We claim that momentum is conserved, yet mxd jqa 3v8uyo48 jv :;gs9g7,ucwijx+ost moving objects eventually slow down and +j8w9vy3uxo iq sj;,j8 d:agx7 uv g4cstop. Explain.

When a person jumps from a tree to the groub: hk00ep 5v bg 0f/r(9gxpewz t34zlsnd, what happens to the momentum of the pe bwbxpz/s 0e5krh349 l (0tzvgfpeg:0 rson upon striking the ground?

When you release an inflated but untie di /bh4qawb3)d balloon, why does it fly across the room?ibhbdw 4q)3/a

It is said that in ancient times a rich man with a bag of gold coins1rz )n2ow 3l8+ykunp o froze to death while stranp z1uo+k n2l)r3yonw8 ded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is essv88lklh 1qw +uo(+ h v)ajwxb1rtib;-entially in a vahwi qw(b v l1j) 18 -hxu+8vrlo+tkb;acuum?

According to Eq. 7–5, the lttdmwsq-7))::c) wc gxob6qnonger 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 collision and reduce the possibility of fracture or degb7ttm-)cq:)c)oq:xwn6s dwath.

Cars used to be built as rigid as pos esrhu3t.o5 *tp *z/hzsible to withstand collisions. Today, though, cars are do st./t**pzhure z53 hesigned to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched b1 zkyxug,ep;8e ys u42aseball further than a ball tossed in the air by the bae1pzyu;4y2xuke, sg 8tter?

Is it possible for an object to receive a larger im9y;y +rkd1xzbn5b qfdd (d,:xpulse from a small force than from a large force? (z yn:fdxqdd b, 915b xykd+r;Explain.

A light object and a heavy object have the same kinetif *(ag0q*jr*rku7 oyo c energy. Which has the greater momentum? Explairj f(07aky*og*qur* on.

Describe a collision2:kdx 2;kha3e()tat/gkkqku s :u e k0 in which all kinetic energy is lost.

At a hydroelectric power plant, water is dir*2s.g diwkjnw8: t+ fz:n4qdlected at 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 a dead stop, or so that the water reboun 8+li2qnswgz:df:kdt n*j4w.ds?

A squash ball hits a wall a+2 hsr+tst*l ghn5l;at a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height a1a/gy+ 4gdxeh onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c)dg+1 / a4xgyae 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 in y0 8f,b)e c*+jqietv erour arms?

Why is the CM of a 1-m length of pipe at its mid-poin qbw99t5cz 4mft, whereas this is not true for your armqb95tc4w 9 fzm or leg?

Show on a diagram how your CM shifts when you change from a lying posnn0br)9 u 1thqw *by)eition to a sitt)t90 he)yq1urnn w*bb ing position.

If only an external force can change the moment q /ejt+q7:objum of the center of mass of an object,+bjqo: qe7tj/ how can the internal force of an engine accelerate a car?

A rocket following a parabolic path through t ,6d4pf9jtd+sh o dec1vp6 c*ehe air suddenly explodes into many piecevdfhp6t1 j eccdpde6s94*o,+ s. What can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g spat8rnvm,my 9(1cx noapgw+kt.s++b e /rrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a evbrkakz p:z-: *r or247u1qg65-kg skier for 20 s. What is the skier’s change in veloc2 7z:r:up k-gzqa1*o vrkebr4 ity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drivcl,v708t kms6 oke cl,e straight back toward the pitcher at 52m/s If the contact time between bat and batec7o,0lcmk,l 8skv6 ll 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 w ofc mz-ioxmo rf7.y)ffp eh+46451bf ith a speed of 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, a4)fbf-e.x m mpi zo6+off7y1 5h 4crfond that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given thaakqs5 -v1k .rat the propelling gases are expelled at a rate o1r s 5.avq-kkaf $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving xu *ub0y(u f no8sp/)2l.p 3cwtggtrp+p/f (r 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 fra1l2qfcj*, rb 61gwc+n1d;oa bj8h h dictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new sp* foa qc1 dr6hln,hdjg 1cja8b2w+;b1eed?    m/s

  A 9300-kg boxcar travelingn.hwa0,he 5se ;sg-m c 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 horizontapk-x4d:* + evo*.ys )xfoxeli lly at speeds of 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 and 0.50 m wide. Compare to the typicak d*ef)e pxv:s*+ixo4ox -l.yl 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 carlx x231j spq3r 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 t3prjxq3 x2sl1racks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in the direvdnw gdgxxlk(s) o )/4v8g 3j)ction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it i (l gokxgx8v))d)vgjs3 d4/n ws emitted?    m/s

  A 23-g bullet traveling 230mm.ei+gz.5 u qm/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a fr5z+euq. m .imgictionless surface when hit, how fast does it move after the bullet emerges?    m/s

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

  A rocket of total mass 3180 kg is traveling in outer space with a velocicu)w bmyeli0 gnq u;n,3s , )(6z1zloety of 115m/s To altew36z1,gol z;e l n)nu)(mb,y0 iecuqs r its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0e +q*azf4n8zc -v;d bu.045 kg is hit off the tee at a speed of 45m/s The golf club we azf;v-*84d+ zucq bnas 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 8.5m/s and comes to rest id nu/(n )d)hfqruxi7d sh5b y,iix:8;n a time interval of 8.0 ms. (a) What is the impulse given to thebr,u)7f(8hyh:dini5q/ )dx;d nsx iu nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.q4y bxys5 ij0)d ) .5qbodrds:06kg and speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthines66 xkji/h1xnpk 9/neis of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (kx6ie/i9n1kh 6n x/pj30 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 r 4qx.n+tf 4yneunning at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Calculate xnqnt 4e.4 yf+
(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) po.j8 mo,af+) ng wob loz2s*e9eints in the +x direction and is given by the graph of Fig. 7–33gmo*s8eozw 2a +ejb l9ofn.,) as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump withut );; z+ozwowout breaking the lower leg bone of either leg? Ignore air resistance an zw+w;t);z ouod 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) (z4fyun p)4 bpwith a speed of collides head-on with au y) 4np4f(pzb 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 B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-on collisi 17:nbv cs-8fzsm3axqw vu8l(j(i +roon 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 puck, and let B represent the 0.900-kg puwv1o+f7b cuzj8a8q( smsv: (3lixnr - ck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equalev:k x5 y b6/*bkgce;eo2 z4ze mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite directionb 5kokve;4cx6/y zze2 :ge*be , 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 speed of 2.5m/s collides head-on with,s zwni mmg3 -fym7*l9 a 0.090-kg ball inw9f-3m7i ml*gsny mz, itially 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 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with xnuetlip g)n/;x:oq5;z f px.k o76 f5a speed of 8.5m/s collides head-on and elastically with another ballino.q )ze gppo:6f 5t;; /5kn7xxuxfl initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusb3p k zv-/bq.yement park ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B b -p.qk3bv/zy 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 second ball,4e.ghmc8 py l initially at rest. The second ball moves off with half the original speed of the f, eyl4 cgp8.hmirst 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 frictionlesm7(jzpw 0rgwgs thr+si *96 j:s 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 horizontall 6rti+s:z07r9*gws (mpjjhwg y.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of mass xs: n(am*0vfs 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, projectilb.k :kb*hbdvw/cyu 57e 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high v /k*bb7khd:y.5 bucw, $h_2=5.2\mathrm{cm}$ 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 ita csgk3apf o8k26js71 bmve: 6self in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displace86ogkbpm fv2:s61jcsak7 3aement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lost,dv6o+(,emu b5 xc- mae $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at y5cc w6u4-ulurest, 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 -5cy 6wcu4u lueach piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg5qa ljp;:vybu9 mjw93s 0gf f2 SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed o ;:gl j9sf5f20p uq3wvj9mab yf 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 height of 1.20 mm-k (cyjri1g 0. Approximately how many jy0-(k1i cmgrrebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a headk (qo-ei+ h;h(z 6synf:n1 kic-on collision of two objects is the coefficient o: s;y(i6ikz+f(k hhon q-1ne cf restitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the m0yz 6xf ;uo:o,5dur roass 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. The reassembled block is set on a rough-surfaced table, and the fuse is lit. Wheo0;uyxf5d z,6:o u rorn 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/7 *roae+,ime4ska l; x9t0cvnvph 1, ys collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final veloci,e4ka v;+09h y eca,it 7*pxv1nslro mty of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an elec2wyyp-,no93xhd9 vc j8 zs8wd tron, and a neutrino. The electron and neutrino are emitted at right angles and have moment9,xz pw-vojhc 8d89wyys nd3 2a 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 mm;k(.* rs/(bh acqvs/9 9bl2as lwzviass $m_\mathrm{A}=0.400$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 colliyt6uf5dkd r73sion between two objects of equal mass, each having initu7d3fd 6t rky5ial speed the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass mx *zqf0yv8ko s*w:a1 xove at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of b *0o y18ks*:fxvxwzqaall 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 elas ;77 ac-8kr2ksx op1rdffwqq8mqh + ,etic collision with another atom at rest. After the impact, the neon at+x2fpae87 qc,ko7hm rwkfq8s 1d;rq-om 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 with anoth7did6 9s9znz5;bnvh ber atom at rest. After the impact, t65 dzs;7v h9inb9z nbdhe 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-pof 5oor0q u )f:1wyg( gzrj((mass system shown in Fig. 7–38. Specify relative to the lefto(5j(rq: o g1 fg)(yrpzo0 uwf-hand 1.00-kg mass.    m

  The distance between a carcn9 t 4lk dfs7t*4 6hm68nilaybon 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 front kt8qs8a 2xpv()ne-u fof the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 sapvn t(fu)8-kx8e2 qm 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 k ht02i4yw/ld6hk dn.v g, 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 loaded yhktd. /42wid0 nh 6vlferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides yx2 zm*wyu kk vsnq188d9cq,/ $l_0$,$2l_0$, 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 tomato pastehy;:p;wq693 prse jwpr 2ji 3p 4-ntgr (see Fig. 7–40), each of which is a3w- s6; irqt p:rgphw ;n 4jjr3peyp29 cube of length 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 +5u,ba k0ov g1bul3p m96pa2 8xlox vfhole 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 is the positi 50m ukauop6p2bv8vaxg 3fx l+o19bl,on 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, a0i-cn bex f26gew 79kjnd calculate the mass of one of g i9 c2w6-jf0kn exb7eyour legs.    kg

  Determine the CM of an outstretched arm using Table 7–+nnp;6 v hq1 cadeq0(k1.   % 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 iyk (snc5(o*ms g2 j2dof an arm bent at a right angle. Assume that the person is 1sodjy(s5( g*nikm22 c 55 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms andt/f x8r8 hjaq; legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM wil q;8hfj x/a8trl be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth a+ut, aok3t:jjf ch+ t,1 nxfb2nd 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-k)y5 ak54ync-hk5j7xy i *0 lbkbo9v rwg 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 unifoo )e9y+d kqjasmqnh2+/b )ab )rm cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinnin +da)n 2jb )/+ea9bhq qso)ykmg, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of4da .08m cyywp a uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length cdw 4m0ayy.8p 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 p/7ah b41crfh2 vu(xq (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and uz.mdly3 gw: mj6lz4;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 directizdy6mw;glj .3:zm4u l on (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at wk ewnv: tub s2+t; ;zil;cc2(uvh+p6 strikes a bat and is popped straight up to a height of 55s;w(;ltvk: iu cbn+26cwe+ hv2p u;tz.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 traveli ycxjd00q .4f ;pkz4mhng with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shi ;*or b5pwi:yown in Fig. 7–43. Relative dimensions are also shown. Should the player be woo5b:;py irw*irried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by pushing m;l rq/ep2 c3d bqdgvbi(f;+ 1off;fil/3+c;q q2bge (d p mdbv1r with his legs 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 initiallya:oh+j:c3t vx at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut has moved :jxh:cv+3a ot 12 m?    m

  A ball of mass m makes a head-on e) jiltc)3 ht ny;9q+ ,juj7kgxlastic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its originalunch kgly)tjjjqx)9t+7 3i, ; 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 c j/k 0.prak6m.tv*ldaase involving an automobile accident. The taa * pl0j kv.dkrm/.6accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the 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 tot940)yv bctje sal 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 collisions are perfectly elastic, what is the bounce heightbjc409 s)te vy on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertwxdvkxf o e753(xb:c) ically into a 1.40-kg block 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 block rise after the bullet becoxfv73d:)w cx b5xe (okmes embedded in it?    m

  A 25-g bullet strikes and becom2yqrhoewo5qn..,pj ge 63 e 3ses embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surf23 e3p n. w.gq,h6eoqj5seyorace 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 60 kg, sit in ii86xiuji,2 +km oeq 4a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite 6ii,j qexko im+iu248ends 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 abou pn:irie4/m7j2c+ l4 pw )yxyi lle sfvc(c8.5t $ 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 a +s)-q ux3bx,oo lj)jdn explosion. One fragment acquires twice the kinetic energojqo jd+bu 3xs))l x,-y of the other. What is the ratio of their masses?   

  The force on a bullet is given by th7y7 a-ujodyim8c +*hzsrv,s.s5bn k+e 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 masses bfv6n /x pdmw5xcu,-2b11cuvso: /hp$m_A$ = 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 partict ,dm;ako6ux (le and a smaller nucleus. Whtkoda6( m;,u xat will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angl /zqg2*,4jse.hqvcjfp*i p -x e 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 dre x0*x2 .hef.,ckpjtown 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 utw3s mvxe-7 x-pper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collidwsvm- tx3-x7e e with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet S3 /-utvssiq9 raturn moving in the negative x direction at its orbital speed (qs/3ru t9iv- swith 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