We claim that momentum is conserved, yet most movi rxt (yfdbi4*+ng objects eventually slow down a(ry4txi+ f*d bnd stop. Explain.

When a person jumps from a tree to the ground, what happens to the momentul*otetuhb 3m/g g-2f8w oo/r3m of the person upon striking th 38wmlr o go/ *g-htobetf2/u3e ground?

When you release an inflated but untied balloon, whyn2wk ss+ mzt;bni +;tx5pw9s 6 does it fly across the roomnb+ xnmsi9ww 6 tz+s p25s;kt;?

It is said that in ancient times a rich man with a bag of gold coins frozeguo; ./rmuo50/y .ovioq ti 1a to death while stranded on a frozen lake. Because the ice was frictionless, he could not push hi.t r/u0/oogm1 yiq5o v.;uoaimself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket chan dspfed 8st3hzfnyg9d+) 12i3d6,c +mljtny* ge direction when it is far out in space and is essentially in atl+ ddg)6ic+3fs8znd9s d y3mfheyt2, j1*pn vacuum?

According to Eq. 7–5, the longer the impact tiz4km*e3 a+o)o nes-ysme of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deforman ossa oe34z+ymk) *-etion of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. To+s3ucmzchh*cn h 502kday, though,h 5sck+umnchz 2 03hc* cars 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 thhgzux kci63:2an a ball tossed in the air by the batter?:z guxci3h k62

Is it possible for an object to receive a la ctb)8f6m *:iwro b12emn ;fezrger impulse from a small force than from a large force? Explom6m e1 :er28f wb)c;n bti*fzain.

A light object and a heavy object havzf*o gv 1r1u :(,jhqrke the same kinetic energy. Which has the greater momentum? Exour1rv1zq khjf( *:,gplain.

Describe a collision in which all kinetic ene7a:azx ,: vacjrgy is lost.

At a hydroelectric power plant, water is directed at high speed *9z(hy at zbz .eocq7vwsu u3/*j 9h6bagainst turbine blades on an axle that turns an electric generator heyu 3b9*wtqc7j zh*o.9b szz(va/u6. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a p54 .; klpf-hhzk0vz ewall at a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h ont9s+f* 8du ;ny,5 , q /mm9t p6wh-pikboudexfuo a hard steel plate (fixed to the Earth), from which it rebounds at very nearlyin,8mmo/s uk*f ht p p-w96;ddx ueb,yuf+59q its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a )uuf,fz 422 bawda. s2uyp /q2wafyj4heavy load in your arms?

Why is the CM of a 1-m lengtu. g l w*t:j9uxvm r.,pe3gx3sh of pipe at its mid-point, whereas this is not true for your ar vg.xr.ew, :9 u3ups3xj lmtg*m or leg?

Show on a diagram how your CM shifts when you change from a lyit o1 4w5b-mcvdz )fa:png position to a sitting positi :cvb)ad wft m4-oz51pon.

If only an external force can change the momentum ofe f yw+gz2jk(2iq 9e ja;tnk+; the center of mass of an object, how can the internal force ofn29k2ijq;a;(t+ ey gfkj w+ ez an engine accelerate a car?

A rocket following a parabolic path through t skt0vv;xs5d)he air suddenly explodes into many pieces. What can you say about the motiont5d kv)s ;vxs0 of this system of pieces?

  What is the magnitude of the momentu5t+ju u( lqb;pfjm7+d m of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force6/kkys3aallcg8 8 0yp of 25 N acts on a 65-kg skier for 20 s. What is the skierlal/8308y ygc 6k pska’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive straieef yisozf w.bi ;5+p.p7t* g4ght back toward the pitcher at 52m/s If the contact time .opsg.7ze e4f5w+ib fit;py* 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 horf*wg/h qw) +doeh27 opizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26po q27 o*gewf /hw)hd+.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 ex v9c+j thds1 d*ks713o+mwa4 icxgje/ -3od uxerted on a rocket, given that the propelling gases are expelled at a rate of kce1asjjs w 3h t4v93i1dx+m co -/xgo*+d u7d$1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movqmgz; 9/nx lqrx9,lg yg-d 09ling 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 track with a ctu ws 4 ,8mtwif*ux56vi*jy/a onstant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speedui/*w4yxti am*v8f j, t6u5sw?    m/s

  A 9300-kg boxcar travelr8m)f za+q1 oling 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 sr;1-s+r(( s) slficdvrj rj3cpeeds of 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 0.50 m wide. Compare to the typical maximumcv1 r jsr )3j+;(ir sr-ldsfc( 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 coana- vu y0nx.k;chc80-j5zxym sts along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and.mvyxnk jyc hcu80za 0-n-5;x fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alphiwdqbru 5+d; 3o9)2mqzt xbz) a particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 9od t2d; ru3zqwbbi5+mz x ))q222 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 woodw ;ytq (wvz**c and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move afteyqctvw(*z w*; r the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a sp*isc/8x1rrow eed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a velocity ofzp rfiv-6;;lwb x qtv(0 fv3g/9iat.h 115m/s To alter its coursexb ht/6q;0f9zi ;tp-3fv .(vgvliarw 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 g)l81vzspt+gme8bp yg5*nqay9cu6 . iolf club was in con1z86e l t 8cq.bgp5yps9niy* ag )v+mutact 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 rws; yy*l82 va42nxev at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the y;xvn lav2wr8*s 42yenail?    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 dihp4 3- mlxbftf1 74ua 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 1 xtm0 n8 r7p ,wwmsp3s7syig(crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on3in (0s1sx, 7r gmw7y8ppmswt 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 dk92p iu ,i :n.sxvsy1;,fdmy4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler ruspnu ,12,xvdiy kf .9m:d y;sinning due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points in the +x dirnr(jrkkpy 8l)w:g mp dv7 86k1ection and is given by the graph of Fig. 7–33 as a function of time. Use graphicpgdryv1 )n:(6 w8prmk78l j kkal 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 p mj hdl:s/emig/;uijqn1x5; 25z mipt u:5w5j erson jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that isexji /l1/ng:ht uq jmwms ;:5m ;iid52 5up5jz, 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 direcon t3k nn4;6vction) with a speed of collides head-on with a 0.220-kg ball at rest. If thno 6vncn k;t34e collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a spxhi cl(26i9d heed 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-kg 6ix h(l h2idc9puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass u ih;jk0c,ba1d ndergo 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 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s d;0k h1bj,ic ain 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 co*nhm6vs:g7 ht/3 rc davob-3b llides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the spo3/7- g msv*:r3 bvbhh tnc6daeed 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 of3gd;mv.pfw*k7 hn b 2j8jov3i 8.5m/s collides head-on and elastically with another ball initialb; 8npmdhv *7ogvj3w .j2fi3 kly at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in ane*szlzi czw85 :w 9cy, amusement park ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a macesz yw5:8c*i9zz l, wss 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 as :tj(q;7+u*j acxvbu n elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original st qjj:bv+cuusa7 ;* x(peed 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 frictionlj8y -5egc +as7rrwlh.s- 0kphess incline as shown in Fig. 7–35, and elas gwhhc7psk8j 5r-a. e 0ls-r+ytically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of massuy/g+ nhz rc lw/bd++/iy. 9dh 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 hzn o l(wf xx;k95kq)r- of the pendulum equal to 2.6 cmlzkr5xk onwfqx;9)- (. 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 /mv, gb49ftlx q(uji6h vgwdz0/z o7 3/psd8tburies 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 the0h/z,7dvu4fgs l9z6/bj t woq8gi3x(t vpdm / pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy losta*x2tl ke+2b2tk o; rp2 0jgwd, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an objl/ )0l*p egm(dvvk 7m /axlr/xect, 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 heavier particle, and B represent the lighter particle. ) KE'/v )vr lg/mdl x*lempx k0/7(a$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of gbx e(mxas.cl gi;j+kh/k 7 0-a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars slgxc .(;jmah+ -k ki0g7ex sb/kid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from ara,aqd1 j2 kv: height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its energ1aj,q k2:drav y?   

A measure of inelasticity in a head-on collision of two ob z0 *5:gcnolqjjects is the coefficient of restitution, e*c jzg5:lo 0nq, 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 9-8 .ss cknlktmass 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 st c-kks8l .n9is 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 thjj7;ia)t, c9f 0us nd:ifwan 6e +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 final ve;,fafc9:j si nun6 a)j 0iwt7dlocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, a w jwd3y37rw,rn electron, and a neutryw 33j7dr,w wrino. The electron and neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of masse z(osro94 w.a9ej6( ha flp88 zqtjq6 $m_\mathrm{A}=0.400$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 mass, each h q++igyml(dd6vnk9qd :0 -k wwezsmpo; )o+q+ aving initial speed th0)oesq o( -k zqdp9mi+6 :+dww++ky n;lq vgmde two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the origi pgo :.r5dpw5jn 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 ball A and what are their two speeds? diro:drjpg5.pw5 ection 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 w8rhhudl i;5*rx .ckc+j+ .yacith another atom at rest. After the impact, the neon atom t*lu.c;x5c 8+ ycdahj hrik.r+ravels 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 perfectln9 r 8 cyiext)kzu6g,of7kkh c5fm99)y elastic collision with another atom at rest. Aftez ,xkk9c9yf)k8tm i h7f e)6cu9ongr5r 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 shown in Fig. 7–38fp v.6h ocde9 +tl:3: loip by) ,yr:ohfeqk+,. Specify relative to the left-hand 1.00-kg mass.h tk3oerfd9c yo:.q):pp+ 6f,,e+l lbh:iyvo    m

  The distance between a carbon atoqxz6 hgwwd4y84)lukk+p l1 r, m ($m_{\mathrm{C}}=12\mathrm{u}$) 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 frontmyhw/8 y/ m2u1qe6hov5h itz( i9r9kszh+ x5h of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person ha/shqz +y2i 85vhh5 wte(zh9kriy oxm1m6/9hus a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a ferztr(mw rt90g ,ak ;bb(ryboat. If a9bz(t(mw rgtr ;, 0bkthree 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 sidexgwev3iq 7*r , wu.8lt47qoyq 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 identica;u bf *yf 7l 9z/rnvztz9v5rg3l cases of tomato paste (see Fig. 7–40), each of which is *n/vl79v ftr3;z 5ry9uzz bfga cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cut 8 s77/wpxonl1 80l3fum-vgiu cwoj2 wout offw wgo/n7i-u3o 0j mvx82uslc7w p 8l1 it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions qtyy9srv3)a85x fng8are the same as those in Table 7–1, and calculate the mass of one o3r yfq) ynx8s a89vt5gf your legs.    kg

  Determine the CM of an outst7n4o hztczh s0(gu 18oretched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent at a right anbzt( diy692c zgle. Assu cz2(by9z6 idtme that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such thfz(ido7 mwv.7cm62 k dat his arms and legs are hanging vertically, and his trc 7 2wdzo7f.d(immk 6vunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Mo d8 c9m(xt/lhvon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on frictionless i xcj,,/mh8f:uwd j(oi ce.
(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 mass 2.00 k0u7nnfe qs2 )ng 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 handle is the point thsqnn)u 2e0 7fnat will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mag;s3 8 dt1ddnnss 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 handle is 3d nns;gdtd81the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fik-uofper + +u3g. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mu z16az*by p/m/v mv;iass 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 the balloon. With what speed and directio 1uv/6m p; zmzbyv/ia*n (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 pofrc-wzfq:+ b vmx:w06 pped straight up to a height of 55.-:c w+vmrz0 b wqfxf:66 m. 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 speed2ihs58v yysafqo o0/l)u d,o9d1-mbv $v_0$ 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 isv+uhoaw:tjh :-,mpj : a0-pds faced with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this pph:-d0 am swt+:u:vj-j,aohbeing a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space su qs8wdd7 oi mt0a8p( v0g:jf0eit) acquires a speed of 2.5m/s by pushing off with his legs from an 18000 :am 8d(fwdt70s ej oqi0vp8g-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 ofi hbxh0,e 2m+k mass 60 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How fa xmhe,+i0k hb2r apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic di(jpjmlt3wpfl*7/ :p/q y 7acollision with a second ball (at rest) and rebounds in the opposite direction( /3wtlmly*pd :ijj7p/7a pfq 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 jm.228pimwk w expert witness in a court case involving an automobile accident. The accident involved car A of m 8j.wpi22 wmmkass 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 totatm+5 el;xt pt8a3z1tyj- 3lkdl vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the xam ejzdt5p33 ;t8yk-l+1tlt bottom of the stairs?

  A bullet is fired verticr4r i(4hr(phe ally into a 1.40-kg block of wood at rest directly above it. If4 err4( h(pirh the 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 t1r qp+v 2 *1,v wp lthhmge2xnq+6rz:1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic fricq1nht+v2*l ,: v m+rzq21 6ptrewgp hxtion between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 pdz v. 8(nn70 ca319mpsycsnmkg, 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 seats. How far anp8cnzn 3p(a1 ymncs9svd .m07d 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 ai-qf r3mz g. y-v6jtiyx4g-52(hmp m ybout $ 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 exploixo;)l e+) izfg;b. bcsion. One fragmente)o. b;xfbz i)igl;c+ acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = hybrd2c7.*fs ox4ch 8 580-( $1.8 \times10^{ 5}$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 massesx 2xea*nbv.far:bx5v)/xdh( $m_A$ = 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 decay 8bi +yht7s ccrgxnv) 3/nzb+4s radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus c gxh s bz84t+irbnc73/v n+)yif 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) fxww;ldorvh s1 9g6)3 u5i(yk 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 slideshx7qo61zsqmox i9b 63hy2 .up 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 m ah+wmrivwige;48l;k 30eprivc0 8*is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide dr8kw h vg ;4ce3i0;m*r +ivwa8mli pe0own 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 thvqx64r81amx we planet Saturn moving in the negative x direction at16vxq8a4m xw r its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s