We claim that momentum is conserved, yet most moving objects evo1 4omlcq* h. e1r/se ;,gtoldentually slow down r4oegm ,do1thceql;1l.* /so and stop. Explain.

When a person jumps from a tree to the grou;,a sahy-ougv2* ;lv nnd, what happens to the momentum of thay lv*2;usv nhgo-,;ae person upon striking the ground?

When you release an inflated but untied b3jmgp j y0,+t3 luqq.lalloon, why does it fly across the room,3uyll0tqjm +3qp gj.?

It is said that in ancient times a rich man with a bag of gold coins froze:i5nqtye y7(u to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been s: 7qu n(5eyytio miserly?

How can a rocket change direction when it is o74c fm guj ig5o h*r2sa415pxfar out in space and is essentially sx 2 ma1fj45r57o chugipo*g4in a vacuum?

According to Eq. 7–5, the longer the impact time of apr *rkv/30pi* :dwm ffm:dc8 ln 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, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.r*wm8 cd0p3f: p kmfl*v: /rid

Cars used to be built as rigid as possible to withstand collisions. Today, tpi4c 0z kp1f97kb . ohzv-no2yhough, cars are designed to have “crumple zones” that collapse upon impact. What is the 0-k27iz fhkp1b .pvcyzoo49n advantage of this new design?

Why can a batter hit a pitched baseball further u a+bet9+0.hq h ty:mqthan a ball tossed in the air by thhbthtq+0amu .+e 9y: qe batter?

Is it possible for an object top mz-: * c xz(2bf0zff:p3katm receive a larger impulse from a small force than from a large force? Ex capmm*zffzt -f3bk0z(: :p2xplain.

A light object and a h6e cv1ccw-cqm8 pqq10eavy object have the same kinetic energy. Which has the greater momentum? Exp1q -p wcm6c01eq8c vqclain.

Describe a collision in which all kinetic eyon,()t 5 ekzg-(ofwb nergy is lost.

At a hydroelectric power plant, water is directed at h:zr u(u qpi*h*igh speed against turbine blades on an axle that turns an electric generator. For maximum power generatio*r * :pqihzuu(n, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a tl,xz xj((o 4zwall at a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixed to thev z oqps/+x bkvu1.7yh 2ya5-b Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part vo q5+2b.bap1 yx /zvuk7syh-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 carrt0l+ k* qp.fpeying a heavy load in your arms?

Why is the CM of a 1-m length o*8g) rfvp ztu m,3h.n)zq2i enf pipe at its mid-point, whereas this is not true for your armrv 3n)2e)uf tmz pnq.hg8*,zi or leg?

Show on a diagram how your CM shiftsf26-eeyq 1f h;3svn ca when you change from a lying position to a sitting pos aycv1e-62ef h3sfn; qition.

If only an external force can change the mo0w zjw(uhbm+ eu) *u3sy 1; qaxd+ucs7mentum of the center of mass of an object, how can the internal force of an engine accelerate a cacy+x)7(b 0s awq1u;u*uzh sjmed 3 +uwr?

A rocket following a parabolic path through the air yrct1qk q2(tg glr610 u*8ejksuddenly explodes into many pieces. What can you say about thegjg0u(t 6eq2l*8qrkrkc 11 yt motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed of f39u .2ucxeps$8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on 1puqioiq ch18w qw2w+r 5ct e:yh32-ga 65-kg skier for 20 s. What is the skier’s change in vewp 18i ihqw oq -3hc2q+w5e2:tryugc1locity?    m/s

  A 0.145-kg baseball p8dz7 v5(srip oitched at 39 m/s is hit on a horizontal line drive straight back7szpov( rd 58i toward 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-ku8r*anfr).:evqbr4g ba f*l*(d nn w/g package out horizontally with a speed of 10 m/s Fig. below Ca)b8(nn*bgnd4 / lr .r: *rvf*fuw qeaalculate 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. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given thatwsk)ugl-5j i+fs ;,xi4p.y gqy /o3yb the propelling gases are expelqw/,s.gjyfky5gu ix;-y) ol 3i 4+bp sled at 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 movi e iz:ip:hp 1yk.fmi8yy812ylng at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless qn63m/o0xpm +s.o codtrack with a constant speed of 18m/s A 5350-kg load,initially aq. po3cm6o0oxdms n+ /t rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at )uimp218flf3 ugp * wu$15 \; m/s$ 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 spe5h1zqzqcd; z*;bkzm- eds 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 thedmz ; -z* bhqc;qzzk15 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 cox0 fhis9a:o*god+1og acz/ 7 mnstant speed of 8.6m/s on a level track. Snow begins toh9*gd o/xao01 7sfco :i z+agm fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving hg lj67e4f9ubhe7yu; at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has aegujly6b 7f;4he 7h9u 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.27l1m c aolxj(xl 9ed.x-olf of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hil.ld x a(2joe9- lfml xx7o.1ct, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speedd a3rz/muk,)u9ww f/i 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 travelinc4x1fvkjiu) b8pl *y/g in outer space with a velocity of 115m/s To alter its 8jkbc1* /l u 4)ipyfxvcourse 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 tmj* 17g e6d fu(b9j4e:oebiyuhe tee at a speed of 45m/s The golf club was i db:eguy19ejo6je * uf(74mbi n 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 aoww4z1h. kfsbuh+ee5.7yo 3at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse g+4y a73o.1fkeh5o .wuewz bhs iven to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.0sqm3um y7 9.1bagnep)6kg 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 en ysn/v6lg4d*d-y1klc3jh p c(la w/:e gineer in charge 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) Calculate the average forcy6ye3d -p lncvk4l:c*h/g j(a/lws 1d e 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 e 1vg9cj:dazsf/gbs 28 ast and is stopped in 0.75 s by a head-on tackle by a tackler running duegsdz8agb: s 1 /fvc29j west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points jsm -)0hf rs5swno28x in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphics0so 85sn2) -fhjmrwxal 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 ahjpb-eeusu* 11id.z 6 75-kg person 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, in breaking the fall). Assume the breaking strength (force per unit area)u*jszb1-1e6h. di u ep 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 klj2iz 6bb+ /fmg moving east (+x direction) with a speed of collides head-on biz+blf m 62j/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, 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, .eqwey.ws 23t moving east 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 the speed and directio2..se yw eq3twn 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 a3ydyq6 ez 35e5v v,cum perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite directio,5mzdyvu3635 cye e qvn, 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 o:m :w4*xy zwzgwm,x5mf 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball aft* 4xzwm5ywgxmz, :w m:er 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 z)ro(h9 )xrwz)yxcwy+ z,1ad moving with a speed of 8.5m/s collides head-on and elasticallzo,1+cw 9)xr rx )wz(yaz)dhyy with another 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 as7/o.9 2qzun5ls.yo kkeeoxg - one approaches the other directly from the rear (Fig. 7–34). Can- k5oz /y.2kqexo9l7 oe gu.sr 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 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 collision withnol90k x8eg:v5, w :jvsy;apv a second ball initially at rest. The;,9jxkv5 w:s0vg aol pey:vn8 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 frictionless incline as s*z5ed 2 gphq*y-i9qj 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,yz*-d5h9q2j pqi *gse where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of a us5j,)9uwtk kn 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, proje h;pdmb0w/)r f5c lmm4.c7iy fctile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twf lm0cw.h ;/ )by5pdm7rm if4cice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg 5 p0:f stpp0ljpendulum 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 pendulum’s displacement.pl 00 :s5fptpjvertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energ).d *qvia 4-g.mlwiab0d2idh y 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 bf*toalj5q rtt ) * nvxx;(s(38dtox;jreaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in rot xa( xs v(;jfl5;*qx3*t8nt o)tdjthe 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 collidef-* 1)xz;bo ;el ,rjcg5 qisqts into the rear end of a 2300-kg SUV stopped 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 qef;)s-z ;b1,x lji5r*co gqtthe 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 1oh -ur i)e6zwa height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90%uri 6o-eh z)w1 of its energy?   

A measure of inelasticity in a head-on collision of two objects issqkno: /uyp.3*lnj-;k9x5 c*ideonp the coefficient of reso/sipoupy cxlnnkj -5e.dqk;:* 93 n*titution, 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 three times the mass of the othe:4awjki emw04zbguj8e4 *ld6 r. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the feljjmb46k4g0 w*ewi4ua 8d z:use 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 -zjqn 8hd:7z2:i q psfwith a 10.0-kg object 2n -s i8:jhp: 7dzqfqzmoving in the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest deca3c pv :h6ddx*9yym,gn ys into a second nucleus, an electron, and a neutrino. The electron and neutrino are emidyv m ,:*cnhx9dpy g36tted 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 mfpi901 f2lnciu8 2 kwgass $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equal mas9yc wxh6cwf 59e79 pklrrp8- ts, each having initial speed the two move off togethe-9 hxc wrl8e5kf9 69rcwptyp7r with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mac g3 41/v*r/lxwrhzm ass 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, ball B is moving along the positivezw 1mvc/rh3l /*4 axrg 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 collimt( m z:ax8y09fjgrw *sion with another atom at rest. After t:* xfmtyz9 jamwg08(r he 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 anotheh jn,tg3bw)jrs lpbp k4 e/3.)r atom at rest. Aftersl)npkgebjb /., ph4)3jrt 3w 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 oa7 p:,0b;9ktzmo ubvaf the three-mass system shown in Fig. 7–38. Specify relative to the left-haboav9p,kbt 7au0: z m;nd 1.00-kg mass.    m

  The distance between a c9 mc+;ughq2 cx9e nhh*arbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m b,zd9sr6ttxg 1 ehind the front of the car. How far from the front of the xdtt 6 ,g1rsz9car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person 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 ferryboat+a oa 8nbl.pl0. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferranop0 al+8 .blyboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sideqzt/0 l;y77t rcpo*gbs $l_0$,$2l_0$, 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 us() i(i )m wcs6+4sznxxwks7cases 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 the load without tipping it.6(x iszs7u xw (wi4s cs)+nm)k$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole oft w9ie:qzl/s . radius R cut out of it. The center of the smaller circle is a distance 0.80R from the ceez.:wt9lq i/snter 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 calculebs/o xy+./ 7cx2j0 vgx8+ ufpskwi(4lb qnc8ate the mass of one of your leg lgs7qxb 8w +j ocyp0i24 v8(fx u/.kbe/x+ncss.    kg

  Determine the CM of an outstretched arm using Table 7–1. ,dmgvg hpoln.(z /sv+y d(r36v,1hop4z y8kt  % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the positi -/ mwajni3 b,rp b4.hw2ggzjwo8ly).on of the CM of an arm bent at a right angle. Assume that the person is 155 cm. yarljz4.) 8iw jgw3b/n2hp-wom,gb tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a qa. go1t3qw6v ka8i:aq9 8 se*,wuvg tposition such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM willqwsagko*9 iuat8q3ag1 :.evt v6,8qw be. Will this CM be outside the body? Use Table 7–1.

The masses of the Eartv-w2 cv +p:ulqh and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on frict 8hvjhzmn ek1,zd7 h; r2+8xihionless 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 cyli jzk;22ot;zbwj u)zy 8ndrical 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 follow 8w) 2o2 zjjuy;bkzz;ta parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diametez/)r/j01chot a r4p(suqkk k(1s/bu lr 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 p1 / c osrk zblqp uj14(rkut()h/0/kasoint that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fiwb y+nbwexxtu1 lgl 9)r:5iygp: 7w4(g. 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 ux;2mytu8 (ez, 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 z;xye(u28 u tmballoon. 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 strwelj 0 .gfdb2 fb+h;)daight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball)wd2hdbjfe .+f0gb ;l during the contact.    $^{\circ} $

  A rocket of mass m travfa5: ,qjkk-e;* d m 1+uabjxoweling 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 2b 9b5yrm k*e(qdax4y ix.za(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 wil9ar*4k (i(by2qx.a bxezy5dml also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a spc8;rqdt by9 nr,uwh:*/ mcz.yeed of 2.5m/s by pushing off with his legs bwc;ch.8*y:t/nmrd, zr9uqy 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 initially at5za rrpm)hzjb6 7w;:c621u s pdrh: bhr 6db(t rest in outer space. They then push each other apart. How far apart are they when the lighter z6 :1wcbr; :rh6 7bhs pj6(ab 52rtpdz)uhmdr astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic c:0( w3. j khjhytsxqah7y,3ycollision with a second ball (at rest) and rebounds in the opposite direction with a speyyws,3c h(.a kqx3thj:7hj y0 ed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court casuxjq *1jf6w-e ox- h 6i9r0mcgyk/w(w e 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 6wxec -w6wy/kjq0( -o mghix1jf *r9ubrakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total vertikp5 :9 ) x7wggglj9skhcal 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 perfectly9sl7w )kgphj :x59kg g 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 bc-,x4o;p/hbf. -zumalp; fmtz4 t y7.6laraklock 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 the block rise afteroar ptz7l.xla my;z6,t 4ap;ffbmuc /4 -k-h. the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in aj/:y3z xs ahhgwpzo/j +w.d;2 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 of the bullap ;3 y2/ jdh/hzw.gw:xs j+ozet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit iok1t5 s)2aq k *fg)p oeytt:,yn 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 will t*o2 1po5 ystttkqga))fk :y,ehe boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass wom;rj-(rr(r zt0b/ji 3da+ lmbr1 zq3as 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 by a,l0vy o(5c0qr *pw/yqty oug+/ep (xe n explosion. One fragment acquires twice the kinetic energy of the other. What is the ratyol/ y 0,5(w epycxq/(vrptge+*o0uq io of their masses?   

  The force on a bullet is given by tc o9-3abde eztif mwmr .4/jf -kp)dw/js8(a.he 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 ent* kytf1qdpx a9;/945xr vq$m_A$ = 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 xz: m4( 3ul uaiccvz+.and a smallermu z:lzc.+u4c 3(vi xa nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angle of 30;vn f*rrymx3:dg3 3w h $^{\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=2.22:8m,*omhnbq4 ilwiaa6+e eltn.v p 9 kg slides down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 2q/8lby+uogz ve s:48 eya)pe7–46), what is the upper limit on mass m if it is to rebound from evuqelayo+ eb8zsy:/g42 ) p8M, slide up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Seav0lw9 sj5/ x77q5y5itj v qiaturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is7q5j0y7xt5jva9ei w5v i ls/q $5.69 \times10^{ 26}$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