We claim that momentum is conserved, yet most moving objects evq( n wk)/lw j+jc.zry4b81 oksentually slow down and stop. Exy/8srjck qkn. j bl+) ww(14ozplain.

When a person jumps from a tree to the ground, what happens to the mo6(tw5w0 aa n gn)o:yocmentum of the penown )0ay(a65 wt: gocrson upon striking the ground?

When you release an inflated but untied balloon, why does it fly across the rrkpa0jcx. e dm6,.sy ;j)jrp* oom?rrxcj0jj*pmpd.,6e. y k; as)

It is said that in ancient ttjg :j19/w uv- avjo8nimes a rich man with a bag of gold coins froze to death while strv/ a-jnot 8:9vj1gjw uanded 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 been so miserly?

How can a rocket change direction when it is far out in space and is essed al*w lvp/astv v1ch6kr0; mzs,.m ;6ntially ilwv t;psklm,zc /sv;6h*vda1 a6.0 r mn a vacuum?

According to Eq. 7–5, the jn4l/k,lj*i;c4rfwjr d8, ju oky 1)vlonger the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, wh*4yk /,wj1 ulcj8 jr fr;4ivlo,dj kn)ich 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 toi+f8w4 mn4z leb(r7ii)miz/ s withstand collisions. Today, thougfbizs(8im nim l4ew+ )i/r74z h, 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 b aual:/hye twbtj2fi,da1)7* aseball further than a ball tossed in the air by the ba2 law/a1 ef uhj7*y,i)tatbd:tter?

Is it possible for an object to ren b c2b;kt-cs(tjm 3-1lt2p xzceive a larger impulse from a small force than from a larg bxccptk jl-m3;n1tbtsz -2(2e force? Explain.

A light object and a heavy object h d6b*jq1oz 9u4r+pnw ci*i2uuz 1y v8tave the same kinetic energy. Which has the greater momenzv rucp w1*t2*jq 8zu n ii9+bdyou461tum? Explain.

Describe a collision in whichewd mrx;e n..c, bz57y all kinetic energy is lost.

At a hydroelectric power plant, water is directed jo 7ui6y)et j1dev;9e m+p ntu(l*ol ;at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, shou9( ;ee)7nlo+6 lj ;eotdy tu*mvi p1juld 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 ayi- kdcw.9i9h wall 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 hf/8lpjni evdm.12 n h4eight h onto a hard steel plate (fixed to the Earth), from which it rebound.p j/vn1l eh8nfd42ims at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carryhn-5td0 5ae g:g-p fyying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is notd5vrogcjsj382ur . v fi82 hx. true for yourxu8v 82rc52d3. fjijgsrhv.o arm or leg?

Show on a diagram how your CM shifts when you change from fp,;sk z5d3zwd )-oip a lying position to a ssd p3;)w zzkdo,f -i5pitting position.

If only an external force can change the mxs ytuy bm z6. 4/w:t, fj9ksbb+8iqd.m2ehr1omentum of the center of mass of an object, how can the internal force of an engine accelerate a c6bqy 4j, izk29stdu ehmy./.+tr1wb x8mf b:sar?

A rocket following a parabolic path through the air suddenly explodes ifdx(2z5b+t9 e oi d6kbnto many pieces. What can you say ke9 ( 6zibd+2x tf5dobabout the motion of this system of pieces?

  What is the magnitude of the momentumz,le /a 9as2gi 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 s. What is tpb:e,,hf2 jw ds usau3ly)2d 7. 2jfgphe skier’s changea.ue, fjsb,f lug)jds w22 d32pp:y7h in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizon-7x9jh,u ra(wy3au 7gbmd- ektal line drive straight back toermwa 7xhab 9 udu-ygj-k3,7(ward the pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out ho,i-zuqjk (1 3ztm1pjuj831w1tkuk fv rizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initf 8kmvijtzjq3 j1ut1w ,( 1 -3kkzu1puially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that(t cs1* )pvli1zblc7g *p,ohg the propelling gases are expelled acz1pglt1b ) h*v c,7*liogsp (t a rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving a)yxz.3j 9inw8xw b ,vxt $4.1 \; m/s$ 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 tra0 3jx0)91zhj y bzbpdvck with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s 9z b1jv)pjd bxh3y 0z0new speed?    m/s

  A 9300-kg boxcar travey+u*;mh+g, guha0viz ling at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of 100km/h Iftt ,niwjz r4jk y:r jur l3h8d56qy:9hjq1n1 1 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 tj9j1 yydw rntju8ri 5jhk3 :6r1lt 1zn :4q,qhhe 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 carx ir),sn,s 6fu coasts 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 fricfux, sr),isn6 tion 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 particle in the dir3jq;g8pl+8f6v2g qbc t rzs)aection 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 2ltgsf683brqq2 g+ja;)zp8vc22 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s pen( ld2lr28ehb(3h z nznetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationab8e2zl zn(2 dh(rhln3ry on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a sf9*us h s4xuv2peed 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 travelingpog- xvw51ec 2 in outer space with a velocity of 115m/s To alter its courvop 25- gxew1cse 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 tx:+ykz )5*r4qh bcvpyhe tee at a speed of 45m/s The golf club was in contact 5 yp+ zbh:)c*ykvxr4q with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at mhyyo( )zt6jx2 +v+ nn i)0 qov)kaxt)-hsr1j a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. ys vn +tt6(h) xov2r1 m)nxq +)oikzaj-0)yjh(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 speed v=25m/s sta+qpy5y,w6g: 9jgha trikes 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 crashworthinesgrvh/28e nl:m g0.wfa8j :tc ks of new automobile models. Cars are tested by smashing them into fingv: tw:mher/k8.j g8la2cf 0 xed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is sten s-9hpz3c2 /jezvr:0yp-odopped in 0.75 s by a head-on tackle by a tackler runncoyz 0se/z39 2phd-v :e n-jrping 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 plwed 5(4k.jutennis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a fwd. ekupl(j 45unction 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 person jump without breakhk)iq(nixi17op p3w 9ing the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (fo 3nqpw7h1 o9x)ki(ii prce 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 directi 46sc+s p2p;h0g bvqiion) 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 collision?Let A represent thcv ; b+issp0pih64g2qe 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 eas - x8zmqqf*kx)t with a speed of 3m/s has a head-on collision with a 0.900-kg puck )qz*m8xx kf-qinitially 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 puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass un c6k 8oj7rpfhpx,31o xdergo a perfectly elastic head-on collision. If ox7jp xr6pk 1 o,c83hfone 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 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 h;m4yn 2t * eud:5vg (xyjtjxe)v(0k zfead-on with a 0.090-kg ball initialgdy0 jv:z(ytj ee n* vm;x (4x2uk)5ftly 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 that is axfg es2b7s+9moving with a speed of 8.5m/s collides head-on and elastically with anotf2 sa7sx+b9ge her ball initially 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 an amusement park ride collide elastically as o6w 7fw*2 0vh mihq0)f(vx hrs(fnh 7jgne 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/ n*w(xfjqhh2r77m (vsf00f) h wgih6vs 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 makesbk )7rd)hkp0 c an elastic head-on collision with a second ball initially at rc)07bd pk)rkhest. The second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a fripfvwq7 qgjg704 zk;4g ctionless 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: Bothk0gv44qw7q pgf7 jg;z leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of mj*)on 0 bb(u2fu1dnp yass 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, pro4xviex ca/ 65/cm/edgps 2y5 qjectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second proj2e /mc/x gs dq45x 65ey/vipacectile 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 2300q*.ki6ea x6*nm18hheeyxodu *zzi3m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pen hmnxeuqi.ae6 oxde y06z3zh81 *ik **dulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lwl3yr36;h,xdy : ysrk ost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an obj0x:0wra gmv,q ect, 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 rep0rv0 m,w:aqgxresent 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 at a r (drx*piv)rw3gkbmode9()p5ed 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 betwee5r * bgv(p3)e)odd 9pmrw k(ixn tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebl4z g/n38r k:ryobr)eounds to a height of 1.20 m. Approximately how many rebounds will the ball may:r /bzkl8ro )n3r4 egke before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two obr;rhrz m.0o)*o2 jeh,je 0ylbjects is the coefficient of restitution, 0*,rh boj moje )he;lr .z0y2re, 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 masgb/ 9rblesvy*e *l6w(o9d t*as 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 reassembr9oly /s*gw*( eba*el6d9 tbv led. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on with aorm136ek 1paa 10.0-kg object moving in the -x direction at 4m/s Find the finalo1 emr63 akp1a 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 sjw7*xm78yjt jecond nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momentayxtjwm *j787 j 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 maswsn c x zda)i4h8wp/32s $m_\mathrm{A}=0.400$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 equa vq i* tfginm,+ fua-jjsb*:u2nh7i4)l mass, each having initial speed the two move off together with speed v/3 What was the angle between their in+ ms:j2ffi uaun ng*,b-vj74q *iiht)itial directions?    $^{\circ} $

  Two billiard balls of 4jbhytqnw- ),equal 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 coll, )tb4qwnj- yhision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with another atom atj fsq2*e:sd(ixo+ 0qh rest. After the impact, the neon atom travels away at a 55.6 ijq 2e:0(ssf*dh qx+o$^{\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) mw6yr*k4 z;axg akes a perfectly elastic collision with another atom at rest. After the impact, the neon*x wrzyg;4k6 a 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 magj az5 lo -xggz(ci nfh.02d8(ss of the three-mass system shown in Fig. 7–38. Specify relaac2gzzgjo .g0h(dl nf-5 i 8(xtive to the left-hand 1.00-kg mass.    m

  The distance between a4kmoyb, x3. .;ljg iuc carbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg x- 4; oi3zqrudcar is 2.50 m behind the front 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? Ass43- iodquxzr;ume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a 3. prxadj04jsj5)n kd ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW cor3an s.p) djxr45d0kjjners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidex* y1s72ysw zgs $l_0$,$2l_0$, 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 tomato paste (see Fig. 7 * +o bx :40x1kdce1egjclv.pe–40), each of which is a cube of length l. Find the centp:1e 0ceg vj*x oebc+4dxl .k1er 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 p0h oxs y* fe9;8oh0m6s6r habdj57ira 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 circle, Fig. 7–41. What is the prdxa ;85o0ih0 9sf*ejs7 o hm6hb6yrposition of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as thzt u( t0sed1s2ose in Table 7–1, and calculate the mass of one o sz2dets1ut( 0f your legs.    kg

  Determine the CM of an outstretched arm using Table 7–1.gdf wp/e9, qmhw 3icp 79)nj rz-qladr28,g+n   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of thwu0w qhu7u.7;ov 1q eue CM of an arm bent at a right angle. Assume that the person is 07uhv 1 ueoquw;u.q 7w155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and dipofg( l t 21zi7:yb2legs are hanging vertically, and his trunk 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–o7glpy1:bi (2d it2zf1.

The masses of the Earth and Moon clt5 wvaj +5+fare $5.98\times10^{24}$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 frictrp -pvh;6se6f ;jlxq1ionless 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 a4 /hops93h b1u cff)xk uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass u31sh h9 opff b/cxk)40.500 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 trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a d71vu/ d +eu2qcb;* a :/gcbnucg:sea diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 v;gebcsc/d2d:c7/n+ g: *e1 buqu auakg 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 7–14 (Fig. 7–29og2p h0x( q oidvp.x6y jy()0xi(w i2p), $m_{II}$=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 v7by2(z *e0y+tinwkc 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 kz +*niw bcy0ty e27v(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 a bat and is popped st id+:4hg.z gyjbxk /b5.p e:hgraight up to a height of 55.6 m. If xe.gg/zhk5+j:i4. pbbh:gd y the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling maqa +-1vu4lg 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 in Fig. 7–43. (dfzd2*era)4mcdv,22 r mwlq Relative dimensions are also shown. Should the player be worried about this being a “scratcwfm22r damz d4)v(d,2*lqr ech shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by pushibj+ endbh0 xr, ao1g5k3 okn6(4go1ring off with his gokrkrbbx n1(+ nagoh1j 5eido436,0 legs 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 of mass 60 kg and the other 80 kg, are initialy , f1n28c,gf7vtlfo ely at rest in outer space. They then push each other apart. How far apart are they when the lighter astronautfv7cyfn2f ,ge, lo 81t has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision withq d)7 yx,)n:lla8hz kl a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth 7l:ah lkdlxnq))z 8 y,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 exzg0z0le) lvrfo)rgu um2* c+;nyk ; o-pert witness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his 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. Shock )zly)2v;mu0r;* zlo ogfeu-rn g0+w 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 thez c0otmh dl/ww, 5.,yl 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 are0/5dolz., ymtwc, whl perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest direg)eekpyod ;+: ctly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet yo;gek)+ :epdbecomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg b7 h:-vjvxc6v;4zb :twn-e j iilock of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the xvctnzhwi; :j6-j i-v7 b e:v4block 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 m,moajm dyv pw9-53hl .ij9tn* ass 75 kg and the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting ato3dm *n.j h,9-mtlaw9 j5vyi p opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass b0 b+u 7wwgh, fubb-xg 16x)ypwas 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 apar zqmkler0k0h2)lvg7)n.dx *ut into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. Wh vl)0kgq*0 ukdmn2)ze.lhr7xat is the ratio of their masses?   

  The force on a bullet is given by the formula F wv.y +j8b4 v1tsie)-ih r5fl j= 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+kxpy,sn6b.t,pq6/ ne2csus $m_A$ = 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 partikoq v+-: cx1rbcle and a smaller nucleus. What will be the speed of this recoiling nuclex:bck vo +1-rqus 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 ;q0m :xeql: s (.y4slbnoae.w at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.a;;j 3gxo2*i*zcp/sx;,7byy;u wkmvcho 9bs0 $^{\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 oa vyi ;*f/4ksr1*aecqac9q 2yn mass m if it is to rebound from M, slide up the incline, stop, slide down the9fk1c aea/*ciy4;rqqy 2avs* incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slin82q3wr upu2 s+ma.ipn gshot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbii pqp+rnm suw8u3a2.2tal 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