*8on jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of t2x4f6k ef5srkh a*zy b((oq 8khe person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force 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 lk3y(lx4u ye * collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent3y(lyel4 ux k* 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;-6o0-3l cdcaihzc j v/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 th za-d hc;ic36-cjv l0oe 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 mas-0c7cftet 7e ss undergo a perfectly elastic 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 ec7 ecf7t-0t sm/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 cdv)*p j e-f k:8toxy9bollides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic cofpot:y8bkjdx9-*v )e llision, 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 0.220 kg that is moving with a speed of 8.5m/s collides h -k jprl4u4 c4vy,kppm l11. l2u;atgzead-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a spez1l1kg4,ak u4cylp ; umr-2lpt v4j.p ed 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 amusemesc;.i xdw(ej2bpl (, mnt park ride 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 is moving ax; d,jp. c(liebmws2(t 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 hey;fyvqijzp q5xgcd(d1(cp//p( 1 n5l ad-on collision with a second ball initially at rest. The second ball move/yypl1q/idc;ncpvz(fp5(1 g(qx 5dj s off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as shown in Figm 2vm jto2i* wso ) val;g-6--q,5jl)lj fxnsp. 7–35, and elastically strikes another cube at the bottsp tgwlmx -2l ofjivm*)lj)vo26q j-5;s -a,nom 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 objec mc y 4yni;nf3-,kw8q ,r4bpaf-wt9 vjt 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 in a maximum height h6wo jpxru)*5r of the pendulum equal t56u*j)poxrwr o 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 buries itself in a 3.6-kgub4qob/6 e1 qv etb 3r5;uo(ei pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and hou /qvou b15ee3brqbi;e4t(6 orizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formulax9 )mj:.haes p3wr nqw g76tx d,cw16z for the fraction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an n /;5l gbjeqz+fezi n8 nv2,*zobject, 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?/nzbi *ejl, + 5z n82znv;efqg (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collyj kp1x14 okp.ides into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police1jppk o.xky 14 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 0 30d t1ntusph1.20 m. Approximately how ma s013td n0uhtpny rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a hu7 t(- uo mgu2eokvd-.ead-on collision of two objects is the coefficient of restitution, e, definedum g-(uuok72o.et -dv 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, ozuh(x1exux 88 8r(ha7/wy ntone with three times the mass of the other. A depression is made in both fac(1w xzrxue(8x 7 at/nyhh ou88es 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 moving in the +x direction at 5.5m/s collides head-on with a q-wb;k, kspwf3 j+d5m10.0-kg object moving in the -x direction -p;ww+fb kq djs35 mk,at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nuclevdoa0+04umgu ufk0*, s / boow tfo5.jus, an electron, and a neutrino. The e+sf o ua fkt40do.m5*o0ugb0 , j/owvulectron 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 mass kdhxoph6;bx mtoa1 *63qj-c ycy0+j2 $m_\mathrm{A}=0.400$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 ma5u xrov ,gg92gss, each having initial speed the two move off together with speed v/3 What was the angle betwg2org5 xg,v u9een their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move /ic7ph6tutlj*n +f ( c6q d:efat 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/j:hp6l*fuqt7ceci(/ t+6dn fs 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) make /d9,,b nxmw/ mecqegxi- sy,qn.89yys a perfectly elastic collision with another atom at rest. yem,micg,/y esq99,.w8bnxq /dxy- n After the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision with another atom f:sint/1 k6d d 3 khqh1t4)kxtat rest. :t3xn q1tkd ) hdi14s/h6tkkfAfter the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system show;mtjo 6f2en45luc o,en in Fig. 7–38. Specify relativt6umnc4 elo, ;j5fe2oe to the left-hand 1.00-kg mass.    m

  The distance between;uu s38pb58 reww*iwu a carbon 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 the front of the car8t)ufi8 t*x emouze 65. How far from the front of thet*o)t6 iumx zue8f8e 5 car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 68,m1ah6 u5kb sd00 kg, is used as a ferryboat. If thb m 1aks,5duh6ree cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidens9, 9ewxoo7v0b6i ii1 n3b mys $l_0$,$2l_0$, 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 identim8c*: jiygan rjybuvm3r3,x. 1d)(a t cal 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 craneij8n j vd,yg:a.tux)c31br*yar3( m m operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular;lydz0b9p/ 8wbty :ta 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 thtyd98 :wlbp 0/zt a;bye center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7o5j5ttt ),d yg kjbjhiq+f +56–1, and calculate the 6o)5i btjjg+ tqykf5+,5j htd mass of one of your legs.    kg

  Determine the CM of an outstretched arm usi4l t *anvxcpom. h7o07r37jqy ng Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent u v go 896v9;iow,dehcat a right angle. Assume tvcgo,oe6 ;hu9w9d8i vhat the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arfz5*+7 )h4zr phwg spoms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below thepw7+ g*r pzoshz)54h f torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth 1ut)r621taoskcqmu 1ihp n ;9and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 mowuo dlg du:9mfj; l* 9.7-kl..qlntf 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 cylindricaomcxq-+n0 5mzc k,xcmun7st 1 f..y x1l 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 of the s ,oc.x m7m+ mcnzx1k0t-y1ncq u5fx.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 diameterul)3 :rj d9npe 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajecto 39 lju)pen:drry?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29) ad 7o)v s04rcn*9ygf ka*y1kh, $m_{II}$=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 thm;a qz2b8xdt, b 5oy/ke 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 the balloon. With what spxbz ba8/y5m2kt, dq;oeed 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 qwryj l3dg-4c 86:phwand is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, ca:4 wldpyc-q g3w6 h8jrlculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travelint uzrw5/ 9avr1g with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket (u 1isd4 t6umylqlr pkx6*7y 21.jqfs shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot6umk6fij u qs1.xyrl ( 12q*pd7s4lyt ,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5 6fhckw,a u7y-m/s by pushing off with his legs from an 1800-kg cky 6hu-,waf7space 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 1zlt)ez 9te91dw rf m*the other 80 kg, are initially at rest in outer space. They then push eacw*e ft 1zm lrt)e99d1zh 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 elastigh. xfso; q55rc collision with a second ball (at rest) and rebounds in the hrgqs .;5 o5xfopposite direction with a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in 2oqbbn62+2pk2 muucgesq60i a court case involving an automobile accident. The accisu0m+p ob u2b2 6i2keg2qc6nqdent 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 limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total vep99 .heykoxy)/ +tbih rtical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different stepobp+i9 )yxyh/k9e t .h 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 miv nm 9k 6r*m2chf;pgx9*/bg of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will t*ph 2m;r9/c m*6knvbg fmxg i9he block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg .pqo9; v*cv ds*tw /ohblock 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 i v.*v/9;p dhwso oqtc*s 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 6t8l7mhr+e+ .+zfnf5o 1m e us cteqm:*0 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 exchange seatchfe+moe*.srtetz uq 8mn1f +l57:+m s. 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 abouc).kc szrm;4ds+wz : et $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments by an expl+-uhf(r 3 hj*/g;oq,a6khgnxp uht ;tosion. One fragment acquires twice the kinetic energy of the other. Whatpfr,( a*g-hk3g;ux; hh oj +tu/ th6nq is the ratio of their masses?   

  The force on a bullet i0.c /kpi9rl f)x:ve7dfw p,:rnfl6rcs given by 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 9v)lg (/qky, rloayx,$m_A$ = 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 anb.2uprc4iqid 9g h,kvnj)j uae 0:b5mu(,q - f alpha particle and a smaller nucleus. What wil)fvi-r.i u kn4p 5j2uc ,,gejub 9hq:m0d (aqbl be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay targ*3zu * wt(gefiet) is fired 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 sli)ozz3+j1a7qw )y+ cdjihg vx,nsu h23 f09zukdes 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 upper limit o;*bk(7p*h: 8xz d.cxzfs npq dn mass m if it is to rebound from M, slide up the incline, stop, slideh*: cnk;xd zx(b 7qp.8d* fspz down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows theh-k/ybro-dd 4qiow2 1h*4 o de planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn isyw -oq iedk2ohd*-r/ 41hb4od $5.69 \times10^{ 26}$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