Why does a child in a wagon seem to fall backward when you give the wagon a 9o a huih ,qi-/evga7,pkf/gic63e:w sharp pula, v/g/ehci ik,9:i 7hao3eg f -uqwp6l forward?

A box rests on the (frictionless) bed of a truck. The truck driver starts tuiuh m; *x:fmwzd* ;pcpyd+5)))ipxkhe truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground bep xz+*x)pup;h :i fd5)im) d mkywu;*cside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on it? Ex gda9v r,3ar33 3wbbmuplain.

Only one force acts on an object. Can the object have zero ddvq, jgyoksuf,x- cqr (*.68acceleration? Can it havu g8 vkcqydds r-j oq*6.x,,f(e zero velocity? Explain.

When a golf ball is 9*6l+logfjgsq9hxfks 8 b(7 i dropped to the pavement, it bounces back up. (a) Is a force needed to make it bounce back up? l 998 g6ok7fifss(hgjlb+qx * (b) If so, what exerts the force?

If you walk along a log floatinjig9d7o ygnx):n( y1rg on a lake, why does the log move in the opposite directio): 9jdinxyng(g7r1 oy n?

Why might your foot hurt wyn uuyhz+3m 1 t5g)3hif you kick a heavy desk or a wall?

  When you are running and want to stop quickly,2r/ 701 wwk kyj9wgmjf 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 r y mwkjw/k79r01jwg2 fate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, a,*i: /itg-zoevondl / nd a section 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 pet:zn,o ovge/ -d l*ii/rson gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg roq-zop5a fa pt/lmv)9rbs w5:)ck is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall fz95l/q5rwvb f- a: t pm)aosp)aster?

Would a spring scale carried to the Moon give y)su0 5eqre4 iu 4fil01tzzk+accurate results if the scale had been calibrated (a) in pous+t)el4i q01uyzk5 r04f zuiends, or (b) in kilograms?

You pull a box with a conlt 3rxltqws/)ded32 y- hf,.lstant force across a frictionless table using an attached rope hell ed)qy r3t-flx2/dtwl,. hs3 d horizontally. If you now pull the rope with 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 the :k.wnjj ;u429urs ,orv.j fmore is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposijo, 4m.rk u jfvu29j.w nsr;:ote force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10q.1 -aacip * 1+ /tnjzy,eqzwu-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with aw i-.n+a qy*cje/ p1au ,zqzt1 given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulls x7ab4k w:c)yb with equal force on the other team. What, then, determines whic k7cwb4) a:xybh team will win?

A person exerts an upward force of 40 N to hold a bag of groceriesimv e02/na8i s. Describe the “rea0ia8s/e2ni mv ction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the ground exe05 s3objjrdu;615 k wkpk8ziprt on you?kpk bj i;kr8sjo560pduz1 3 w5 Why doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s car i5 k.pnl0y cvs)s struck violently from the rear. Explain why the head of the victim seems to be thrown backny k0p. l)5scvward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck acceleratesx t9j /sz5qy)7zju em d3qcb/2, the crate remains where it is onz u 72ybsz5e qjt/mdq9x)cj3 / the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides;) aga. jjyp2y b;p2ya up a ramp. After the block reaches its highest point, it slides back down but 2a;jjapy a; ybpg.)2ythe magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weiqz u34wffi8b )/e*lj jghed yourself on an inclined plane? Assum/f jz*iuel4fwq38b )je the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1.25m4uc9nvy-hx9 nvy 8 h6k/s$^2$?   

  A net force of 265 N ac k5ft0nfopz3.o o7vi 1celerates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope2w/rg3e 04ejghn/x 5d -wsqle withstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight off 0qtjq*3io5xf od. 2a a $76-\mathrm{kg}$ 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 to stop an 1100-kg cb; jyj)88 te1q0l( s 2soxkkvcar in 8.0 s if the car is traveling at 95jk;bs(y1k) cqo8s82vjl0x t e km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet o3fe:q+ sas g4from rest to 125m/s ov:+ go4eaq 3sfser a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish verticallysjr.2 ep 3 hcnq.vwd ;qgh:-a 8eyj8w, out of the water with an acceleration of 2.5.nj 3 qd,;qhpsg82 ahe8r-. eywj cwv: $\mathrm{~m} / \mathrm{s}^{2}$ 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 car (tw3z.ez zmowtt 4owe)4.mz , 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 4850 kg ) is to be designed so thatsdrh7 8uv3nj . the maximum acceleration is 0.0680 g . What are the maximum and minimurhuvs 3n d.j78m forces the motor should exert on the supporting 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 motiopzch ok *zhkm(xild4mu9m0 /o:- -fe9nless elevator. When the elevator begins to cd0ef-im k /* :hmpolu9m4- 9zhz kx(omove, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a mupprhotr :8i1 aq )5:yaximum strength of 21,750 N. What maximui8tru5r: pq1) a yo:phm upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg includingx:6; w u;r, qgxax,rgt parachute) when the upward force of airt6 urag:x qw;;,r xx,g resistance is equal to one-fourth of their weight?   
(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 3.9v/g6i6 *n)r ke,ip dqn/bnq .azd1k 6p-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximp6dnk/a.e *)pqq1/ zb gnn,6iidv r6kate 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 ressdog)z+ hcrec jxe,x(k 3i+ 9-ts on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side oj( + erdoez)9c-ksx ,gci hx+3f the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagrazyqg i60 f(xlz8c i/qkz n:6.dm 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 diagramduc8,;tfa8,ppg r d:f of a baseball (a) at the moment it is hit by the bat, and again (b) after it has ap:tgf8 d, ufc,d8p;r left the bat and is flying toward the outfield.

A 650-N force acts in a northwe7 c(yd ufv7u nrqm.1l+sterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a umrq+d uvn77cl f(y1 .vector diagram.

  Arlene is to walk across a "high wjz+qiul: ( 8x otljcnyt0- s4)ire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpnxq y(:j+8t ist )juzlo0l-c4oint 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 bucket is hanging b np . r sm f.4axkzbp;v;t01szf fom74cc-y,6gy 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 14b( *l/zy:coww .0$-\mathrm{kg}$ 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 holgnx6noeq,b :9l zy m(..+ksb using unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the xbnel(.9z6m,k.: +og sy lq bnforces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 carzpxlphu -n 21z.1bp0 4cis.ph7zq-xss of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling betweencz0.q.2 puhpihsn-bz 1 1plsp z xx-47 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 up bp3wba pn*,.sing the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward n,pb.w b*pap3 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 began, zh,cb qiu 0c94a 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 *e9ylceq;dvy8b(a w .(mass $ 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 contan.cje4k0ynwt s* u 1u d0*yjz9ct with each other, as shond.0yu* c1ytu4wn9sj k*e z j0wn in 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 initialaxm k+*97 ppje 3ki2pfly 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does th*k2ep7 ijax3 9mpk+fpe 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 heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord of mass (86bzx/rr 1bplc/ m 6xixf3b z1.0 kg . Calculate the acceleration of each bo61z r/x 6pbzb(3cr8mlxfx /ibx 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 friction between a 35y)x .-i62d4jc ouymi w$-\mathrm{kg}$ 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 stje;qit6 tovu :9mph2 h0na 6vo/3-nidart a 5.0$-\mathrm{kg}$ 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 standing h un (4j 5lxax2r+1:lkcky b-son a train accelerating at 0.20g. What minimum coefficient of static frictioh4b+xjya lxl r:uk5(-2snc1 kn must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of fc,c 5.f 16 iuxfhutf7static friction between the tires and the groun xf6c1ff7u5c .u,ifh td is 0.80?   

  The coefficient of static friction betwe 6u* c1kdrk0cgen hard rubber and normal street pavement is about 0.8. On how steep a hill (mdrc1uk g06 *ckaximum 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 unn)bf +8ul3ldi51 ms -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 on a9ak8b. c-dpoi 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 wk3547bta4 .qt scctqzro d m9b79gikap;,cq8 ith an asphalt surface have a very high coefficient of static frictiabib4cq,oc;4.pzat9 9 3 q 7rkc7kmg5q d8 ttson.

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 frreq 5tbqwhk 4hs;,*m,iction 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. 4-32 (Exts8yn6z8 x7umample 4-20) how large a mass would box A have to have to prevent any motion fr 7s 6xm8yznu8tom occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across thex0e ugk/m q2,xo fhrqh7 a;-7k floor. How far will it go, gi7eq; ku -xm/fagk,rx0qo h2h7ven that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in cg4.;z0s lj-qw mofc1ya j7qn0ontact and at rest on a horizontal surface (Fig. 4-54). A 620q jm0ozwyf; qg 1n.l 7c04a-sj$-\mathrm{N}$ 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 coeffic 4878l ksyi5jsk8v8-xf,5o fikbpj fl ient of 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 avois5s8 jfyo,bii8x 8fp k47 8lkk j5l-vfd having the crate slide against the cab of the truck?   

On an icy day, you worry awd0,5.mht g-dbuq j71dr 8 tzrbout parking your car in your driveway, which has an inclib dugd58.-,mtrr0 17dhtzjw qne 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 slide wx3kk4: r8mi6slfjfv1ith 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 Fig. 4-55 lies on a plane tilted at* u1fnmwgdnc )0n.o1 nhmpw.; 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 3.*2wq ax8d5i)p v oh0xs0 $\mathrm{~m} / \mathrm{s}$ 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 reaches the top of the steepest hill with6tj+ v00q- qtruw 3dhs 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 wal9c-i r jxo/e w9/j+yvsl by someone pushing on it with a force direct9+ x 9iojyr/c v/jwe-sed 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 projectiles as they mec8i9 ; r.vk cvo(u8co:q xuk,ylt. Consider a chunk of snow at the ridge of a roouykqco.8:8 kuxr o;v, (c9civf 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 di k-h q+egih./hstance for an automobile traveling at speed v is/h+qhhg .- eik equal 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 dashjdsj 6 cb 73r)5gv;puh when the driver decelerates p)jj u6v csr5bdh;73gfrom 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 mass u-(suplqkarq h1+hj8bw, 2 q( 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 bfu 7:+l*bmean-a ls3zelt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished 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 b* +3am: sn7fub-llaezox?   

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 kineafsr1 n o720jw+1ipq ytic friction 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 tke7+(ou c/wb.ti5hqkh+ee ;khe bicycle) 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 -bvkr 2b 5y5zxpulse approximately 20 g of blood is acceleratyxv5rzk5 b- 2bed 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 surviving an automobile crash if the dec4x/et*vp hgq4 eleration is no more than 30 " g 's." Calculatetp*/ex h4g4qv 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 pro)dnpt 4jplt4e79bvd 3duced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with t bt7tpl9d en )4j4pvd3he 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 acciden7.aznxp a /ruw 19og0gt involving two cars, measure 72-m-long skid 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 0.80g97an1o a/u.gp zxrw 0. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means thagf7,- hl6vu5 mb5(:j1pcnny p2upoaat for each 4 m traveled along the road, the elevationaj2cu, fp16(nvg yo h:m lpan5bup-5 7 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 Tower of Pisa a xu)vw i2,*0.ziuxif znd falls 55 m before reachinifzxix .)i uzvw02*u,g the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a stead8+ +i1rh q8wrqtf7u yppysp3w8 z5 weiz; 2sm9y speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. 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 emergi93+ ;qiz qp 8 8iwr szywu5sfmtrwyp2e7h+18p ng?   

  A city planner is working on the redesign of a hilly portion of a ciar; wxxqvt59tg /fmft* z +0j8ty. An important consideration is how steep the roads can be so that even low-powered cars can get up the higmfvw *q + z58 9jt/0rtfxtxa;lls 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 physics c)2u oh)pqy ,el6 qfb+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 strinob+)h qu yqel)f26,p cg 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 superma()d ty-u 0s ehueq4vu2ys 4e8lrket, there are to be several ramps connecting different parts of the see yt80 u uuy)lsvqh-4d2(e4store.
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 is needed to lift the1 q2fq r cy1s4o9tm,pe piano (mass M ) using the pulley apparatusrtf o qcp14 91qm2,eys shown in

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 accj9h+: yrba 5bfelerating at 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 engineer considers t;clwy/gq 9s-fj,)hsc he following set of conditis ;slyhwf -cq/,j9g)c ons:
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 (660,000 z)von1ys+3l+ 4rc rpw$\mathrm{~kg}$) . 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 o2zlw,; xz mv snrje5ygk6o)3 v11vn9f f similar length. 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). (a) 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 z1kvmy,13rn ;9 e)vlo zj26n5sx vwfgby 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 boat is using twoc,ldb 88m2o/v p:us8k8hw 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 allobj1ta /ep)3vo wed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ 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 ascendin 3+wsiw5. wcx gn p(edm-jp);n ye;c)ng an ice field inclined at 21.0)mn sw.ic p)g3 -xwyen5d;p+nw ce(;j$^{\circ}$ 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.