Why does a child in 1c6t:rtt /aqzkq-y;a,+ 2c+je i ddot a wagon seem to fall backward when you give the wagon a sharp pull ,c-;d16+yd:aqkjrc otta+qi /tz 2etforward?

A box rests on the (frictionles y+hi:e.bvjx0zpv nh*atl) : ,s) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the te,yxh v+a* 0: n.i jlbt)vzp:hruck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an objgmf)tp8lvz92 *,rgbnect is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acy)rw ed26a9z7f3ql hdceleration? Can it have zero velocity? E67 wrd)2qhlz yfda9 e3xplain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is6n oxg h)s)4rt;y9.er8gk kck a force needed to make it bounce back up? (b) If so, )ekc6)h4 y orgtr;x89kks.ngwhat exerts the force?

If you walk along a log floating on a lz36:* (w eifv ydg5wj-qk-bji ake, why does the log move in the opposite direq -y6 3(5bjwi *e:wfji-dvzkgction?

Why might your foot hur7mxo:u821 fh)x fld w0pwj0 zhxrb*m8 k5zal8t if you kick a heavy desk or a wall?

  When you are running and wae3wjqfr q-+13jyy q-h nt to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person rujfej-hq 3q-+yy1w3rqnning at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a sg 4 4x7urscl8i0).xkai b)/ jhf jvr+mection of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person ilv. 4fxsu a4)xi7h/c0g r+k8mbjrj )gives a slow and steady pull? Explain your answers.

The force of gravity ojqmykzbrg l ;ai,qc w5aw:9(q+ px; :;n a 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier r:; a5q pj+a(lx:wwg q9;rqzk;imc ,ybock fall faster?

Would a spring scale carried to the9x yhjn/ etck tijno/esn1):ln;f5;wm/0g2 q Moon give accurate results if the scale had been calibrated (a) in pounds, or (b0o/ k/; temt2fe gy)nnis: j9wn/1chxj5 ;nql) in kilograms?

You pull a box with a constant force across a frictionless table using a k sp+dep/k*8k ov,el z9 ,;x;+arf6*tklku bqn attached rope held horizontally. If you now pull the rope wipk;du9xt6*v + ls ,p z*fo/ 8l;+ekkrkkqe,abth the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is a net f)teekd w2u1l/ orce mg exerted on it by the Earth. Yet by Newton’s third lwe k1lud )t2/eaw the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or fodsyy5 iw6 lqis4s+y /+rce) needed to lift a 10-kg object when you are on the Moon witiq 6wli+ y+ /ysd5yss4h the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pullcw hgaqi3 k6*vm e)y9 .de8oy9s with equal force on the vg8*md y 3wcak.e 9 h69eoy)iqother team. What, then, determines which team will win?

A person exerts an upward force of ) xuxbn(t0+ zg6u eh1l40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitudel(1xuzug) 6h bt+0xe n, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the gebr w7ng t+x50round, how large a force does the ground exert on you? Why doesn’t this force make you rign5ew x+btr0 7se up into the air?

Whiplash sometimes results from an automobile accident when the vict-e+gkdgi0c3ioqj o6 ud +v69 bim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?96-qeo d ob6cgv+ 0jk+iu3dig

A heavy crate rests on the bed of a flatbed truck. When the truck acceler4qxs5zml 2g9oates, the crate remains where it is on the truc4 osx5z qm2g9lk, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block i2aq3rip :ye9reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. :pi39yrq i2e aWhy?

What would your bathroom scale read8jsyu3kx n v3rgok0hp/a .:v . if you weighed yourself on an inclined plane? Assume the mechanism functions propp0v3ru.aky.onsg8xk v:j /3herly, even at an angle.

  What force is needed to accelery48knqv 9* m :t wxgojl9aq9h 8qy ji:::6wlifate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ridewszks5 wt/r72r at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to acc(bhj-5 j4ywyslt, o y0elerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of apn/fad-k0 - k weug2j- $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required tgy (5-pgjumn qs5 va7e0ipp09o stop an 1100-kg car in 8.0 s if the car is traveling at 9i(p m-5n7yua0eqpv 950 gsgp j5km/h? -  

  What average force is needed to accelerate a y rm7b:d0 t*iqgp0m6h 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m mrqm*yd076 b :h gpit0along the barrel of a rifle?   

A fisherman yanks a fish vertically out of th-b3nn/c2mo 2d wd1/)g ffmac te water with an acceleration of 2.5 mwc)mdof-t1 ng 2f 2nd/bac3/ $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race carqmdj)gsl7j:(9sz x .k can cover a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 485y:n5ei i twox9 5cta,:bthc790 kg ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supportingxtnto 5ic5t:bh7,9c y:a ei9w cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in a motionless elevator. Whn, ghpcq 6fdp4*4)fss en the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of accelera)h6s nq*c g pf4s,4fpdtion.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. s kc(inm32 r,wWhat maximum upward acceleration can it give the elevawmcr2, ki3ns( tor without breaking?    ( two decimal places)

  (a) What is the acceleratp79 6 ;sqph glf7u-oreion of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of their weight? p;7o-u 76slgpr9heq f   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. Wrvdxltx om.j*q1)24+ie:nul hen he strikes the ground below, he bends his knees so that his torso decelerates ov tqx+ urixe:*4dlv).nl o j1m2er an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to oc:s.jpdkt uw-r)-liw g p6p +uvo8 :+the box runs vertically upward over a pulley and a weight is hung from the other end (Figi+ jppow.d8t6+:ko - r-pu u g:lcw)vs. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram jx;6bj)qo xx0 -wf0c a4czat63yp;qf for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the nt3ujd1 d+x1, q4elnsmoment it is hit by the bat, and again (b) after it has left the bat and is flying towa1+tudn3l 4 dj1q ,ensxrd the outfield.

A 650-N force acts in a northwesun;x/ (04 zwkl8mq sndterly direction. A second 650-N force must be exerted in what direction so that tl/unxk z4ms; 0qw dn(8he resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two buib+j k sx:iah8+ldings 10.0 m apart. The sag in the rope when she is at the midpah i+ 8xkb:j+soint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucxy( oc)tz 6x -jruzyr) 3l;t:ulawk(9ket is hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.0ign*; 8+fa non b(wxo-$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing *8f-cx +eee*+vcoqq gw t8*gsunit to a new location at McMurdo Base, Antarctica, as x*eoft*v g8 we*c+-gsq8+qce shown in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the six2u 9/- 8qys dtontuczw :3h.ame mass behind it, Fig. 4-47 . Determine the ratio of the tensioywi cuxou- 3sdtz.n82 t :/qh9n in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley a cb1oa7gt)c5 apparatus shown in Fig. 4-48. (a) How hardbtac)oac5 7g1 must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race beg-dmju1/cxgsg 24 z ;nf dy/y:pan, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (mass 73 y5zralvi5n $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact with e6k l nlx;5h6tp6f os8jach other, as shown ikfl8js5 ;6xptn6 l h6on Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m above the gcetm+:7k6zs+l j9h v1+lelmfvfy2(b round, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the( 6lf+9cs7f:k1h t+2be vmjvl m+zeyl heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on am v 8h/1ljb+tq frictionless table are connected by a heavy cord of mass +l1m tvjq8h b/1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic frict9ch g,c6oi8ptk afrf4y, a or4-s3,bdion between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a 5.2y s(*i.qkbb*uj;n yk0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are s4z1ii b.ltsfgm9kd:sv dq;.7o71nvw tanding on a train accelerating at 0.20g. What minimum coefficient of static frict9knmifb4szvitws71ol1 dv: .d 7.; gq ion must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a ca3 fq kc*hmj3zw v/5u-e;-gajs r can undergo if the coefficient of static friction between the tires and the ground is 0.3heq/ z-amu*;g5j3k wjc vfs-80?   

  The coefficient of static friction between hard rubber and normal street m+r5twbgf )(lpavement is about 0.8. On how steep a hi)bgt5w+ mr lf(ll (maximum angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at 9+mba 5ndl8i.4vu lye -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest 6.mldx 95+ns 8kbo :ll eq+bdpon a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surfag1cvv5f y.(lnce have a very high coefficient of static.l51c (gvn yvf friction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetic fr( 1ij+1frw2lyydrt6( tz ku,liction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32c myg 2(4tbc:6d5)gpoi8aftu (Example 4-20) how large a mass would box A have to have to prevent any motion from occurringd:tc4ca6 b8i(pog52 f utmy )g? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push s loa7)czi2b/z yum5x f +p+q.do that it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0qp a)7ycz +iu.dmxlzbf + /o52.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kgv: ;oyo+u cp 1gmtlz6; and 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54). A :ol; z6 uy m1pt;+ocgv 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient oh*hx1g32i2:ah law:yesq5q 5y d,sm uf static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the 2yxuq:yqia 2:m5 dhh gss5 h,1l3ewa* cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which hr9 kp)p +a,56bch +s tmfrlmh/as an inclmh / cm5k96fp r)+lsahp,r+btine of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a sliwnls27 )ulr;imsxf+ yy x7b0jp/,vk; de with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Figtd*r p5 )8rkyz. 4-55 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3aljzn3e.; uy, c ne;t+.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reac0 pnggtr4;b:5nn2 jsdhes the top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place against a rough wgoz8u ,d2j kk40f4z4 rsvsdk7all by someone pushing on it with srk djfdg8s2ovu0z4 k,4 7zk4a force directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous pro g4jh-)ny6gdh1srcn9 jectiles as they melt. Consider a chunk of snow at the ridgerh149g6nh cj gyns- )d of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for aj5qw8j/m 9jnl n automobile traveling at speed v is equal/nqj j85wlm9j to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash when th)h4i hwjpgst, 3s* r5he driver de hhwt 5,rh)pss 4*gij3celerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of massflu zm8i;i2gr9k,nn/s (juv5 m is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they are filled cb 2kgw9 h8qcns-t+x. to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is .whb9 s +n8kc- tg2cqxaccomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of kinetic friction w9ga(8zcdn x;between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicyc 1to pv-+mja*e+/ e jn9qasmsy z.)*uhle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse appz k.nmznahbp4) :;f 1iroximately 20 g of blood is acz ban hipmnf41):.; zkcelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of survivi nm3n*c8u 3zayng an automobile crash if the deceleration is no more than 30 " g 's." Calc my38a *znu3nculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , and if anm( :ked/lg,ktw7o 3xg lpt5ph (g4 i:b object is going to "hold its place" on the ground, show that the coefficient of stapg( k7:g35blk ot(h dwm:,ti/4 l pxgetic friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scene of an accizjf4mmp+p ab+z fl l++1/,q wrdent involving two cars, measure 72-m-long l4mp ja+f1p/fzw r+m+bq + ,zlskid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 5g1 t84 hwr hhl l(fx/y2daru0means that for each 4 m traveled along the road, the elevatih/8g4l r 05t(2uf1ayd lwh xhron change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Toweqp j9 8th b 5(9i 5*oj2tbv+j:0trtigzpt9jejr of Pisa and falls 55 m before reaching the ground with a speed of What was the averbt9t8oppjirjzbq:(hj t e5v*g 9+jjtt025i9age force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but en,xko9getybk e4 m-;j,ters a muddy stretch where the effective coefficient of friction is 0.ejgtbm ok4,;,kxe9 y-60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a cityf4(s98c kh f8y4bxn ojs um*v3. An important cooksm vjbsu*(f94fn h8y4x 83c nsideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes phy xk* 2.na3oavots,k -s8 psm7hsics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the str 8ak7so2mh3p*sxat .vs-nk,oing makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, there are to be se dgg:nm,wsl7xgn43f1veral ramps connecting different parts of the store: mxngf ds1wlgg,7n3 4.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F 6ers/-v,q**zg a ey ah is needed to lift the piano (mass M ) using the pulley apparatus shown i*yh*r,6 -/gev seaz qan

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is accelerating a t x8e;gohdwt;9:rw;d; onk:o t 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an qom q: m24knlcui9k)d;5q uv8engineer considers the following set olmkkmvn9iq5 ; u:q) 8oud cq42f conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian train has a mass of 660 metric tons (660,0 uhcnd3+ct r9(00 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safety ropes of similar len.sq 14w/salv igth. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (.ssiv41qal/ wa) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boae5 os4ag w)/a z.-vnvwt is using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum speed of 3dd csh(l;:hn c+t9 0me.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers who are roped together are ascending an ice field inclimae02x rh.ct7it/2unr9 b oy9ned at 21.0m tc2ur0hb7na t/o9ye2i9 r. x$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.