We claim that momentum is conser ckge(e f7x s4z- dm02)qmr:xv ud57qbved, yet most moving objects eventually slow down and stop. Explai(4mdkf2buqzm-ese )5 xrqvdx c g770 :n.

When a person jumps from a tree to the ground, what-smy:5e j0au,1gnlec happens to the momentum of the person u0-,nc: a5sl y1jgmee upon striking the ground?

When you release an inflated but untied babp t6z(ki;j8(arvfv ly;eh(clul c b25 o+o49lloon, why does it fly across the room?+h;pceozr y(a8lb iv(t c4f9 k ;ul6(2bojl v5

It is said that in ancienlejx1,8pqxlr .p w-- ut times a rich man with a bag of gold coins froze to death while stranded on a fxxwj uq1l prp8e l,--.rozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is essentiallys 1gpim-j3qj9pv 77/pdg c*rd in a mr1gds7/-iq79p j* p pvcgjd3vacuum?

According to Eq. 7–5, the ,t7lqq3zig a,v:v c(klonger the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bav:lva,3,czqgk ( q7itgs, 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 tokxs6cq) *.u hr withstand collisions. Today, though, cars are designed to h x c*k.hqsru)6ave “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tohlox3dba cjl ;q4v9; (ssed in the air by 93( dcv ;l4qxhj; aoblthe batter?

Is it possible for an object to receive a larger impulse from a smaa hpyw9)og*+vz-fdy (ll force than from a large force? Expl +fga y-w p*)9z(odvyhain.

A light object and a heavy object have the skbrb c2n+z-9nkp6t j4i-o ryi..n 4 kiame kinetic energy. Which has the greater momentum? Exryj4+ iknc.9tibo n r426kbkn p .-z-iplain.

Describe a collision in which all kinetic eneru vsv f+rd,07sgy is lost.

At a hydroelectric power pl1pt,f 9mi 7mlaant, water is directed 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,pm7ai1fl,tm 9 or so that the water rebounds?

A squash ball hits a wall a3s0c0 gvp)hyilxb( 2s t 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 onto a hard st)ts xscnnix49qqg* ;8eel plate (fixed to the Earth), from which it rebounds atc8i;nng4ts )s q*xqx 9 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 putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a h. .fz wdnz7fgjo2bn4 ;eavy load in your arms?

Why is the CM of a 1-ko1-ryukmvg5z , * (zum length of pipe at its mid-point, whereas this is not true for youor1( -kkv*ug5m yu z,zr arm or leg?

Show on a diagram how your CM shifts when you change from a lying positir3ws:6 0ow1o idp:lcg on to a sitting positionpo3cs 0:iw6glwd1r o:.

If only an external force can change the momentum of the center of mass of a6 dhi 26ygrha8n object, how can the internal force of an engine acceleratdih862r6ahg y e a car?

A rocket following a parabolic path through the air sudde ktnq9.6rdm- only explodes into many pieces. What can you say about the mot -t6ok qr9dn.mion of this system of pieces?

  What is the magnitude of the wng)kx5+4ugahh ,+u m*v m1z srubw(,momentum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 kyskx2w+3 s6 es. What is the skier’s ch s3s6y+ kk2wexange in velocity?    m/s

  A 0.145-kg baseball pitc2w/m9kw51lo en x e,elhed at 39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact ti le 5 wl1/m92exek,onwme 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 ho6(6z1:kpy heunuo 84zmj ;ksvrizontally 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 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance 6v 8pz(hymu41zknu6oks : ;ej. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, gij+ 5/ qbc2hy ven(sco8ven that the propelling gases are expelled at a ravsc(qn y5j2+/ c b8ehote of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movipuxj 3ceq9;y+wmj xm1 6w/ h00j:vayh ng 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 )v- m*y c/vf,s 08/aolszdk s6iken-yalevel frictionless track with a constant speed of 18m/s A 5 k/nc lzkyd-)s6oif8aevy0*mssv,- /350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travb;unq /ij2f)qeling 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 horizontamm,q +hqy6iy3he80s blly 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. 3h y0+q8b sm h6ie,myqAssume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a ckro ,u/ hk4 njtazfzj)ci r4z*r0v; 84onstant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/mi 4zn) izfr4h/tzujk kjar0c84,o;r*v n 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 alpha p)o 32ip:femz-o yqlpc5 icn. :article in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of3ql 2.i)o:imp: p cnce-fz5oy 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood andj648vs ywv*tv emerges cleanly at 170m/s If the block is statw v*4v s68jytvionary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a4f4v 4( o yj r0,hik7ie/ebxdr 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 travelingj9l(9 yqd)p3gwiuc)v z1 qn,g in outer space with a velocity of 115m/s To alter its course by 35.zp,v1ldj(9q9 3ynqg cgi u w))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 4+korc t-d+i/z 9rdy aat a speed of 45m/s The golf club wra rt-/dc+oyz4 dk9 +ias in contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail apn7 x.pn*l8*fucd oh7 t a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) W c7n 8nd*pfhu .7olp*xhat 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=0.0v6; cp)itat)nw d x*z; 4c)qff6kg 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 engineer in chart7k;u at*v-,fcuz yg8ge of the 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) Calcula7k,ut t8*; av- yuzgfcte the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to v6;crg)r9gpe pv2 w/zthe east and is stopped in 0.75 s by a head-on tackle by a tackler runni2evgwr9vp cp 6;r)gz/ng 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 (madi 6t z ,wg/k)nb)g dsc0q9rh:ss 0.060 kg) points in the +x direction kd)tn hgid )src: z6/9g0 ,qwband is given by the graph of Fig. 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 x x6-cm2 ofeiv*dol;mgqb,,6jtb- u /mvo .:jperson 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 is, /o ,mo-fx gj6*6;:ub-ocqxb e.v dmil vm ,tj2in 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 t l-u3g9/jgrsof collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be3g-rt lg9us j/ 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 speed of 3m/s has a head-on colli g+c 5/q(v8nh d1twyfision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic (inyqwc/5v 8hgft d1+ 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 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 perfectlyu7, 69 qtmzmyc elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the oppositeucmqm6 yz7,t 9 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 in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides head-on with a 0ik,db0, aci(k 6+bx zwr3gxlmh ,hu)0.090- bak l h3ih6+cwbm0r ,xkz,d)u(x0,igkg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 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 tt jdnxk l)60/9p k;xolq; yhelu+5sa 3hat is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afte0/3ske5+ khyn; xlj 6au;xlo )pqd lt9rward 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 ridecnel0tz2yi; o (7:dre 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 at 3.7m/s calculatoe:zc (eitd7 02;yr nle
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a second ball pxm2urf)rv;((vt ; vyinitially at rest. The second ball moves off with half the oru2(x t ;y; r)vvfvmrp(iginal 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 cu7; d2iff)o) tic7m e0f-skym,l-qm ihbe slides down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leafi) -ct ,kq;li0o myd2ihmme )ff- s77ve the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of anofc7z*q 9e-vhtc ()gna /d0bi object 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 h ;qlfvwn.-c dzj hgs e f-3r;:(of the pendulum equal to 2.6 cmvw slq:;e ;jfrhgn-cfd(3 -.z . 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 travelinhl6(nv ve i6*z4xjk+sg 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upwar6 izsnj4h+( 6kvel vx*d in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kio 1actr7jp3c he*c5 n3netic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into two pieces, one god8e k4e.zb6*)ewd9 zc:l*oav ; oln 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. ) kw. g69e**cled dbzv ;o8nze:o)o4 laKE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped at a ry+yg yoo85b97dv+ :igo x *xoqed light. The bumpers lock, the brakes are locked, and the two cars skid for x:gdgox85ibo y7q+o*y9oy+ vward 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 7 mib11-fiefja height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will 7j mf-e 1ibif1the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision qqmta(qlx* n 8/ +f75it.srse of two objects is the coefficient of rmt(8s +q.leqa 7txnfiqr/s *5estitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with tht )wf ndj0upy)hp :yb.lk6)f*ree times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed flfb6 .j0 y)h: pdwpn* y))utkin 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 dy8f:d-w.f f4rqn yd (mirection at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each:dr 4fwmnf-qy.(y fd8 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 inton axyk6 8-iwp0 a second nucleus, an electron, and a neutrino. The electron and neutrino are empy0nw 86xika- itted 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 masi; mhyb7vxrl ,21gp;) g of qv81ko(fws $m_\mathrm{A}=0.400$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 col,/b es.b:oczddi6rsb84 il: m lision between two objects of equal mass, each having initial speed the two move off together with speed6zble od sd 8.i,c:ri4mbs:/b v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equa7b20x tnpj.p ypx. ev7l mass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic,.bxjp.x 0 7nv7 t2epyp ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly e zcr5lvm+ h: dd0+ 7h9-m vtjdvdw8tw6,zw z2ulastic collision with another atom at rest. After the impact, the neon atom 0dv5ww-u9 t,w hlmc7 tjz+m+d6v 8vz:2dhzrdtravels 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.hl9k2d3 5n qp, xsz2umfub)z a perfectly elastic collision with another atom at rest. 3hlf2.2 sp)u9md zxubzk,5nq 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

  Find the center of ma+1i3pggpv5l2,ud z mlss of the three-mass system shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg gl+1,5ul iz2dppvm g 3mass.    m

  The distance between a carbon atom613gxf 6m:g5s tpi/hwj uz m4o ($m_{\mathrm{C}}=12\mathrm{u}$) 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 car. dif1gch hr-k2e*o:z5 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? Assuk5*zg e hdo-:cfir1 h2me that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18dd0l3:ghxy1p m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, hp 13yd0l g:dxSE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides cg)b ep;aangug5pv0.yh1. cl+-*rue $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of c /yz) (b9kl4m*a5 fuv l9wzeztomato paste (see Fig. 7yz e m49(9 lkbaufc*l)/v5wzz–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick 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 fcnhah-n u5y;fb:;0f out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig-fhf nb c:y0;fun; a5h. 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, and calculawh eq(n-0a cekqvn 40/te the mass of one of your lea4q-hvnqn wc0 (0e /kegs.    kg

  Determine the CM of an outstretched arm using Table f6 gurer . qc4c+p1m,q7–1.   % 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 ayyn2-s;hxm*i bv -elc177mev n arm bent at a right angle. Assume that the person is 155 cm tall. x1y 7by -mevi*vsnel-7mch;2$X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position njetla+-(p3 jjtv, j3a21zd rwcx1/ nsuch that his arms and legs are hanging vertically, and his trunk 1+-j jvtpn2ez,ajjxct n3dr3/a w (1l 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-dh u73kyj,d zuz:gs 8n3i yp, 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 mx3. d*fel)qn4 1dtxnkrajq(;an stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head ot --lw 63jwlvkf 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 t-wlvlk-63 jwtossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindricok e m,vezyy1t)x+2)jal 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 handle is the point that will)t,v 2jx1zo y)y +keem follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–293f0q,t h0;yq; c khra mf:ya2abz2/ox), $m_{II}$=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 i,3 p0;r: q, ,dfihndwrjpu 9dmts gondola, of mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happe9h,pfdr3rd;i,mjp q0 uw: dn,ns if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is popped straiuvdqz0 emtv8n8*ur 9jj5k s /q5 k+,lgght up to a height of 55.6 m. If the contact time is 1.4 mszq r55 dq+g tjnum8/ksl*ev0ukj,9 8v, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travelinge(t2 cr pqaf(p/mmx8vu2r*1x 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 shot shown 8qpnp w2ile9 jmh2z9 7ax4aifk;k40h in Fig. 7–43. Relative dimensions are also9w0iik8efx 27 42a;pj9zhh a4lk m qpn shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suii 3j 5d9 zxsp7uw,qod 1w,u-bet) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-kg sj3s 579uwq iwodz1x-u,, pdebpace capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are initially a286f+ao;gy,i;smykcy b8c h e t rest in outer space. They then push eachiyfhc;;ks8,2c8y 6y a+m ego b 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 elastic collision with a second bavh*qm 8tdm10sll (at rest) and rebounds iqdmh t01*mvs 8n the opposite 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 asn2efg4s5aiopog0veo f95 5 j; an expert witness in a court case involving an automobile accident. The accident9igf 2j g0a oofep5;55v4eosn 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 of0bh9+n an43ub:8ib ah :quoaj3u4dsdf the top of a flight of concrete steps of total 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 perfed40 +au9bbsa 4oduna bjhqn:3i8u 3:hctly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically z 8lhg,z: xl inwu*hbp62;w-einto a 1.40-kg block 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 lz8b;wniup6 2*xw g,- e:l zhhthe block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood plac-uubmm0- 2f-qhc 7; stfrnrw ;,r .lnr6uf8eied 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 blbir 7 26s8-ur,um.-trlhcn-u mnq r0w;f fef;ock 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 kg, sit in n rzs d*/q* 0bf-jdqde0vb00o 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 and in what direction wilo0r0/-dbq sd0b*ez0 j*d v fnql 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 wadd0an s 8yz-o wfyz j9fjh26+0s about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments b u kumoo5kh1.( 5;bo1hm/zxkry an explosion. One fragmeho1kh;rkb5oo/x.5mu m(1kz u nt acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by anr9afpx /u8)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 g7(4yk/uw ejhbyd*)u9 q *vc:o bq)eh$m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha partijx,thsd-;l zbc2vxx(.lzw4-p4i / fw cle and a smaller nucleus. What will be the speed of this recoixbj;z4 (2zvix,p t4 lc xswlh.f-w/- dling 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 target) is fired at an angle o5*zd6 kf+d gbz.dec4q f 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides d1;sy ksz2q*ff vf6 )/it;skz8wnpvf;own 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 on mass m if it is t+8epaav;bo2 n5dp fo6o rebound from M, slide up the incline, stop, slide down the incline, and collide with po 2;+d 6apfan5v8eob M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturnjganjv2u b/ 46 moving in the negative x direction at its orbital speed (with respect to the Sug nj26/ub 4avjn) 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