We claim that momentum is conserved, yet most moving objib5 d5 fk4n/1u(t wlglay:)ktects eventually slow down and stoptkgl/ft (y5da4lni5:1 ) k buw. Explain.

When a person jumps from a tree to the ground, what3/ tvyeo )q-ir happens to the momentum of the ty)e-oqir v3/ person upon striking the ground?

When you release an inflated but untied6mugqja1u h8bf (* f0y balloon, why does it fly across the roomub80fj6 1ymu qh*f(a g?

It is said that in ancient t4wdlvn)9-/ mbbt3 -fet4f zvc imes a rich man with a bag of gold coins froze to death while stran-ff/tt v endb-)lbw39 4vzmc4ded 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 s:) ko2ar8vquv pace and is essentially : u a8oq2r)kvvin a vacuum?

According to Eq. 7–5, the lojys 8;k3gmcl1zr hnn6ctu) 94( gvdt2nger the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation ofcvc)9n8 drmg l(k3j tzgn6;1 y24 suht 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 w mxg1l(b (xk9 kd;zl*1wk 5dquithstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this new dkbm*1 gxqk (xuwzkd5l( 1d9 l;esign?

Why can a batter hit a pitched baseball further t;ry:d e9cjasmh w/ -fhc0xo76han a ball tossed in the air by the batmcy97;h/ow 6ce: fja x 0-hsdrter?

Is it possible for an object to receive a larger impulse from a small force thanko(n0eok(f5 :uk d w*mndd+,l from a larg k:e+0nol 5(m(n, uof d*ddkkwe force? Explain.

A light object and a heavy object have the same kinetic energy. l7e:v a8lw. hf1k/ev.p fk-kiWhich has the greater momekpvaf:. .wi 71/ el-8hklfekv ntum? Explain.

Describe a collision in which all kinetmx- ri,6ryi2y6 u 5giu*r/ fi6.ldb*r,ectiiic energy is lost.

At a hydroelectric power plant, waz2 ;7sne dyel;ter is directed at high speed against turbine nzy7dl ;s2e;eblades 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?

A squash ball hits a wal4e9xaik c0ulvmi 5u *e1+: v4lud1zqb hfg24sl 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 th/ :yhf+l y aia00m;gx)3v aoqle Earth), from which it rebounds 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 a3vo0/ +a)ga;y hmf ai lx0:ylqnd sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in your arhlb5e4nwbt /1)v isno 4,t:r7qzir/x ms?

Why is the CM of a 1-mo 4jv/bnjs,+atn5 n92 jlmo. v length of pipe at its mid-point, whereas this is not true for your armotlms vna+j2nbjovn/., 9j5 4 or leg?

Show on a diagram how your CM shifts when you change from a lying position to a 1p+7he0ocn9tepwa (j sitting 7tjne e+w90 p1oc(ahp position.

If only an external force can change the momentum of the center of masss ,e(9s*y 0 cwg/q 2n2wg *tuhhohx1ke of an object, how can the internal force of an engine ghy e2 gexwn, okswch9(h*t 1q*2/su0 accelerate a car?

A rocket following a parabolic pat- xmkhwa39g n9h through the air suddenly explodes into many pieces. What -wmxn 9h9k g3acan you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow ft0gqzw/(. ctq6v a .;9edcdp qlying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N 2+;vz nq(o w nr+gki1wacts on a 65-kg skier for 20 s. What is the skier’s chkvr ;1iwoz nnqw(2++gange in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal l 2xnbx (kb7w: -x2fxgsine drive straight back toward the pitcher at 52m/s If the contact-x7 bkbfgxs(xn:2 wx 2 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 pat.x+cszr3, tdxt v +/sckage out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assumin.vxt+dxs3z+ ,/c t rstg 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 thef- sls5.p9 u. qghxx+q propelling gases are expelled atq sls9hx qp u.fg.-+x5 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 atukdu) ,ld z(*m.o9tgn $4.1 \; m/s$ 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 frict /gzg0(q+/)d bjpjkwfx( hpah 04ykf6ionless track with a constant speed of 18m/s A 5350-kg load00j6 gpx+kgydazqh /kw4/fp)j b ((f h,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travcvg8/;fw qd.n(slh g.t,9zfjeling 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 If t ;f4nm6myo,eg (git3ghe air strikes a person at the rate of 40kg/ygo(nm6fti ;g3g e4m,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 constant speed of 8.6tn w 8apk)g0+qtc h ,zdd98k5em/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, wh w dpa+ edzt,8gt8n9ch 0)kqk5at is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emitrp:-xj)5eue z2a+ hrmic n6 o (z9cmy0s an alpha particle in the direction cj(zhi0 5: a9)m +urxzeryc2p ne-o6mof its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood a/ 02u3t1wrp tpkgq /gnnd emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move afte 0 /2tq u1t3wpk/gprgnr the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speed zglqzr (:m x-1v dni7+ gdb-;jof $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space /s8 k pl6o/wceq5q4f cwith a velocity of 115m/s To alter it/cq wq6cks p/e485lofs course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the *uku /j qizwx( vks(l o94-x4btee at a speed of 45m/s The golf club was i*k-qu z4lvjw4o9( i ux(sxkb/ 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 at a velocity of 8.5m/s anxfgh/0p /i( jyd comes to rest in a time interval of 8.0 ms. (a) What is the imyh0fpg/ (ji x/pulse 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 a sekwxg(uebb(3fw87 2 nd speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthiness of new a(9r, mwkh4 7yuup ;endutomobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A ;m,kpu(w9n 7d4heruy 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 stopi:vtl/mj 3h(y ia3 1bhped in 0.75 s by a head-on tackle by a tackler running due west. Calculate 3iy hlh bva:(i t1/j3m
(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 tennisfg)/va2dpqe pua, 71nal 9c.l ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of timead2,)c a l a.pl1gq7/v9pfnue. 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;j(z(a5svx89 dcga hx can a 75-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of v ( 8xgca9(sdzhjx5a;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 kg8 bs .bwf 0a-xyr+iifcmxn4mz9(c83x moving east (+x direction) with a speed of collides head-on with a 0.220-kg nfmzx8sax br 4x 3 +-9 (b8m.0cfwicyiball 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, moving east with a speeo (z 8yuo+sqo-xlc 89ed 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 dc e+- ooolxz(y9u8q 8sirection 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 .5ztp7 tau sr8elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite zt .7uprs t8a5direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a spxcf9r,2 b/,dhoux ismu(q/ / teed of 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 9xf/shqc bm(/tu/ , ,drou2ix 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 moving wi5t 3dr 5wf;gnoth a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softbalw5 5gn;t3r fodl 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 ridz dq3g9plv6 6o ds-(uye collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passens- odz q3l(y 66vug9pdger 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 makezc0a3c kgwrb,*p:mey r- +9dzs an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of 3z d+azrgre0k c9wby-:,m* pcthe 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 incle68.z yplcm 29l lom*oine as shown in Fig. 7–35, and elastically strikes.ly92pc *mo e68lom zl another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case ofj9dao)m 9 1zin94aq za an object of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a maximum heig4u lu6)pl4w;z f;h*f4 irdpn iht h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to s4) *u w6p4rldnzhp;i;uf fil4wing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kgyz+b,.rew.lbc 5h+hgq72 ta r pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc.,bqhy5rcg7a+.lzr w+he b.2t Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of khnj8nxo4s;ivg w:tx3u ez 5j23 e:yy0inetic 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, init k0gnry./ag *bially at rest, into two pieces, one of/0brg.ay g*kn which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into thyva8 cx olqu 9tx1cn868exoio0 ;;vo gr :w-+ae 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 the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact.vogxxno 981v 8- iqao y0o;ec6wa 8utrc x+;:l 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 rebounds to a height of 1.20 m. Ap7ykln k -xvbuvp,qzj53p*4-)v/lxkq 16zyu bproximately how many rebounds will the ball make before losin nylzzvj7y1 ,xl kp3*) bqv5k--p u6/bvuxqk4 g 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the co rz /;f/spn2dnzo2r 5sefficient o nd/o/frzn 52pz2srs; f restitution, 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 th d8rhoa.; cv lq6,onlkl.* -rl ,/qwvue other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-sur-l,ll *o lvqchwn,r;k. 8q.u6ovad/rfaced 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 direc6 .xuu( 2-x yeqh;xap tiqz,5etion at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass ipq6u(e.5xq-uta x ,y 2hxze;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 seco w7yohto.11pand nucleus, an electron, and a neutrino. The electron and neutrino are 1wao1yp ot h7.emitted 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 mqhwcc e0v-,+ x.rzn)y2f,agr o0 1dybass $m_\mathrm{A}=0.400$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 betweeg(t r8 l2nd /5 .whhu:dg(yo7jl x,dqon two objects of equal mass, each having initial speed the two move off together with spo27qldw .,y(lg(oh: t dhrxj85 nu/dgeed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move aqns ox.+rdi,a.u)z )ct 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 . d.usr)zaic+qn ,x )oto the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A 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) mak2*t qc /sur3fkes a perfectly elastic collision with another atom at rest. After c uf q*3/tk2rsthe 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 c0f+s0b y,idev5g op+mollision with another atom at rest. After th v fgs5pbd0+o+,e0yime 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-ma) x*z utwuo hm+*t(ghu,28u kxss system shown in Fig. 7–38. Specify relative to the left-handuxk* 2+g x(u,tu hwh)zmo*8tu 1.00-kg mass.    m

  The distance between a carbon atom (o6m ;c6y xvn xll19u5w$m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind tht0u:k+z + gvn5q(lhgce 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 ktnhg:gul ( q++v5cz0m 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 a0xwa ne1 tylf)lh) 1/jmd 2+cc9r,cpks a ferryboat. If threecmt)1/y n clxj)1+rdl20eakfp cw h,9 cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides t39op6lov 9vx ,i4bnj$l_0$,$2l_0$, 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) palletmnjwc.qa z4uh t- x+dz6p-(h6 has 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 hwc.m pd6ujzzx-nh-+6t qa(4 crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of ra z.b :-c*3f7yrjfrvs ldius 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 position of the yvr.cbrj 7fz 3l:*s-f center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table;o8wyjsmfd/,e b rmqt:i44id u21 9jc 7–1, and calculate the mass of ono;j bmj4td 8qys9/ur : cw 2e1,4dfimie of your legs.    kg

  Determine the CM of an outstretche get63ouv :j:td 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 + 38ze2fu7h(o vobcy4uu g)wiposition of the CM of an arm bent at a right angle. Assume that the person is 155 cm taug4b3oo+z e(h8yu c )iu2fvw7ll. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such af*1xaj6q71 z g6su lkthat his arms and legs are hanging vertically, and his trunk and head are horizontal, calculatj 167kau1lzf*xga 6qse how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Mdh*k-4lkn6jj 2k6y;o/d k+e-qfw sg ioon 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 apar2vir+.(o wm f8b xgd( g2)cswsw8akj ,t on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg anr8-xp)plpwf8r b5i *rwb l x+1 2+k:xjegpd9 pd a diameter 0.0800 m mounted on a uniform cylind) e g1pir8pp+p pl2j9xlr wf :rd+xw*8 k5xbb-rical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylo1ys ,1rp-81nfi;dn rn48;f o d knrcvindrical 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 n41nf r,cnkfy; n8 ;r-rd1 8dovpsi1o bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Ex s8*x mejlwqp(v n*5 .sv0ta;tample 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, f .t:/0dx *,z/a55* erj wxusqldjiqtare 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 bf 5ed5*0jsj,lza: *tqix q/.dxt rwu/ alloon. 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;yhtw y:ep6 8mraw-nh dc(,o ( bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the a t;rd ywa(cn,m6epoh8 (h- y:wverage force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travelinggigxjd(p9 ,vx2qki2d6d-8ch, r uh.a 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–jd3x-weh y2:nt ;y g7o43. Relative dimensions are also shown. Sho eng:t2d j7w3h ;y-yxould the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires avm*n2b 9 ckpm7 speed of 2.5m/s by pushing off with his legs from an 1800-kg smc7 kv29mpnb*pace 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 other4 if yfvy eiu;(qs4k,o k7,u)o 80 kg, are initially at rest in outer space. They then push each otoykqif f,o;us7uyi 44) ev(,kher apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second dcen*4k ;8k qzgh;, 8 ig8psrlball (at rest) and rebounqp8gzdke;48* sgk8cri ;h ln, ds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a p2) ke()phck z:g,zlu*e4tar court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into2r:z hpzk*te,4 pa( leu)k)gc 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 concrete steps of iug plg74j(jnl j3 ruhi7:/ k1total vertical height 4.00 m. The ball hits four times on the way down, each time stri:(pgujlu77i g inr1jl3/k4hjking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest directly a9zq6( wcql1b qbove it. If tc6 q(9qqzwlb 1he bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes andp9de / wr2lox.-gkh1itfg1 e + becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to res/d t1wf1-o xrgg2p.e le+i9 kht, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowboat of mti)ot*pv6 8avepv90y ass 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 far6v *vo)vp epy8a9ti0t 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 ,h u)vc49vlel 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 an explosp nhhnlfo-z9kwr+636(l uo rq)6wqy /ion. One fragment acquires twice the kinetic energy of the other)wlfq66 ( 3nqow/ 6r9nl pyr kohuz+-h. What is the ratio of their masses?   

  The force on a bullet is given by the formulamn+(ghs 41+bx6ojb wu 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 kr7gig.s . t o(btr)97,iflh i$m_A$ = 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 axqq(58i 1iu:y1 mt ayrn alpha particle and a smaller nucleus.uy(t:q11ii amr8 5 xyq 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 fire-wc3 -wgsevh; d 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=2.2kgk6,/:nivyqnji rj881 ucm bv/m 0z-pk slides down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the ,z.t8ywdp uy 8g2qf ;lhuwe2:upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the inclin:lw.t2 y8p ,ydz ugwhq;uf8e 2e, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. ts5 c;)p3 swg3( 1yy4l-sn+swb kc wsoFigure 7–47 shows the planet Saturn moving in the negative x dire yws5csg4 n -c(s1wpsw3ybs;kol)3+tction at its 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