We claim that momentu if) z/d,cv h8 w:o/nnlgch74mm is conserved, yet most moving objects eventually slow down and clvih,wz:7g/)fc4ohn d n/8mstop. Explain.

When a person jumps from a tree to thgmy(h e4*zk-6-g uzog(0 zrnpiw3xo . e ground, what happens to the momentum of the person upon striking the grounnkgg4ezo*0 zy-.wzrg(imo3p- ( xu6hd?

When you release an inflated but untied balloon,ux8w 3t2s3fjhnzzz. r+i(v5j why does it fly across the roomzs 38v hjzwrt( u n5if+xz3.j2?

It is said that in ancient times a rich man with a bag of gold coins froze t ddn*cxargm5u e8ciirly: c65,n681 jo death while stranded on a frozen lake. Because the ice was frictionless, he could notc5l ncdu* :yirm,5r1gi8cxj 8d6e6 an push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is essentially u w)v2 (77w9tzqrt ;zqs0cblo in l0qzqw7;2)w9 zrv (tso bct7ua vacuum?

According to Eq. 7–5,o.v*fqjlk 8a10am vwd t4r38u the longer the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to l.*f v0m k uq4aor8 tvdw8a3j1inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid ek;ip5sg t9awv9y49was possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advani s9tgv ewyakpw4 ;995tage of this new design?

Why can a batter hit a pitched baseball further than a jjahu49;mgl, ball tossed in the air by the batter?mh,gjl94 u; ja

Is it possible for an object to receive a larger impulse from a small foz-o izr7qw-- cod d5xc-c.2hsrce than from a large force? Explxdw d h--ozo7q z s52cr-i-cc.ain.

A light object and a heavy object have the same kinetic energy. Which has the gr4czw0 hg(;- eazp,igseater momentum? Exppw-sh ,(aeg0z;i zc4glain.

Describe a collision in which al*l/m cb;9os rsl kinetic energy is lost.

At a hydroelectric power plant, water is directed atg)9x: r(e,tpez0hnv 1nmmq ,v high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to ae,vtmz9hq m npn01(xgve)r :, dead stop, or so that the water rebounds?

A squash ball hits a wal5o*;t-c naivh /xykj1 l 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 frq 4 lf6wcwp bie:l7g6+om a height h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the eiql 6p7+blf wg6:w4c momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carry)zb vu h; 2g;6foxu.oying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas th7rihz :) hda 9.xpzi7his is not true for yoh)7hdipaz :hx9i.z7 r ur arm or leg?

Show on a diagram how your CM shifts when you change from a lying position oy bp,ikm1(f*8ydv k9 to a sitting posidfmyopiy v(9k, b1*8ktion.

If only an external force can change the momentum of thehos 6*jrz-.vr center of mass of an object, how can j.v-rrh 6zos *the internal force of an engine accelerate a car?

A rocket following a par :f*bpadi*.n rabolic path through the air suddenly explodes into many pieces. What can you say about the motion of this system *i b*a:nprdf. of pieces?

  What is the magnitude of the momentum of a 28-g sparrow fi cmoiek6yt)*7 i*4v mlying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What i lg*qu,n 3yka ma5qq9df)1w 0hs the skier’s ca*g w la1mh0qdknq5y9f3,u q)hange in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horz s*f xbhk**lzj k1:2rizontal line drive straight back toward the pitcher at 52m/s If the contact time between bat and ball f**2 br*zk zj xhsl:1kis $3\times10^{-3}$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 1ip/psmhf gdl /1/,c d30 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 that of the boat is 45.0 kg. Ign hmdd/li,p3/ 1/gsf cpore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocked d.0o xwpsbmobv 75p:fc69e* t, given that the propelling gases are expel 7:dp o 56fpowbx9s*c mbev.d0led 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 +j(un hen5+hqng 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 track with a constvismm ;)j83sc b 0gy3oant speed of 18m 8s3bis )v3m; c0gyjmo/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelingl m83toh)h8 0i kgnbu6 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 swvcl, )e72l71y ng nict(wif +peeds of 100km/h If the air strikes a person at the rate of 40y7i w e2v ),n+ll1fccn(igt7wkg/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 8.6m/s on a lcp4z ip 6b/ypc9fz (3devel track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/mifd49c p3(bpc/ ypz 6zin Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits0v 79v gk9dbt-hd7b fh an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particlv d90vdtkh9 bf7bh g7-e 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 lig-ym59 jf vokpn(3-hr) n n.wood and emerges cleanly at 170m/s If the block is stationary on a frictionless srv-hf 5gnm(ok3y.ln j-i )9 npurface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket 0n u r:al 8w2i tk2h.2naiw6hdis traveling 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 travelinln/ia ja+* qlfr4k53 og in outer space with a velocity of 115m/s To alter its course by 3koqf45naail l*3/r+j5.0 $^{\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 tee at a speed of 45+ffbgc,u 2-sm m/s The golf club was in contact 2fb, cgfum -+swith the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes to rest in a)(p ;krdc pm-o time interval cr- ;dopp) km(of 8.0 ms. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and vgia)doyv )x2c3 ( zu5speed 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 eca ghk+i2(r*c ngineer 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 thh gcc*2(+ria ke 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 *hfrb; h)xzg+to the east and is stopped in 0.75 s by a head-on tackle by a tackler running fr;) bhz *g+xhdue 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 vs0hx nu mem :9z.5qw+0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Us0ueqxn9 z:w. smvh+ m5e 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-o s6( a9x,be4hst4kdc(+m -c miq5hos kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a di co ( 4ms- ks,tq+ma(e9ohc45shid6 bxstance 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 e 6 --/yoqrikpdast (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the sqi rko /-yd-p6peed 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 speed o ah9kr(3l 3uwvy(1mdeix b/9pf 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly mvr a9wp (xbi9/1e3yh ul(kd3elastic 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 perfectly elas 5k ufws*zp hs-,;bwwi1s) r2ttic 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/2k5rts s)bh- z*;wufwi ,swp 1s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s colliff0 13uft +ocedes head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis feof c ut10f3+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 with a speed of 8.5m/abqktk2r5,pfkj n( 7 8s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a qbka ,5f2tpr7k8( nkjspeed 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 w-yt;/.w+cqjpowwqp9eo q):elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450;yp9w/ +pejooc)qwt.qwq -: w 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 with a seconrcyn906j+ch yif;f you1d*v8 d ball initially at rest. The serjff1 hi9c yy*nvd;y0 8o6+cucond 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 downx9 ew wko04d fw2w,1qw a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline ewd1 oq2wxww9wfk0 4,moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of :ou4)u p2rc9 xm v,ztfan 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 maxi1xu 7nhu cf6g0mum height h of the pendulum eq0uc f ug167xhnual 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 hangin15swfl -x ki9scti )d7g on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Dx5i -l)sd91w csiftk7 etermine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energpj;ol/z , whw qpx7a3*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 breaiphi:k43cfl0 3 smwap46 sq8 nks 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 the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter paq afh s nk:mpp3li3ws6i4c084 rticle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped at av0.zzw*xq y bo+io+ z) red light. The bumzwx+b y.oz0 )+*vqozi pers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a hmh 24ozxmyz;xiwu6ri: +85i ti9a b) height of 1.20 m. Approximately how manx5thuab4 :i ;+8 im2zw6io9xy)hri zm y rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objecek 1))6yn9j zv.xfgqb mp9j(0-uezfbts is the coefficient of restitution, e, defined asg x )bjj0peb1q9.kf y9fzve( z-6unm) $e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
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 awcm* v(ke 6aou;av9y z*w+ein, (ur 7into 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 reassembled.*k,n+u ;irezvauw(6*oceavym7 9a( w The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on witc48g p0n (y*l cah,wxlh a 10.0-kg object moving in the -x *np (cc lx,hyawl8g4 0direction 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 m)zkk7v.mcr6 chbd74;,dn puv.k il; rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emi46.k)zd7kmn di pcvr m7 lkvu;cbh .,;tted 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 z9 :*wxw*b9aooyvt b7$m_\mathrm{A}=0.400$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 lfcyon+w9qf9*am9k , between two objects of equal mass, each having initial speed the two move off together with speed v/m, lk *c9y+qnfw9oa9f 3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the orig*j9)e dp pyet jby+.;fin 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, assuptje)e yyj+p*f .;b9dmed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision wity nj3( zp2uutabv9h9 -h another atom at rest. After the impact, the neon atom travels away at a 55.63bjv-auup(t9h n yz92 $^{\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 wqr)c oz:qgx9 9ith another atom at rest. After the im9cz) gq9qr: oxpact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig.qssac/24dia. +xm l6g 7–38. Specify relative to the left-hand 1.00-kg magmsa+a 2s 6xc/q4ild.ss.    m

  The distance between a ca12qu t*q(ub uir/rga:qh :h+r r3m:efrbon 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 behind the f.-k1 m u/c0fg6hdktsu ront of the car. How far from the front of tcmu u hdsf/ k0tgk6.1-he car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? 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,am6hr. t/h 8m el+ri0a is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loadedm0mt.h l/hia+err 6a8 ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides ff ex4dl*a1zjy 30t2l;lsb13j 1k me h$l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of tom3lc/fpg- i7s iato paste (see Fig. 7–40), each of which is a cube of lengtl fi37g/c-spih l. 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 holhh4. bh- nc9(oy jwhzcm2 1(k-fi wrg(e of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What ismjhh 2k9ch .c rb1yown (f( (hz--i4wg the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same amh m .:ud;wvjc-telx118 af3cs those in Table 7–1, and calculate the mass of one odw ;:.mtl138xju h 1m f-ceacvf your legs.    kg

  Determine the CM of an 36hd1 x gvhn 7woz7wv+outstretched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calcuxh3,vk3 ( owjrlate the position of the CM of an arm bent at a right angle. Assume that the person is 155 cm tall3hxrk(, v w3jo. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such th t9wpp1 kvbe 3i4 :n/ e-ov(ldwn6wq6sat his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s media o14 edlqin3:n-stp 9bekvwp6w/v( 6wn line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth a1 nm;:k kd ,/1h mcepx ki8t+/ckwurc:nd 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 y/evuh(0tbeq ub0-xm+ c*dp, 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 2d 1g2oiza6 x;y7vedbym ow. /5.00 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 a parabolie.ixov5d6a/; m71 wb d2ozygyc trajectory?    cm

  A mallet consists of a uniform cylindrical head o:2)w oy6zfwc.*) xaiskf aov6f 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, spinn oa)oiks acffx .wzv62w:)*y6ing, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29),:+m/t+8c:c+ajfwvdbme+b ps3m o ux1 $m_{II}$=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 the air and stationar1ph f 0,b.gppxamydh;sj4 3 592gsibd y 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 wda0p.hb94g , hbm p ;i3s1f jdgs2yx5phat speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched1- n b ele-hs* l.f)nf27fzkpk horizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is -fnlk2l bz)*p -f.sfhn k1e7e1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m tra :1jrq cdd en2,lhrv6xgk.+s, veling 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 pockp;uz w79n s6yr +gfi6ypqo /.qet shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “6ig qwu f6+.o;rpp9/ qyy zs7nscratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acqutp7kehq x(dm rxfp) 2/z 7:u/zires a speed of 2.5m/s by pushing off with his legs 7x/txhfz2zd7 m)(k erqupp :/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 at r*eujj7t.c t0c q/ jczxn4h-ebr 58be3est in outer space. They then push each other ap*.j38jhr cubc0z ncebeqt7 x5t- /4ejart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elasticc/g nx(m6* 2;j tsb sa(5vjhd-+ moaiu collision with a second ball (at rest) and rebounds in the opposite direction with gu52(sd-oj6nasah m/vc jb*xi(mt; +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 ex,g(*2xg cnayipert witness in a court case involving an automobile accident. The accident involved car A of massgi(c ay,xn2* g 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps-w r(v5uf3ge x of total vertical height 4.00 m. The ball hits four timesv gfrux-(e w53 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 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 direc +0:.rw y)eyjuo 7 k5c3skhddqtly above it. If the bullet has a mass of 29.0 g and a sperou. dkes+ y037)qcdhj 5k:w yed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-k9d 1e +fkqp x l80cp2zkoch4l/g 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 blockz9cpxq01ophl8 2 +4kcl kf/ ed 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 70gfvj,j)hmnoqk98, b 5 kg and the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will th)mjg jhq9,b,8o0 vkf ne boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass s goc4n7.x:5cwi3m6ft a au r+was 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 / (km0rdhr qo)c;nb0 clcl b.(apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the o ;() .qbl kc/r l0rnb(0chcmdother. What is the ratio of their masses?   

  The force on a bullet is given by the formula F =f ht;5wjjrm)x2we 0(v 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 ptnr6 re 34 wr*il1l3p$m_A$ = 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 m3gv8)gfp ejzxt7 0:fm:wx :l and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha pvz jl8tx7:w gfm)p 3m:egx0f: article 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 3ujkb 8 3 ymc;y1f/:pqq0 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.p.)k1qtgcr x0,vi7r y0 $^{\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 iodn-h m.33; cn uge6ctmjc8e;m5be8 js the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, teje gu63;cm 5cmo8me;n 8d.nc3-h jband collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Fiji3mnlr(m ))z0 ttoe9t l1wu3gure 7–47 shows the planet Saturn moving in the negative xl9w0 eit l33u)nt1)ormtj(mz direction 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