We claim that momentum is conserved, yet most moving objects eventually s-dq/ximrymp 5 fo w +gf(xy3 6))k)crwlow down and stop. Ewm( q)f 5/3)pr cd- r+o mxf)yw6yxkgixplain.

When a person jumps from a tree to the ground, what happens to the momex0is5e -.uvd1lt ci5 v rp-ao:ntum of the pst0a v .uieo 5c vlxr:-51dpi-erson upon striking the ground?

When you release an inflated but untied balloon, why does it fly 9(hpn( +0(ak alvord e2q)afcacross the room? f2 + (haal(op0anqk)d(c 9ver

It is said that in ay/p2, huvgk x2ncient times a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What couxkyv 2 2gup/,hld he have done to save himself had he not been so miserly?

How can a rocket change direction when itl)lc-5e m azs oyqdn9ui 67w,560xgqj is far out in space and is essentiallyeo0ix)qclw76 9 6,5gslzd- uqnayjm 5 in a vacuum?

According to Eq. 7–5, the longer the impact time of b 9g/p)zzju5q s g2v.yan 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 bag)g9qbp 2z j .vg/y5suzs, 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 withstano-h*zla ao1f c8s1 wd/d collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. Whal-zc1* 1/foa da 8hwsot is the advantage of this new design?

Why can a batter hit a pitche, /byd*u3m wbe bq:ukgt845esd baseball further than a ball tossed in the air by 5 umd,b u43b gq*yb /8wkese:tthe batter?

Is it possible for an object to receive a larger1mt 5mx )z*top8x0kff impulse from a small force than from a large force? Ex x)m xk5ftm8po0*ftz1 plain.

A light object and a heavy object have the samwlh9j5lz d0v/e kinetic energy. Which has the greater momentum? Explain.ldz5 j0lh 9wv/

Describe a collision in which alqys)a52qkre : lhn+ hwgh/-7 fl kinetic energy is lost.

At a hydroelectric power plazq155t qyci p8s cj)b0nt, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turb81cyz) c q0p5i stqb5jine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a walw( wdmm s1q2;ml 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 )i zb+n5sa tg*the 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 fallsnsgb)i*ta5 + z and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in ybd za- r l9uo1j00ym1.p3mf geour arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is not trzi rk)/cyyv.fz:ix;u 1dg5r9 ue for your arm or )r1 9:dzcrug; viyykx/i.z 5 fleg?

Show on a diagram how your CM shifts when you change fszc s(*fhf24grom a lying position to a sittisfs(*c h24gfzng position.

If only an external force can change the momentum of the center of mass of a-xh6lqw tv7a 8n object, how can the internal force of an h7xa -w8qtlv6 engine accelerate a car?

A rocket following a parabolic path through the ai; m-hi 6hxgf8siah+xn+d6x*q+bz )j tr suddenly explodes into many pieces. What can you say about the motion of this system of piec+ dm*bhs6ghh ijx8n6-z xxa+ i;)qft +es?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed of im.f7 75v8no/mss;xep7 dygx $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 254 kx(n f5c rd2.k0mmxi N acts on a 65-kg skier for 20 s. What is the skier’s change inn0k( r.xxd m2mi4cfk5 velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a hori2 ch./p*oi qmdzontal line drive straight back toward the pitcher atpc*q2mi./hdo 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a speed of )3nk a8)wok zatgk:(c 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and tha8okan3)kwgk z :t) (act of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerte/4 cqoaw p, x/y:kuf6dd on a rocket, given that the propelling gases are expelled at a rateod4k:pwf x ucqy6 a,// 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 a7 nb/ n/ 6jhs5n vqcu7uf,dkz(t $4.1 \; m/s$ 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 c8 yc v-n/mnvo/onstant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the cac/8yon-m vvn/r’s new speed?    m/s

  A 9300-kg boxcar traveli,urz crc 8 ;qy4whayp8gsx): /ng 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 the +fh b-r0f;sk pair strikes a person at the ratfb;0hp-kf+sr e 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 constant spel +py ws-t4j,oed 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 friction with the tracks, what is the spee4w +yljp-,sto d of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpz,l6h)c2+zt,ogbqer: 8u bo fha 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 a mass of 222 u, what speed does the alpha particle have when it is em:cz +e)uhqb2 ot , r6,bzlf8goitted?    m/s

  A 23-g bullet traveling 230m/s vcock6i 21m7n5lalv)penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emergvc m26ok7l5v1c nail)es?    m/s

  A 975-kg two-stage rocket is travedo3s38i dj *uiling 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 outer sh-ym 7-nkmu9h c9 8ifwpace with a velocity of 115m/s To alter its course9w - n-fk8hm7ic9mhyu 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 t-4tzx 0iy9ek;d0 .sdyw)*f kjmsp2my ee at a speed of 45m/s The golf club was in contact with the ball foi-szk9y 0yfktm.0pe ysw)jdx42* ; mdr $3.5\times10^{-3}$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 comes to rest in v ,rsmqo1znv5k9 g g0u 5wa-b;a time interval of 8.0 ms. (a) What is the impu5gbav-n;0v mqg1o5 z u9kwr s,lse 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 strikesvun p4w2+ t )qcyepmo5;s ;w/k 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 exgo fyj (67xc7ngineer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive bay 6o77jxfx( gcrriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in 0.7v li1ct) -q cfg;bc0.snxp(e:5 s by a head-on tackle by:sfi-n)v0;tecq xp1 lgbcc( . a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points in tlb8t)zdvk p592 2rbm rhe +x direction and is k8p)mrd25 92l rvb tbzgiven by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kge*aziz bqe:tt nj0( 7: person jump without breaking the lower leg bone of either leg? Ignore air resi:nzjzbe *a:0itt 7qe (stance 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 kg moving east (+x direction) with a speed phb y+;k 4.varof 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 thh+ a.v;byk4pr e 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-on colli,r:bztftf1,div27u q sion with a 0.900-kg pudtt,7uz q,v bf if:2r1ck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfeq)1 cuna:(e41d zo .some:b .lc;rmktctly elastic 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 aft tcoenemzu41)1 ;s o(clqb:.. ak:r dmer 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 2w gm1vs(-puq ) f* zrj-7r3:yiodnd1 s.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming 13dn jss:ip1mr7v(qfo- dgw r) -y*zua 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 f3l,,jq:hm9je+fp b x) xv b-emoving with a speed of 8.5m/s collides head-on and elastically with anothjv9)+p-efm,, bfqx3 h :ebljxer ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as l2:kdqx;uro sat he9p7i,)o 6one approaches the other direp s 6kh :eo il7d;a9,q2)uortxctly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s 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 baz1iratf8). mr ll makes an elastic head-on collision with a second ball initi .8ar)1t ifzrmally at rest. The second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as showt c +;c8/vfsrrn in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half itc rrv/scft +;8s 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 of an object o,sfywmrat4i c39:r5yli835 vy zzv9jf 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 maxk,fo ky* . qfb drz/ezxopx7+-k4)3nzimum height h of the peo7/4ynre k -zkb.z*f xk)z3q,d +xpfondulum equal to 2.6 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 in a 3.6-kg pendulum fs- xn9i+/k8gz t8, rfwdbhc 3hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Deterh8d ,ztfcs kx/nri wg93b8f-+mine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lg( xdh-g(kh7t rtv(/:6 vbbjkost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into t28frbrg4 mhy1wo pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how mub 2m1y rg8r4hfch 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 r ekfw*kuki /n(p -by6-ear 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. What was that speed?(Let A rn6 p -ki*eu(k-bfy k/wepresent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m an czu*23wx x+wad rebounds to a height of 1.20 m. Approximately+xx *z23aw cuw how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the cm;ir r z:s1n8koefficient of restitution, e, m1z ri8krsn; :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 intj,si e) u;lmdtr92(m2 v-ofwjo two pieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block rewliej(2;muo ,)2d9f rmtvs -jassembled. 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 cox7)8 de:gobis a6 s +8ci2dypqllides head-on with a 10.0-kg object moving in the -x directi cy2pxs:78)diaqs6 e+gi 8bo don 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, ax80fi9 ; jbmyjn electron, and a neutrino. The electron and neutrino are j xjbi90;f8myemitted 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 mass t6 gw)ati-umbw t.*. g$m_\mathrm{A}=0.400$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 om)dmax cykk :0 y+e/)ft 6rvf-bjects of equal mass, each having initial speed the two move off together with speed v/3 What was: t/y)c6+ fk-ayr0dk xvm) efm the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet ayftue8fs+ wp*.bvwwq y zk -**9xi ;j5t 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 By q;8by*f *e9ww fskp5j-tw+vi*uz x. 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 perfectlucys. t(mn u;;y elastic collision with another atom at rest. After the impact, the neon ; uc tmnuy;(.satom 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) makesqb7 bsi,)2qqe a perfectly elastic collision with another atom at rest. After the impact, the i qb eb27qqs,)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 s zat7m-*5rw ugytxq9,uw bq70 hown in Fig. 7–38. Specify relative to the left-hand 1.00-k 7q9q y-gt0ua*5wrb,u7tz wxm g mass.    m

  The distance between a carbon l,otcv(unwrlp 2+9 1ratom ($m_{\mathrm{C}}=12\mathrm{u}$) 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-/:iyr-be +pm:n8qos sc) a/s; afroj(kg car is 2.50 m behind the front of the car. How far from the front of the car will the CM be wh+ossi8y) ;(rs/: amebjra/ fn -pqo :cen 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 ferryzvr6ex 5vj d9t e:v04sboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of ther:54v z9je06 vsedtvx loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesbk44rut :mwel0 ga3 3y $l_0$,$2l_0$, 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) pallcu;ve o(s/n x,1pn.f set has a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length csp,e/f.(ovsn ; 1x unl. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of rat.t d.5wfnb 9qdius R cut out of in .q95 bwt.dftt. 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 center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those if)d0 p)ptn ir9n Table 7–1, and calculate the mass of one)n9d0)pit prf of your legs.    kg

  Determine the CM of an outstretched arm using Table *o.m waws e02qyy/362dl t grj7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of t-ji59of ss5py e.kf 4fhe CM of an arm bent at a right angle. y9i .5jo 4 sfps-5fekfAssume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that hijrzcy:534la69or b,ukpfaz* s arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM4f b,c 3 ryzrl5*pkj6 a:uaz9o will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth grgfy6u krg-uvr 3-f744kbws5* fj0vy*(y h h 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.edx49l 8;8*owdwm 4j zr8.dsvfxb t6 f0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kgc r (.wn9zsm78awi- qc ,mhye; 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, sp m7,rn8-czs mhy(qc9a w. eiw;inning, 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 bv -kazf(l*r6 head of mass 2.00 kg and a diameter 0-rzkv*( af6lb .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 a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fi6q3e w0;kb4ekxb oo(1 jwfj/wg. 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 s8u0i jfzy,4abbvr3 * the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenge08ui,b js 3rv4yfbz *ar stops?

  An 0.145-kg baseball pitched horizob9vsxbpw c/ml1 1 t9o6cb9al2 ntally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms,wtvo1 lb9sl2p9 6 m9ax1/c bcb calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speedkz b.*,1 )jvg mwhgxo4 $v_0$ 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 * ryrb,7s(:pdga d8w5kuz)n kaced with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried aboutzsw 8 kayd5( u ,g:rpdrn7b)*k 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 a speed of 2.5m/s by p2 oja56y.z;(xeau kjcushing off with his legs from a.5 ojxe 6jyka2uzc(;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 masx/ 0.pei:1 kwqa*bzx xs 60 kg and the other 80 kg, are initially at rest in outer space. The0 :zaxipx k1q.x*ewb/ y then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on ela*sf)d xd )m)r+hr6k)lq kko(kstic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass ofqkm+klr * o6ksf rk)ddh )()x) the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case t635rwocz yt:q*xbco s97u h)involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driveo6cwtqh7 :cxs*o 3rtu)yb 5z9r 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 vertical- g9uhr z.x)g+omvqv .ok (k6u 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 perfectly elastic, what(gz)moxv o.69hg.+urv k -quk 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 6jz kz ua+w f( orwv-64)f+yawabove it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise afte vwwyjo+w6 f(ak)6a+ ufzr4-zr the bullet becomes embedded in it?    m

  A 25-g bullet strike b5qs f9zj0lc6s and 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 frictio bs95flqj cz06n 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 bullet?    m/s

  Two people, one of mass 75 kg and the other of ma4) xznn6 f kt;jn*m6vtss 60 kg, sit in 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 apamvnfnk4;6z)6jt* nx trt 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 awxe f) zqwe 5oy(9v5d4bout $ 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 explosion. O 4c 3ts tjwv0yhw3a:ct,k hw/,ne fragment acquires twice the kinetic energy of the other. What i4ws3jctc/vth: a,,k 3w0hyt ws the ratio of their masses?   

  The force on a bullet is given by the formula F = 580 f uwi2va.- ptzv2qwpy)fa. lt+*ac57-( $1.8 \times10^{ 5}$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 massesgjq88 l)aiw6vd6+l k4z h.qhd $m_A$ = 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 and a2kbe49ejfa.c- nq1 +lmq6z 6qpv 6vbo smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha 1c6koqbbaflqnm-p6v e.j +64 zv e2q9 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 taho (8,gd3f (.oad4oy ;kl vkisrget) 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 dompqgq dd4 s,1/jrr9 omdjo i.k+4ps/ *wn a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit oqpv w06j8dyszk ;zco;zo-4jql2 )g4pn mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide dozc04q zp gq42;vjz;ljy6)pkw s 8-owith M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet j;vkr;tplp . 4Saturn moving in the negative x direction at its orbital sp4j;;.pk tlvpr eed (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