We claim that momentum is conserved,3 3j wkdv-p iwu9ymuk* -kf(j3 yet most moving objects eventually slow down and stop. Explaiupjkm w f*(33yikk -wu dj39-vn.

When a person jumps from a tree tox4xyt; npluz6xne1h-5u ,m 5z the ground, what happens to the momentum of the person upon striking the ground?n;m hnxt5z, luze4 py6x-1ux5

When you release an inflaj0-zap yn3klq 4 o-7jpk1v0 igted but untied balloon, why does it fly across the roomv13q -gkl0 jjao0 nkz-4y ppi7?

It is said that in ancient times a rich man with a bag of gold coins /;n+vhai g,tav+z +7v9zes 4dl;r cin froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not lia, g74 ; rand/e chstvivnzv z++;+9been so miserly?

How can a rocket change direction when it is far out in space and is essential,dsi:igk(d0dl h(-ac ly i(0(sgahil-d di c, d:kn a vacuum?

According to Eq. 7–5, the longer thenf*:yzbh/zkgy;- u p: impact time of an impulse, the smaller the force can be for the same momenbzyz-y: /*h;npu f:kgtum 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 collision and reduce the possibility of fracture or death.

Cars used to be builtld4:u 0;.t,yij)uqo/g y kupm as rigid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impactu0/g q :i lmd,u po)tyj.uk;y4. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in the air4sg 4oolcflm(9 1-ufw by w g9u-sc14oollf( m4 fthe batter?

Is it possible for ansbn d.crjc3.ku,vi7 +c-zo 9p object to receive a larger impulse from a small force than from a large force? Expla. vb duicnjocp 79+sckzr3., -in.

A light object and a heavy object have the same kinetic energy. Which has l1obecw*ir33 the groewc13br l* i3eater momentum? Explain.

Describe a collision in which all kinetic energy ila :)vig:m,wws lost.

At a hydroelectric power plant, water is directed at1g.yra slzy71 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 wateyar1.s z71yglr rebounds?

A squash ball hits a wall a(ul). u;gqzwj t a 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 ir)de cv -fn 9;e8p3xwfrom a height h onto a hard steel plate (fixed to the Earth), from which it rebounds at )exr w-p8dvf;c in93every nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backw uzox +uf+ kib rsk0 *q;9dr:tojt38f7ard when carrying a heavy load in your arms?

Why is the CM of a 1-m leng24ycp7u ahd.)b9:olpg m 0gszth of pipe at its mid-point, whereas this is not true for your arm oruogz9.2p hb4)0alcd 7g :smyp leg?

Show on a diagram how your CM shifts when you cf2lazq.1ngkw 7v rs)vau:no 3 k3 :o06d0xvtihange from a lying position to a sitting positio:1wrxa7s)k akovi3uz0qv ld nt6o0fn3 :gv2. n.

If only an external force can chi )nyy9 oei (cr2xd/j-ange the momentum of the center of mass of an object, how can doi9(y- ny jix/ce)r2 the internal force of an engine accelerate a car?

A rocket following a parabolic path through theoxo.de;toy 6 : (c:p6l8nuymn air suddenly explodes into many pieces. What can you say about the m; xyct.el6monn d u::yo8o 6(potion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a sp0l1+jdc0ezz,zazas l+ qc*/t,ek q l:ck2 (vueed of 8.4 m/s+l0cz1/, *eskzq a(jatcc ,: 2qled+u zk0zvl    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg5givtc/ w fad xerivj0 0;+k67 skier for 20 s. What is the skier’s change in velad;+/ g 6xicwv rivekf050t 7jocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal lis ite kdn9t3q4.9:emune drive straight back toward the pitcher at 52m 4q dmet:it.kns9u e39/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 horiz5rg,- , *w zgqmaalt1mz1mm8zontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it w8*zm ,ama-qm,tmgz5 1 lwz r1gas 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 exer-e 8gw:9(qr zy*o iujeted on a rocket, given that the propelling gases are expelled at a rate ug yzer* -q:89ije(owof 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 apparent breakaway for a touchdown is1cq4ep sigjyfk 8t 05+(xt,qr a8/dnr tackled f,r0qtk(5x8gc jd/ft4rae+ spi n81 yqrom behind. 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 con,hoo38iwimirm7 m u/+nmgd1( stant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be8u m/go7 r3 m+miihmi(,odw1n the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxsm+sw/9 o a2gvy *,bj/qh.q cfcar at rest. The two stick together and move off with a speed of 6m/s What is thew mcaqy* /fq+s2bs,gjv /.o9h mass of the second car?    m/s

  During a Chicago storm, winds can whip horiwsd+/ 7zwz; mlzontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compads;lz7w +zw/m re 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 ;5qib.)egykqfv 4zsb9 rk;lc8o3 2u rcoasts along 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 with the tracks, what is the speed of i .g ck9)4krzrqq yu;;8evb f352osblthe car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in q8e 5 *sxyp6aithe direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed do6p*eq5s8axy i es 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 cl lrdp*p 7i88udutjw; o0oy+ a1eanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does 0uo a 78y+oi1*drj8 lwupp;d tit move after the bullet emerges?    m/s

  A 975-kg two-stage rocke ghwzn: moc,2tigd4 80t is traveling at 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 spaceajt )e-c,c9sphop;s2 with a velocity of 115m/s To alpp j9- oc;tech,s2)s ater 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 speebyp*dp6p)aj7 d of 45m/s The golf club was in contact with the ball for *d b)7pa6jypp$3.5\times10^{-3}$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 comn(jh . dz5j2-qxixn8des to rest in a time interval of 8.0 msx5n-8i2xqz d jd n.h(j. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and sqe5rwon 7nu l 5/ceq/+peed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the cr2*w,onbuz., 6 3n7zxi7gpdm ia .b .xhr6gmybashworthiness 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 on the car by x, odz y2a.x.z6 *7hnimiw.3rbbg m,un67 gbp 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 and is stopped in tn4zn 7*rzus50.75 s by a head-on tackle by au z7n z4t*5rns 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 the +x direynj. *mulp(hok q0yi4x, v(q 5ction and is given by the graph of Fig. 7–33 as a function of tiqh yp*(x v,yk4om.u(lnj5q i0me. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking the uq5im lqp 1*05vvwe;hlower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m fwiepu;5hmvqq1 0 5l*v rom 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 irns7*yj 25t cdirection) with a 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 ball after the collisnjc2sr 7y*5 ition?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 speyt0nz , hj/txn3ih79z ed 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 andxt,h0zj/ 379 hny nizt direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perf5qsl cco. zgz1p8bv1i y96d+c ectly 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 movingc15ciozbv19.ycqlsd 8 +6zpg 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..sa si:8 1y +qi6xu/m t;yyroe5m/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 elastic collision, what are the speed axqt8is :+1s ;iuaoy/y6rmye. nd 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 collide34 idk :alt l/hn0v6pis head-on and elastically with another ball initially at reanvk li6hldt4 i 3:0p/st. 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 an amusement park ride collide elastical 40qrig i;) 1apdruqx8ly 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 carxgi ; rq80)adp14uqir 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 an elastic head-on collis-ysbi8gy k sph-7 b+wz/k(4r bion with a second ball initially at rest. The second ball moves off w4bb yb/--(k8p7g k ihy +rszswith 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 inlqyql z,j(3rq/w7s1u: wf6 q mcline as shown in Fig. 7–35, and elasticall:z36l/lqf w7y, qsrqjw(q mu1y 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 objectrwjrh 9x0 0ci( 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 heigrr+obpyzea(9o*4 slzv7h1r 8ht h of the pendulum equal to 2.6 cm. A second projectile causes the the pen*holz+vrr 9(84ps1zoa 7ye rb dulum 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-kg p /wl8lx;,amh8 p :au+qpntj4 nendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertica84pw tx8;/aq:p ljnhamn u+ ,ll and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fracqe a-ae(c mg(hv -)lf-z.g0 bytion of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion bre-tj9 u nn/-6fn gn1rmpaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let Af69/m npn1ungn-tr-j represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped a6bn1ac yhjvay4x57m g/u, y;lt a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the spoxlhy1 /avnmagb564 7cj,u y y;rts car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height of 1. o7 1ukieltj9zl1 +zn*,fsv2n20 m. Approximately how many rebounds will the ball71+ lnzv1si t2knj* efz,lo9 u make before losing 90% of its energy?   

A measure of inelasticity inzbjo*o6 w80cj a head-on collision of two objects is the coefficient of restitution, ec wzb jo068*oj, 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 mass ofnbj2f (vcta oq8 5q1r: the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fu2 trja bfcn51 8:vqqo(se 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 y/*p 2gwoxbm0u x() xu1 s ks7)gr6:v ujy3wbk10.0-kg obje/usuxom k(sg)v: 1jgubp yr*0yx wk)wb 73x62ct moving in the -x direction 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 nucleus, an electron, ip2 w0umfmjte0k -g(9 and a neutrino. The electron and neutrino are emitted at rigt0e2k(uw0g-pjifmm 9ht 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 61jme x51tws(y9vbm $m_\mathrm{A}=0.400$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 collibm k*fd0.hy7pco-m: qoqs/x -sion between two objects of equal mass, each having initial speed the two move off together wiom kcx-qy -:. mhofq/p7*b0dsth 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 origiu- / 98xtog)vxhc hg7x-4gbt9 6kyytkn 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 anuo8x4x cgtx9/y kk7yht6-b-tv )9hggd what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with a47hn/8g k pmrzjtcbd+x.3qa q( c)q*inother atom at rest. After the impact, the neon atom travels ai c/kg *hj3amdn . q8p qzb+4cx)7rtq(way 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 anotherj 5c;1,tpr5hy zi,n kho)mlw* atom at rest. After the impact, the ne5,ycjt*ohwln1 )kzri,;ph5 mon 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 e3l wm ,3ot1 kp hkfw*ds;8ti4Fig. 7–38. Specify relative to the le htlf3pi kmow;d1s w34*t 8ke,ft-hand 1.00-kg mass.    m

  The distance between a carbons2 n7ahuk2ki q5b b3:o 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 00:gd+-n (ur ph9l unxijtt (mfront of the car. How far from the front of the car will the CM be when two people sit in then t 0rjm:g xi9u0u-+thn(lp d( 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 68q.d2q4 d vn(na00 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, dd24 nqq.n(va determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesl** gm, ju u:j(qdw*w kcc-r:a $l_0$,$2l_0$, 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 hiswcy-cl-28kose0 + zas a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center -0+ci8s2woyzc s e-l kof 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 );vg+-. 4, u:xnogx,hmdei2 d eashebhas a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circlbo; + ea:msg),dxehh.4d u-v2x,i nege, 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 7–1, da q)qg zk..3nand calculate the ma .3g. )dqzkqanss of one of your legs.    kg

  Determine the CM of an outstretched arm using Tabq0octo)c.q vdi3 r - pva7r,yelx+c9)le 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 angldf n2co.+-tfw7 4aj3urfl6c ue. Assume that the person is 155 cm7f+4o3 f2.cnajluurdf t c-w6 tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a p qn;lqa 35z9xj) jfhp)osition such that his arms and legs are hanging vertically, and his trunk and hj) qz9l;q)f n35x hjapead 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 Earthxea ox./4dtsz6,jk5 p and 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 m apart on frictionless ij- gz lh,dyd *(9nldze u4kfv4(3zc+b 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 kg and a dio- vffe )xc..nameter 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 trajeco f)f x-.nev.ctory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and +um8dr; r j q,,yzgst4a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.5d ;r8,stzjy g4umq+r,00 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 trajectory?    d    d

  (a) Suppose that in Example 7–1/e bqynfqdr90t0 2 5-ykcha9z4 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and stationaryyg+kl-li; 0bg89c4wim98ye uxt +x ry with respect to the ground. A passenger, of mass m, then climbs out and slides down a rcy8xr;e0x-8b 9tul mg 4 g+y+k9iw yilope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes si/ikq+h: : xvdfa 1ty4f4r u n-t:n.pa bat and is popped straight1 tnxki avdn ::q p:f4+.y4 ist-ufh/r up to a height of 55.6 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 traveli2. bh 9okn;rdwng 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 playerv8hcn rm l 7i(aa.p)v8fd dx;5 is faced with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about ifl)ha pdc;v8.d 7a8(rvm5xnthis being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space sui ,1mjfp( o1ts(k h+aoot) acquires a speed of 2.5m/s by pushing off with his l1 skjafo m+t( ,phoo1(egs from 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 o2 cjn-6 2qwlcyqt4gq2f mass 60 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut ht4wjq2 qyl q-6n2cgc2as moved 12 m?    m

  A ball of mass m makes a head-on elastic collisioexj9o6)t u8mk7.ez dg4kir )zn with a second ball (at rest) and rebounds in the opposite direct.zmjge t7kor69i) dk4uz)8ex ion 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 a court case involving an odud mcpk +1 q(1;j 1jjfia7.oautomobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collioc .d;o fqjj1117a ukmdj +(pision, 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 totx /byo/lv+e ;ral vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal r ;/b vle+/yxopart of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vev.l cn:4( nack ji(xo3rtically into a 1.40-kg block of wood at rest directly above it. If the bullet has a mass ofi ( 3.l4n nk:jx(vcaco 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 becomeb zkkr,,h7ky 7s 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 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, 7rby,kk7, kzh what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowb/8 feqrbuzjym9wlpw* 1 s845x oat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposiul5z8 4x9em8f yjw1sw*rq/ b pte 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 about ;;th:0lj jpnx$ 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 ad o( g1m.zt/ubroken apart into two fragments by an explosion. One fragment acquires twa/ u1t .(dmzgoice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the forxgt5 -f7wv 5tm3n- gdtmula 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 massesqi 8l0osc3 x yyn12(dc $m_A$ = 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 deca7 ovb+w t3uz )ujkj;la f:g/p0ys radioactively into an alpha particle and a smaller nucleus. What will be the spee7:jjp lguv/ +bzfk0 w3)o tua;d 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 targetabu th1jpomdg .-of* cs *l0))) 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.;hzjikbo*g+r5 .4lcm 2kg slides down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is9csy:3dpxp/)vsr4 ; tzcm da5 the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slid9zcxvtdp4adpyms) / 3; s5r :ce down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figus;q+3mgz7n8t:zzz sxrlwt 7w+ 9,y myre 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 mm rszz ;:z+7 mxtgwn3879yty lqsw,z+ass 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