We claim that momentum is conserv01f* j+zdfblj12 qhjh+ipc; e ed, yet most moving objects eventually slow down and; b2j1j+fh+j0i dl c*zh1 efpq stop. Explain.

When a person jumps from a tree to the ground, what happens to the momentz+)hc .if)e; :d kikicum of the person upon striking the ground)iek c:.) cfk;i +zhid?

When you release an inflated but untied balloon, why does it fld 2uk+ gslse5-y across the room?u d l-esg5+s2k

It is said that in ancient times a rich man with a 2l(g zfx4xmt4qd: u1 vbag of gold coins froze to death while stranded on a frozen lake. Bec 4m(f2 zut1g4xvqdx :lause 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 nv ,4hspsqoo7k (2e/pspace and is essentially i(oq,4 h7ko v ssn2pep/n a vacuum?

According to Eq. 7–5, (un(b*my )(xzqzzr a8the 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 inflate during an automobile cb )za8mu(qz( z(*ryxnollision and reduce the possibility of fracture or death.

Cars used to be built axhh/r to**t d3s rigid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this new des*o t*h3rhdxt /ign?

Why can a batter hit a pitched baseball further than a ball tossed in mhsrvz,* qf/mq/c9 w,the air by the batter?hrq/zmv*/ ,f, sqm w9c

Is it possible for an object tjv 6kogsmu) (lm/4 5o mjn7.bdo receive a larger impulse from a small force than from a large forcgs6b7v (jon.u l4km)dj om5/me? Explain.

A light object and a heae**o7g8o owpmvy object have the same kinetic energy. Which has the great *mop o7ow8g*eer momentum? Explain.

Describe a collision in which all kinetic e9ss4 qr9g5n txnergy is lost.

At a hydroelectric power plant, water is directed at high speed against turbinegi m0g+bi,v;n / jw.wa blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water riw.n/gb jmv+ g0; aw,iebounds?

A squash ball hits a wall at a ulfzl* f2a4d41 oq /cc45 $^{\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 9 ;v b qk/;3gteif+ak.tbr 9ldfrom a height h onto a hard steel plate (fixed to the Earb a/3 b;vlt9;efdgkq .t+kri 9th), 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 and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load *ev a9zl(*c(wjh/ qkain your arms?

Why is the CM of a 1-m length of pipe awzmyb*v j b46.opdbvn9/ jj5(t its mid-point, whereas this is not true for y.jv5jod*4 9 y 6v(zmnwp/bjbb our arm or leg?

Show on a diagram how your CM shifts whelok k: -hse/xg./ nf/vn you change from a lying position to a sitting/.xen: ksvk olf -//hg position.

If only an external force can change the mopm45w +wh3ncsmentum of the center of mass of an object, how can the internal force of an engine accelerat3whn+ sw54mp ce a car?

A rocket following a parabolic path throughsmp2xwsh(ub*j:tf, f td6:k 4 the air suddenly explodes into many pieces. What can you say about the motion of this sykj,x 2w*:s b: td 4usmfp6fh(tstem of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed dr6o;we m 6jdey)0l) fof $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skie/a6s 7gq kxk2qr for 20 s. What is the skier’s q27sgax6/qkk change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line r.. mybxvs ..vd6g8zn drive straight bacg.8 zr..y. dvnbmv xs6k toward the pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a speed of 8mk; ,p9jvc o mshp2s( 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 that of the boat is 45.0 kg. Ignore water resi8;khssppcov(2 m,m 9 jstance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that u ;:p6lylcgk;djhj-1w 2u m5qthe propelling gases are expelled at a r6jpdul cq :;hyg2 mluw-k;15jate 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 atlpp(zmyczr9fdo 7(3.v :6 rfm $4.1 \; m/s$ 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 frictionlesqfhpg8 bscwu 8b g2k05jf x213s track with a constant speed of 18m/s A 5350-kg load,initia3b h 1gxf2gj8b kwsf 05p8uq2clly at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at j8d-j( tuxpi ,$15 \; m/s$ 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 100k-b) m6h- zl l(*gc eqh z:w5jvpayj87rm/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wi*(5gz hcpql)6jzw7- vrby :ha em-lj8nd 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 cawn mii/-gr-f4w+q8x nr coasts along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the fiqwn-+4 /-r8 gn xwimcar after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving atap8vhner 96l;:/zb mf 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If th;9lr 6: npmf/e h8bzvae 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 and emerge hesu10of z) )vaxu3x8s cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges? xeu 8sh)oux)01zaf3v   m/s

  A 975-kg two-stage r3(,g9od f zksmocket is 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 massky*,,/bzu/vsyr ze8/y iu4cg 3180 kg is traveling in outer space with a velocity of 115m/s To alter its course by 3cy/ vu/i 4uyezy/8 ,g*z krsb,5.0 $^{\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 45m/s The golf cltx/ q:-rix.l53 5 ynsccgud6mub was- stc.mu gyn:x3 i 6qrld5/x5c in 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 g89b55 wsg9kayviq0 v8.5m/s and comes to rest in a time int b 5swk8q99gva yi5gv0erval 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 speed v=25m/s strikes a w zde6am 1cdy+)all 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 automobioa4wk,j i1qzyxu ;-hd *5 ezd3le models. C 4d;ai31q,yjehkxz-zw d*u o5ars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is runningnke;b03 -+lf8 d bx4 awhc1zeq at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a zbx8 kd+qlb3 eca fn4;-e0w1htackler 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 the +x diu s9et3 8c9ahmrection and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimatcth ea39 8us9me
(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-kg personlx6apg+02m xezsy- e. jump without breaking the lower leg bone of eith0yexe ls2.m6p -axz+ ger leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) 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 :.p*xvoyfl) cuqvjqga0 d.ak4:0e +mof collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what we dq0*av vckofx: q)yg+aj:p0.lum. 4ill 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 ak(pnoc8 4 cbwm/4jv q; speed of 3m/s has a head-on collision with 4oqknc m/jwc(; b8 4pva 0.900-kg puck 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 perfectly elastic heb4dajkq+fx;3 dj b97had-on collision. If dk374 ;dbj9jfhb+aqx 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 direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, movbu7z0nx)vy-*71rcf:esd qg d ing with a speed 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 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: 0fdes-7xyvn7* rdb1)q czgu.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/s collideq6v7ucq ic+mu/lo 36w s head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backwa+3c vu 6l6mqqiuw c/7ord 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 park3 8dxggh6wes mc8z0ck d9 5zs) (mrf5a ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car(xe )f8 08mhwa6d gd5kz9gsrc3zm5c s A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball ml/9 cf 0u,,plpqb4x qx brlw9+-l n4sqakes an elastic head-on collision with a second ball initially at rest. Tl9ls pq+n44p, /9wr bqx ulqbf-x0 lc,he 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 )lwo k/b5xcp/ 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 ixp lkbo)cw/ /5ncline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object(+b* .:efer* c u*j+vzy gybjw 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,: m )*se;fclzm z(fzq* projectile 1 results in a maximum height h ofes(ql;mcz* ) zzf*mf : the pendulum 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-kgy/ .j/ pza,k unytmaz+ui*-2vv i9y8d pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the8yyzu9,d yz 2mpavv-ni ju+ / .a*k/ti vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lostn brv;gd5z;3 x, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion brldxxr 9j8s-f6eaks 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 xsj9dxf6r -l8 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 they6xbggna7 f z1l1 fvu67 +5hdz rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes ardgun+161zaf7h bylxg756zv f e 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 reboundma9o54scw7j( qpu7 f fs to a height of 1.20 m. Approximately how many rebounds will the b75f97a(ujf4poqm w csall make before losing 90% of its energy?   

A measure of inelasticity in a head- cn t-.5yi vrryli;d9;on collision of two objects is the coefficient of restit-v;i9ytnd;y.ir5 rc l ution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the mass of the cj k,;ed 4cndx4k:2zw 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-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks 4,kx w2z jncdck:;ed4separate 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 colli( 2f f ogx09i xt592pdgr.ygrxdes head-on with a 10.0-kg object moving in the -x direction at f(gi p o02 dftxxg.2 9r95ygrx4m/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 restg.u* f jz,y6vm decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are ygvm z 6ju*.f,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 mass m+6.5 mzk fp9hpumyuji/i/ (oxav * 3c$m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equal (iwdys y8l9zrak2 vwxs10,7t mass, each having initial speed the two move off together with speeyits 1, 2yvws w0(axrkz7d98 ld v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meetkuu:v+l.:dt -rfr. ue at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the urtfl.u ue:.v+ d- rk: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) makes a perfectly elastic collidncz o 9 g48jziwli4-,sion with another atom at rest. Afwoz94 d-n,cz4l jgi8iter the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision mp:xx246y sbnpujst h.* pk .1with another atom at rest. After the .tn2pum bx: ppj.64 ys*1xkhsimpact, 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 my ai2 jc3tod)0ass of the three-mass system shown in Fig. 7–38. Specify relative t)0oti 3djc2yao the left-hand 1.00-kg mass.    m

  The distance between .3yf: m:a 7dby .aovdh zhn.m-a carbon 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 behinc3u fc/3wv7v*gb5 fk1 vz,mgvcm,k v: d the front of the car. How far from the fr/ 3fckvzvg ,:m 5vvg cmb u*7c,1wk3fvont of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit 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 1et bd9o2-zg 6w8 m, of mass 6800 kg, is used as a ferryboat. If gw92o -e6dztb three 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 sidesn5yq ,jw0alm 2edy+5m $l_0$,$2l_0$, 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 zj0 +1wh-pge cz4bmh5q(-fmt cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick gc 14befz0m mqhtpz(-5w-+jh up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cut o/grke fq.z +;xut 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 i.x/+r; kq zgfes the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calculs; /4 nc0ihf(irj89dhz zw de6c +gqq8ate the mass of one of your l;d0snfj+ci hi84( wqzd/6ze ch8q9gr egs.    kg

  Determine the CM of an outstretched arm using Table 7uwitf v fz1h. /(50 xmsy.4ail–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent at a right: -4if4 oca vfx3 uap6yin5*4lhhuj9a angle. Assume thata i* yu54c:p4iafhh6uxo an43j- vf9l the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a p69fd r.ej4afm osition such that his arms and legs are hanging vertically, and 6mja.d4ef rf9 his trunk and head are horizontal, calculate 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 Eartw 84sgn*/fje6g44 psvx 1q wirh 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-+k 5 w/l xma8ry(di 12bkgbnj 80-kg man stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diagb ,2omq6ce,kh3 op0 4b v9sbcmeter 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 k2o cqvm,ob h6 b4g03c9 bspe,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 head of mass 2.00 kg andp.s 2oeg3vuk 6 a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as g 6ok p.3usve2shown 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–k7mj l)k)pfgv d)zvyr.ee1.9 q6b m-i14 (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,1gn15idgyw oygf 73 .t of mass M, are in the air and stationary with respecyg .g7 n53dwi 1t1fygot 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 passenger stops?

  An 0.145-kg baseball pit+*fq;pnv/bxpw( 4mm iched horizontally at strikes a bat and is popped straight up to a height of 55.6 m. If t i* (xnpqfmv/+m;bwp4 he contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling wi,a isww(/s *wv,l .rlwth 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. 7–43. Re m,au-v+ igrx5tr lt,;lative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give deirtu -,l xv,gr5am+t; tails.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s :w(zf+t8jz9qd ;do( zhhz f4-e ze ne8by pushing off with his legs qh zofzfe8nj( + edd;hetz8 : 9zzw4(-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 re(jfd.qp(r + agwyd p60(g arv(st in outer space. They then g(ara .d6fvpgd0(j yr(( q +wppush 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 6*id e-aphl-v:odz/o2l vpi ;elastic collision with a second ball (at rest) and rebounds in the opposite v6 l -*ddpvzia2el -;hpo:o/idirection 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 court case invo3 bl6izt/qqw2 lving 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 ziq3l/2wtb 6q 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 euybmluvwc+tol v0(3+tm )-3 of a flight of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisio tlbemy-v )0v+o+ m(tucul33wns 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 abovkd,oxs07k8nve+i -o ze it. If the bullet has a mass of 29.0 g ne+,dsxz kok0vo87-iand a speed 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-kg block of wood placed f9cof q t/8b-gon a horizontal surface just in -boqfg/ 9tfc8front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass:hhdig(nadwk 8b d+ mak :-)m* 60 kg, sit in a rowboat of mass 80 kg. Wimd) d:kh i- d+:agwb8ahm*( nkth 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 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 w5bf897nux llw o:ql+tn3 u.bpas 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 s(skn3xt +o 1z3a8ywosuddenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their masses? ok3s swz x13+(tyoa8n  

  The force on a bullet is given by the formula F = 58 p n:2eph/g:g*l,xj+oxqmx awd(wp.70-( $1.8 \times10^{ 5}$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+l1 lvnak34ky s2abu. $m_A$ = 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 an.e yu2+: hbc h mc:hkxw3m /0mwa04myjd a smaller nucleus. What will be the speed of this recoiling nuclh yx :m0:ae34hw02.kywu+jmmmh cb c/eus 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 (claa-r.bfkha(04w6kkd)r 54sabwc3 ecfnu :p:v y target) is fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.0il 3ew 7xgi9 2/kjytssk2,-y m $^{\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 on mass m if it i)zwnovn3s )a;s to rebound from M, slide up the incline, stop, slide down the incline, and collide with M again? v)szwao); n n3   kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn movini sxju.99c y (*sdtwav a0:av8g in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Sayv9 d0u :8.vxjc(ai stwas9 *aturn 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