We claim that momentum is conserved, yet m9:.n-w7k7i6lf w qc 5brmq.sngnp * pvost moving objects eventually slow down and stop.5w v9-nqk.nqw:nf6rips7 c7b*m . pgl Explain.

When a person jumps from algll qfn q9n+4u5ml9-)i 0auy tree to the ground, what happens to the momentum of the person upon striking the grl4 nq9 u0nu+f)5l ai-ml lyqg9ound?

When you release an inflated but untied balloon, why does it zci:hsiv c*v:)q1 7qd fly across the roomqihcvq) *sc ivz:d71: ?

It is said that in ancient times a rich man with a bag of gold coins i 1w q dvt3q*cfx-7 zczu07,tsfroze to death while stranded on a frozen lake. Becasuq0t cz 1v7 7d3qcw*zt,-xifuse 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 directio*vc-hd46ikx4 bxvbh )7(bld on when it is far out in space and is essentially in a h-h k64 ()d cbl4bo* i7bxvvxdvacuum?

According to Eq. 7–5, the longer the impact time of an imeaa7nm4ue m-6 pulse, 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 aa76emmenu 4-basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Tz+zh tehqf2bx:(2c t f),f.maoday, though, cars are de:bhczf ) f2q,ztxm(fae+.h 2 tsigned to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball furthermj g0;chltb w1)4 fg:o than a ball tossed in the air by the batmlwh 1 :g4 0t)oj;gfcbter?

Is it possible for an object to receive a largerwd 6q my6qy*z2 impulse from a small force than from y*qdzw6 2 6myqa large force? Explain.

A light object and a heavy object have the ubaw 5 ;fqgz.6n0z 2cgsame kinetic energy. Which has the great2u; zb.fa6wggz n 0qc5er momentum? Explain.

Describe a collision in whizr2 u-fd,rd0w(/g dmd ch all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against turbine 116b 8nod esch 0m14v kkmp.pfblades on an axle that turns an electric generator. For maximum power generation, shoulk1h .mmp4nf6dvk1b 08 peoc1s d the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall atr 4b6 vnhj3pw9e0lychs:w77r 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 (fip *vl .i/dj9 z2u1hmoqxed to the Earth), from which it rebounds at ver dihz1v lq/j* 29.muopy 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 backwefqf:md6v2/0cc 3 sf ward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is nopujob84(-4++ h uljlqwajdp, 8l: yrs t true for ,j+j uwbhaup4l-+4l 8jd:ly oq8sr(pyour arm or leg?

Show on a diagram how your CM shifts when you change from a lying w/ kzvy9;1mvmo ):g/py9zxbj position to a sitting positijz;9v yp 1v9g/:mxyw )m bk/zoon.

If only an external force can change the mooz 0sv)4g8 jfxlk9 +zamentum of the center of mass of an object, how can the internal force of x9a8z +)0l4sovzf jkgan engine accelerate a car?

A rocket following a parabolic path+6j6z jg tbyhlg (6ijk n83p-n through the air suddenly explodes into many pieces. What can you say about the motion of thijgt(k z6j8h6 6+y pi-nlj b3ngs system of pieces?

  What is the magnitude of the mo9gro4yhr8u 3::t/owpjqg r,s ,bfwt yd ow/-9mentum of a 28-g sparrow flying 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. 77(zl1xdyu)vre(z/c v0vh6j 7 eqsz jWhat is the skier’s change in velocity? lh (7ee)z1yr6s (7c7vv0qzj zjv/ dxu   m/s

  A 0.145-kg baseball 4swwx:b hmvk(/,7 c11c mzjtypitched at 39 m/s is hit on a horizontal line drive straight back toward the pitcher atkzsvh:m4 b1,(/j1wwt 7x c myc 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 107 jz szha c 1):fzj)ay:b)z;u96i4j.krlfpii m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initlz 7;i:jz:.u 16z izpakhc sjir9yff ) j4ab))ially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a roc8 ecv 61+wtjzkket, given that the propelling gases are expelled at a rate of8wtz ekv+1jc6 $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving at+sq-6b6e 81x7l un( owbcc + pdquf9zm $4.1 \; m/s$ 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 af*w4 e1i fnb hx.6,dmklevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped ontox1bdfm f 4,enhi 6kw.* the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar tra*y2tm0dq gb w/veling 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 ydus 5bia1 mk3iz7w 2m)+yr72xme 8loof 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high a 7o kr 1e)ux 8zmsw2m2il7d+biayym 53nd 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 ao;y: c-i/yvg4 llgbt ,k* l(xelong 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 car aftc( 4y;kigyt: -/*ogellbl xv,er 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an:q*mzoe+wc l-.z4v q4bth+ oy alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u al*yq.e+4 - +tcwzovqob :mz4hnd 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 penetv jwb637pfdp6 rates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictiop63 d7pwfvb j6nless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is travp. kar4 als(-gyf;)kqeling 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 cronu g w6d*z jbfup318 6t86youter space with a velocity of 115m/s To alter its course by 35.1rw 6yb6n* djzuuf 38 6pgoc8t0 $^{\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 ofyutf lqo:/guf6c7 a wkg;0s(/ 45m/s The golf club was i;ofg/gtf67 a 0swk/ulc:u yq(n contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at jp1u;f+fu2/n wkj)r- 7rz6wyxt ( uaea velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to theuj xwf 72rw n atrpuf1)6(-e;/jyu+kz 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 strikv, w r uhn8;g svqr6g-9ikah42es a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in chargeliq:/9 vaj;p v;zy -g/i vc9khy o*9pl of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new modvv -9 go;yl pqjv k9 ii9zayp/lc:h;*/el 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 stopp41 ukx o8kye7zfro8ax)lo3z 0ed in 0.75 s by a head-on tackle by a tackler running dl z8koe)k7xouo zy8 4 ra1f03xue 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 balyxg4 pej* 7c5ul (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphic7gye5x4up jc*al 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-kg person jump without breaking the lo:xida g rr32*swer leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 3ad2g rrx:si *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 of collides heb zl)u.oo0 rk;um*r g0ad-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 the 0.440-kg ball, and Bzb lu;.krgr)*mu 0o0o 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 wito9i xvysfqw6wt;8vy7. 7+og(/u 1hpznyfe: sh a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg pucpfqy87g 1novwy(ofwst+ i ;u/se 9 .vxz:7 y6hk, 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 elastic8xt;5* uqezw zk69hyk head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite directio*zutk 8w9yx6 ze;k5 hqn, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a 79nozqw4s zj jh46ws6speed 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-zj7q zjownw9 46ss6h4kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s co. cj 0(ml1f( )lwdcdjy( 9uacsllides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces bacc(dc l (lm)c.jdas f1w9( 0yujkward 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 elatl6 b1yhys6( dstically as one approaches the other directly from the rear (Fig. 7–34). Car A has dhl1sb6y6 y(t a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic h;-fiyu ;ltd-78 b hoed1c*re dead-on collision with a second ball initially at rest. Ty7h;;-l 8ro cdde -eudif*b1t 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 d aq1(brw)u *4w6 ctozi4tnk 2pown 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 moving horizontallyrkwaqcopn( 4tw ti*z) 2u 146b.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an o24 (czvqln r.nfg: :lvbject 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 (-p e )5pmkkbdresults in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum pdbk- kepm)5(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.n*;v s+y0lynjf6g/p gne;92p r qs2px6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum y gjsn pgq2le *0+6y2/pfxpr9;; s nvnswing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the l3e 4,hc+lli3 s;gjr yfraction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion brea0zwz h ff1q,4o: chohu,1kl9aks 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 acquireu:wh04h,9h1a lfk,ozcfqz1o? (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 rear end of a 2300-kg SUV stoibrf, i aj4)*6y7 ga *3p9)ta vshfjgapped 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 a )9,4b pv7 ir i3 hj*atsaayj*fagf6)gnd 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 reboudllk gu 9u 1y*+ xkarpq.y/imp9h)k)0 nds to a height of 1.20 m. Approximately how many rebounds will the ball+ kl)./ u9) g hiarp*ukl1kx0d9yympq make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the coere/*fx. u xdik3e i;*efficient of restitution, e, defined afrk 3i /*xexd*i; e.eus$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
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, ofhjo /,3flv x/d1 xa0one with three times the mass of the other. A depression is made in both faces of th xo03 fj/a1lv f,dox/he 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 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 collide6h( piysr0o)p s head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of oriy(h 0p6p)seach 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, an electron, andvyiz5*k (spvjar b1:m)5hl2p -8lg dd a neutrino. The electron and neutrino are emitted at right angles *zjyd-vhkl m5av2pg8id1:( s)lbr5 p 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 masse.c*utlexe1 00kesrr0b m7v qrc )/:f $m_\mathrm{A}=0.400$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;5b;;jha6t bf oztdpp9; wl *r mass, each having initial speed the two 96dofpz ;r;5tw bpt;b l*a;j hmove off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at thwcw79-bzsra6 i) w wt/e origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along thea w9i/-wrctz6w7bw) s 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 with another atoac4 tn 8bwx5/(suo4q bm at rest. After the impact, the neon atom travels awx4 a/4(bst5cquwo8bn ay at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision with another atom at resm (an26k j:zdq7 /iwiet. After themd/z w a2q6ej(n7:iik impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. Spec0o*rs3k mpqf5ify relative to the left-hand 1.00-kg mas0*fq3 p k5srmos.    m

  The distance between a carbon atolozjian9r2a+olto* ;iu ,9u ( m ($m_{\mathrm{C}}=12\mathrm{u}$) 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 is0f6,s( gjvzqf 2.50 m behind the front of the car. How far fro0zfjqsv,(f 6gm the front 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 18 m, of mass 6800 kg, is uhr. .efk72fux sed as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded hf7e2r.u fk.x ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides b( c9i/dkvjl0 /w.zm k$l_0$,$2l_0$, 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 identiz4 f6lsvdxrl,+,dqh )cal cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in rs)6ddhx,lv 4lfz,+ qthe 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 radius R cud ,eqpgdza -: hw+jvq/oyx6 65t out of it. The center of the smaller circle is a distance 0.80R frov5j ,p+h-qdw:go6xd6qz e/ yam 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 in Table 7–1, and c;agw9ue zlr) +alculate the mass of g earw)lz9u+ ;one of your legs.    kg

  Determine the CM of an outstretc3;gul*d-7t kquq +iqrq0eo m8hed arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an gm n:sbd:k,/.fu*urg arm bent at a right angle. As*dnbu rm.,:uks/g g:fsume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hangaci nd2vn;4m)m0gb:f j0py:ling verticalmyl;2 ) v:bfa4ipnjd 0 m:gn0cly, and 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 Eargexg 75t(ef-b th and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on fric 6:fpba6jfpbb/+2csr tionless 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 diameter zt(z rt /of*l:+ mh.js0.0800 m mounted on a uniform cylindrical handle of massr:.tf+*t lsmh/z o(zj 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg 9 1sv8fggkyo.,zj: zwand 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 bo1skyo gf:.,g zvj8w z9ttom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29),0*gi 6r 2zagdk $m_{II}$=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 gondqmk45 yb 7h*d gw 9*bvok7m9nnola, of mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the banv4n m 9k975 *7bwmdqgk*boh ylloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat 5fmi/ gg3n0 sband is popped straig 3bg0/5s nigfmht up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with si3i zx y1b/+t0 p1lwqvpeed $v_0$ 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 tay;5j9 k2f;twl /w uqshot shown in Fig. 7–43. Relative dimensions are also shown. Should the playeu9wt;;5ylfw q/ k2tjar be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquir-0htx 2 avcb/kes a speed of 2.5m/s by pushing off with his legs fro hx vb2/-cat0km 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 thal uxi1 -dag n3/b*wp n*5hdb9e other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astroi*w-abnn3xl9a pgu 5b1 d d/h*naut has moved 12 m?    m

  A ball of mass m makes a head-on elasmlofwrl:k(j 634sz: 0doj g 9ntic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-foufgozj6:s:m dk 0l4lrwj9 n(o3rth 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 exwdghlu7w-/6kqs0m8f-kh p 3 jvs1j p; pert witness in a court case 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 sw-6pk0;73u fgs khjw /qhmj-dl18pvinto car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total verticc(z owj8fjua. z cl42c vyq.*u+a,8nz+ pki8cal 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 is the bouncezcj.n*pz wu yu cjo(c zvi.a+4,qfck82al8+8 height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg blf5s3a /e 5oolzock of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the b3afz 5ool/e s5lock 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 placedkytcjxm/ ,m8 s4uj/s: on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bu8j cm,sxj:4 k/s/tyu mllet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a ro;rj1ul-ov 4ya2l q z 86rm1etrwboat of mass 80 kg. With the boat in;j1 lozqa82v yr614 rmtuer -litially 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 was about j+: ial)y:5auoa ;h0cg -bius$ 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 exq9 ubjy27nuea 7 qrtp kpbj01u,9r)r(plosion. One fragment acquires twice the kinetic energy of the other. What 9qpqp t1n jrue9r,7u(jbr70uybak)2 is the ratio of their masses?   

  The force on a bullet isf0c iwcl b-9u5 hi,p,i given by the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses59 4sg9ybxpa3w rvd2 zzf+yl, $m_A$ = 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 ra hmswpjbeap77)*u2k 4sf g3n .dioactively into an alpha particle and a smaller nucleus. What wilkp7*h pes43aw f.ub7n) jsgm2l be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angle of 30fysy9 ykd 5ave4+4q,w $^{\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 dowfn:(5p g/)6o fac3u jmgttik.n 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 on:mp /wf2 mipq5 mass m if it is to rebound from M, slide up the inclinep:p wfq/mim5 2, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows t 3fm4dnyhcg :w /vk3e(0e-n jhq h)3nche planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The masshc q 3 c-ymd3w)e:3v(k hhnjn0 gn4e/f 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