We claim that momentum is conserved, yet most moving objectsg-i-(wwq3,d eikc qag2/dod . eventually slow down and stop. Expd-ig2dqq e.,ko gd3 w/a-iwc(lain.

When a person jumps from a tree to the ground, what haoa0 z c54vp6ckeh0f .sppens to the momentum of the person upon sf6cvs0e5o .apz0 khc4triking the ground?

When you release an inflate 3n/gilmz4iex 1x7j -xd but untied balloon, why does it fly across the room?m7j / ze4i1xiglx3 -xn

It is said that in ancient times a rich man wlgg1icd4.k k2 ith a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not pushl4igg. c1kdk2 himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when i-4 c ;jl4;k1tmqntkp tt is far out in space and is essentially in a vatkjc1t4p ;t-4ql; mnkcuum?

According to Eq. 7–5, the longer the impact time4- 9wv1s ubn9kkkq+fp of an impulse, the smaller the force nqkp9-9s 4kk+vufw b1can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. e/7 -b5afjtbp Today, though, cars are designed to have “crumple zones” that collapse ub -7t5jfb ep/apon impact. What is the advantage of this new design?

Why can a batter hit a pitchm49ipq;g(xkh8 agngd1 yj 6b/ed baseball further than a ball tossed in the air by tha961 mgygp/(;q4d8kbjn i x hge batter?

Is it possible for an object to receive a larger impulse from a small fbphjq2 iil6e7a+m9f /)kn(10z ndeeworce than from a large forcej z6(die/ eeia+pbm )7nq0nw 1f9l2hk? Explain.

A light object and a heavy object have the same kinetic energy. Which hasbrh2ya0f4 x9 x the greater momentum? Explainxyaxb0f2 rh49.

Describe a collision in which all kinetic energyh 6r o4(z,8dxnwda ls6h 4m+dg1npmd; is lost.

At a hydroelectric power plant, water is directed at high speed against tuq+)*yi3ponf u5 i+djhrbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?5d quj+ih ni *o3yf+)p

A squash ball hits a wall ai3:r eektr+yic0qh +) 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 acz* hyj uty:n96 p+52cb 2o2jtcya0pk hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is u 0yap*y9 c2j2+tztbk yc25jn:6hpo cthe 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 heavd1o0tz.5ztu p(qrv2w )p1jx yfxa2 * yy load in your arms?

Why is the CM of a 1-m length of pipe at 2k6(8tpp8pd y 0f,con5aswnf4 hc7rd its mid-point, whereas this is not true for your arm or leg np c08swfp6r(adftpy48 h5oc2d nk 7,?

Show on a diagram how your CM shifts wqtwd /.k3ffi6ry,b 1g kv y3my5tq:7e hen you change from a lying position to a si 613yi y:keqg5vk.mr7 t3bqw ftd,yf /tting position.

If only an external force can chanzpq /53o;jbf*txb1m z ge the momentum of the center of mass of an object, how can the internal force of an engine ac 3pozfq; 1bt5jz*xb m/celerate a car?

A rocket following a parabolic path through the air suddenly explm9)wacr, l nu,odes into many pieces. What a,wl9m,c r n)ucan you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying nd fh wzs6 mf.091*sfwwith a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction forc.zgp 5o9/ix 2kki j8vme of 25 N acts on a 65-kg skier for 20 s. What is the skier’s change in vel8 kgzp.i2/o9ixv5m k jocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizo b68hler 7agj,ntal line drive straight back toward the pitcher at 52m/s If the contact time betw6hbrje7a g l,8een 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 7e6pu+tgqk 0a6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the vqt 6ukg0aep+7elocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propellingxv,l 1pywj+*si( ,nyj gases are expelled atsynlw+* xvjp j(1,y,i 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 anawo8w07 tf/mkryb20 qgz 87 nt $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless track with a con60iq28 lxmof szq2 xn2stant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the ca2xi2n6qm8 f 2qxsol0zr. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelingendwf; zjz/m *;2ti jmd4z;)s 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 q/ q y*r6w+zoe 9:/avkk7npq iof 100km/h If the e7o:v9inq/6*wz r kqykp+/qa air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical 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 constane8tcpnxs: )c)k7v j-h,qe*js1)p ydwt 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 fric1 p h8d*sk)jxvpn j7ycw ,tsq:e-e) )ction 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 a-e4:ml d u3-zp ebmh-lr6ozj/lpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If th6z-4-e p ru3lhjm/ :-zob emdle alpha particle has a mass of 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-kg6dvgs:uxal 7khs c- 87 block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move7s ulg8-vdkhscx 6 7a: after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveu,)3gg hyz ,lfling 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 4pq+8:5 mrbn:wc y2(vmgkm qlouter space with a velocity of 115m/s To alter its course by 35.cl( :wqg p+y mvkm8m :42n5qbr0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed of 45m/s dy/d asirs 3 -6pn7s-jua8 nx3The golf club was in p3u-8ji 6 -s3d7na/nd say rxscontact 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 a velocity of 8.5m/s and come7 7w*4)r3 .brkxhjlwca suj.is to rest in a time interval of 8.0 ms. (a) Whatwj r7arlb.xj.k3ic )swu 4*7h 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 strikes a waj:k +n6kqcx ,b0yau/(x zpo :s o.ycf(ll 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 crashworthiness of baf 2:i ldq-joz b+s 2l8djh14new 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 the barriobsdzjahil 1lb :q82dj4-f +2er. $\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 a qt07qn/+h*vj chkbf+nd is stopped in 0.75 s by a head-on tackle by a tackler running due west. Calcul hj7t*qbf/0+h+qv kcn ate
(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)hsri):)o vna, points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical ,)ha:vso)rnimethods 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 caa5nkw / 0w fa8g-qmc)rn a 75-kg person jump without breaking the lower leg bone of either leg?a0nw rgca/5)fwm 8 qk- 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 (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 v7 );bg1uk)hhi1g uz( e)6zkvgje(gokg moving east (+x direction) 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 the 0.440-kg ball, anj1kgk)) v)zzugi(eg7 v;guo6e(hb h 1 d 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 /h,pph0i3azyoxe (j7 with a speed 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 the7, yp/(a3pheoij0 hx z 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 perfectly elastic hee-uv w6jz :op*ad-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/su-:pv w6 jezo* 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 collp xkvb,07,nr vv5p eu-ides 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 and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball,bv 75x0,vpeuvp, -rk n 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 mov y02xjitg 2us0ing with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calcu g0tuy2s0 2xijlate
(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 one approache;hfd1kg tn y3yu9s)k usn72,zs the other directly from the rear (Fig. 7–34). Car A has a mass of 4 2,1nk 7;hns3usf)kzg9y u tdy50 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on co 7q(7 es/2-gu-benuzls2fon t llision with a second ball initially at rest. The second ball moves off with half the ori fl2/uq- sbgtz-s2ee (u7o7nnginal speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as shown in Fvv22o samq zw28x0g*oig. 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 leave the incline moving hor 0*oga22svq 8vm owz2xizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of mw )* mj it7oop*p1yi0vass 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 ob*hr)n*2d6nl 0ns tm jx3 zyu ;j9dns)f the pendulum equal to 2brzls0 3) ; *hd un2tjj9dxnn*nm6)ys.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself t . +n8orgkvn 3 irvi+8:he,udin a 3.6-kg pendulum hanging odr+8: t.o v8ne v 3ikgrn+uih,n a 2.8-m-long string, which makes the pendulum swing upward 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 kinebye +ynzdevxjh:sm9* . u *8x3tic 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 r,ib0* g 4,v;g bxasrfrest, into two pieces, one of which has 1.5 times the mass of the,;,vrg0sgrbifb 4xa * other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV sted9ly, kupxoe4pc ,5s:5-j-gx a k6axopped at 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 sports car, and B repr :9k-djsae-ax,pe5y4p6l x x,kc oug5esent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m a /i7ztk 5cu,t1fjl,v h 7eyue4nd rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of i4,y,5h/ek fj7uce u7tlti1 z vts energy?   

A measure of inelasticity in a head-on colle(ysd d5mn*.dp6 l3wqision of two objects is the coefficient of restitution, e, defined asw ls3 .peyddm nd*q6(5$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
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 withfz9b1 a.tj4qn8yotq n-7uk f0 three times the mass of the other. A depression is made inn.-b7qjkf 8q01 y4z9o ft uant 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 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 withsfl m k-1bb8(y2kdg0x a 10.0-kg object moving in the (0y2f -1km lbxgk8 dsb-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, aeo3d xb/)eu ev,jzys. ;.a wl+nd a neutrino. The electron and neutrino are emitted at right angles and have momebu .a+ e3.yxe ld)z;e /swjo,vnta 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 maskd x fp+qyy-6s c4qm1gw0 zy2,qjh)+ks $m_\mathrm{A}=0.400$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 twe 6alx2 o+xa1*tec am*o objects of equal mass, each having initial speed the two move ofl*6a a*t ceo2x am1+exf together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and 8 rdd:f (z,o(rctsas4meet 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 colli,4ddrssroa8 t( (fc:zsion, 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 atoms1qxj*jy ri zu+l9i 98 at res sx uj8 zliij1r+y9q*9t. After the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision with another atom at rzvltqwh)7)b2 .)lauk est. Af w2) qzbvlal)t .h7ku)ter the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. S( pyf4x 6)g 1q/dpapyoks;fu8pecify relative to the left-hand 1.00-kg mass. sgp)ofu ap xy/(y846pkf; 1dq   m

  The distance between a carbon eeklfk:k2.rtki3 b , *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-kg4-xonxzh) *moc*o,5z;p rra(bgf -q i car 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 nq;r(p b xg4 -mzxiro oaz,f)5-*oc*hin 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 mjduri(.p wc8gbx06 bmupv(g( :t6r y)ass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferrybotbpub)igcr(w8. gyj6 6m (:vp 0xru(d at.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side-;c8abl tjq,r dg+6 mns $l_0$,$2l_0$, 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 ha7sd, vqwf/ zh9s a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up thfwz, s/dq79 vhe load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a cihborp ioerx ,-;l,uf9 y1x+;orcular hole of radius R cut out of it. The center ;+h fu;o-xor,r pilyx9ob,1e of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calcvi s.ip xxx-n16-k z9hulate the mass of one of yx-z.x s nx-69i1kip hvour legs.    kg

  Determine the CM of an outstretch(kml(r. b r5joed arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the p9mgsk,d,xh2 kosition of the CM of an arm bent at a right angle. Assume 2k dkx9hgm,,s that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position sul: 1fs up8zqi5c9vy o8ch that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far beloocvy8z li f8:1s5up9qw 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 andpl 78y p4l*/ lu dlsd7y(uc7ry 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 av,ywgg 4k5 tzb )x.4dman 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 hr+rgifdo9ffu ri5 ;4*ead 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. +rd;f *4f ifugor9i5r 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 heaa;j/l+ af fs0wdvw:1zd 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:f0fa; +1vsla/w j zwd 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 Ee2qkz iw;/* (q5wbbsw xample 7–14 (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 t 6h0 o *rkazcdz9v8g:6 vir9sthe 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 diz896i0rzk dr gvht:a9*6vo s crection (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched houtu f8,;/: zfwgqud)orizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force wfqf8og;t ,)/: uuzud on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling witsb7q(76z pk),on+dh fnwlp1 gh 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 f xz9g m44ruq/laced with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give dlr xg4z qmu9/4etails.

  A 140-kg astronaut (including space suit) acquires a e5 xss,wj*x fu+u9r( pr(nd 9cspeed of 2.5m/s by pushing off with his legs from an 1800-kg space capsul(nu(e xp+59wsfx, s9rj*druce.
(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, areg1g7.s;vkzx j jieggi6 9o4( v initially at rest in outer space. They then push each other apart. How farx.7( ig1iegkjz; jgo6sv9v g 4 apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with - c di; cr1q8/nxsxsi0a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the sx/ s- cd1;cs 0i8qnirxecond ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert w7wx8vut4m ar5) *7 8fosbojx eitness in a court case involving an automobile accident. The accident 8f)bx8sae * o 5477 jroxwmtvuinvolved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concretr,r) 8 d+kwtoa rb-- 6pbyaw;ve 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 pe w8- ay6va;bobt d+,w)-prr rkrfectly 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 fs 7rap6-vv (eof 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 the block rise after the b7v-vse f6a (prullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes emb yqgue.ayjh,.. :*qqg6v 1hbyedded 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, what was the muzzle speed,y6qhyaqj..g1eby*. ghv q:u of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in .sb7* t8u(tyyhhi- fwa rowboat of mass 80 kg. With * 8s-fty yuihw(7 .thbthe 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 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 axl )q)p9my q+kjbv)l2j/v ,hjbout $ 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 fragme 0gtrle (k.h +bi:8zjwasn -.ints by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their mass. -hi8zw+.rtg (ieljns :kba0 es?   

  The force on a bullet is+e xj8 idlhv+swayxf(+p*08p given by the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of massese 9f/qpr1xkykg53shf50r7* zd8r b ma $m_A$ = 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 particle gi6)a;;u9sfm sgnx .aand a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of t9m g.a uaf6ix;nsgs; )he 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 targ4mwj i 2bzm;c-et) is fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 301,ml.kq)zjl d; xa/f p.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 limxv8r d8cycm65 it on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide wi 5vx8rmcc y68dth M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows t1fq tfi y,.51w;u)qc5eok i v(dds2twhe planet Saturn moving in the negative x direction at i ww)f12(ics5df e.o5;qvd tkyqi1ut,ts orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s