Why does a child in a wagon seem to k9f tw)g7vn91x8eyy54n xt ttfall backward when you give the wagon a sharp pull for74x9kf)9t5yng81x t vwtny e tward?

A box rests on the (frictionless) bed of a truck. The t in)/pqiv(xx8z0 :161qf funcwyj*qx ruck driver starts the truck and accelerates forward. The box immediately stnv10f(iyz 1)*6n ji cxux8qwqx /fpq :arts 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 beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero oqo;1:u:bv crmzb).a, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Ca 3rnse ;cig(g*rihkb *p 4n0*wn it have zero n*r*nige(ri*sk4;b0 g3 wch p velocity? Explain.

When a golf ball is dropped to th;nng,h8x(bhpx)9 c*n ti9 p upe pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (tux) gn;99hh pxni,b (*8pncp b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in .mlx0b m.ih6n the opposite dirl. nbmi.m0 x6hection?

Why might your foot hurt if yodfq y fw7ei/-ua)+ u:aszjp+, u kick a heavy desk or a wall?

  When you are running and want to stop quicklyudg ; 1o dwejl1x8:*nx, 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 running at top speed to comex*1ow:d;lx 8 gednuj1 to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a secv8jw1zro52k k tion of the same thread dangles from the bottom of the stone (Fig. 4–365kwkrj18 2o zv). 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 gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rot+i-h sd: hjjj.5r)u lck is twice as great as that on a 1-kg rock. Whhlr-+i jjj5h :t.) sudy then doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give acweckx2 m,8 cp4su3g+ mcurate results if the scale had been calibrated (a) in pounds, or (bpem 4swmg28ckc +3x,u ) in kilograms?

You pull a box with a constant force across a frictionless table usinsjeff,30.tuuth0 mhz3/5 sf . -gnhn cg an attached rope held horizontally. If you now pullhzueg- c.j 5u0.h3s,st3m /t0f nhf fn 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 there1vm+j;c 9a ejn is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts jna9c me ;vj+1an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or forqxgmils+ :thkdh :k x.i4z zhu9,f-bn+6e,k4ce) needed to lift a 10-kg object when you are on the Moon with the force needex uhied:kb. stf,6n4 q+9 kh+i,xlmg kz-:4zhd 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 inj4hg/(um j ja;8kb rd- a tug of war (Fig. 4–37) pulls with equal force on the o (dj-j;4mj8hb/ukgra ther team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a/:o wmn))qkk /0nfxzm bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is e qz/)w0k :mkonn/)fmx xerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the groux/gm1jlaizs6la, -e )nd exert on you? Why doesn’t this force make you rise up into thg6za,e /m)aj 1x- lsile air?

Whiplash sometimes results from an automobile accident when the victim’s car is i5,2b jiq;i l96 owtuestruck; t6,ebi9o5i uwl2 qji violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerates,:ur/dh2ftd r3s6kbv3yj 4fg0 the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerater :f/3rvbh2d4sfjk3dy u6g t 0?

A block is given a push so that it slides up a ramp. After the bhw-2c4-d6n o qk6xu tplock reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descew 6tu- kq-xn6po24 dhcnt than on the ascent. Why?

What would your bathroom scale read if y(.i,:qug sn lqou weighed yourself on an inclined plane? ,( .sqqul:ignAssume the mechanism functions properly, even at an angle.

  What force is needed to acceleratk5ih wpaxfj-a4 s(*j 4e a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerat -v2q: t gk1jv6)yg2th4gfcfees 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 rope withstan+a y:0oe5t olq,4 taold 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 of a b2loe1 o6gy a1 $76-\mathrm{kg}$ 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 car in 8.0 s ifsu j2/mpr dt- 76prh1j the car is traveling at 95km/h? -r-7/thj1rjpsm d u p62  

  What average force is needed 6iqz.*u l4lwcto accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800w lu6c4. q*ilz m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the watoz,gu2e(aam , er with an acceleration of 2.5 a(z, og2me au,$\mathrm{~m} / \mathrm{s}^{2}$ 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 can coveod0d/f flr*a cy0v1 ze3e,b+qr 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 tha( dp +zh6)uabz:lbl y;t the maximum acceleration is 0.0680 g . What are the maximum and minimumhy+6zpb d al(;u: l)zb 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 v3f+x(shh5c/4q9cy-gwdg;bem 4 mfl .va5bq bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration hl; 5f9egv(-wbsf am v+ ymh.g4bcx/q5cd 34q of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg el 34u b3ysch9f 4xvqqw6evator has a maximum strength of 21,750 N. What maximum upvqq yf 4bxhuw3 69c34sward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass pb:8x 0s k0jju132 kg including parachute) when the upward force of air r0skbp8xjj :u0 esistance 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 3.9-m high. When he strikes the nm58oz4v lc 8fdq-5qnground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is fqcdn85n o54 lz-8mvq 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 tag 8;:kermmwnhqtwd51i *-l * gjc0me+ble. 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 ta-ewn+:r;*1 d i kgej5mmg lmh08ctwq*ble 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 for a basketball player hal; ko055ipu
(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 u 3bk5.ym ;egebaseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and3 yk;ue. gbm5e is flying toward the outfield.

A 650-N force acts in a northwesterly directipxbnqs vylx/z.8z;b*um 7/9 d on. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answeb8 xmd.;n/l /*z sq 9xbvz7upyr with a vector diagram.

  Arlene is to walk across a "high wire" strung uu/2 +*bo6j:jgkg,q e*z/b -*: s s uvouucrixhorizontally between two buildings 10.0 m apart. The sagjv: 6uxgq ksr*/ g /2+ - o*ijeuz:ub,bcsouu* in the rope when she is at the midpoint 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 hangilt45 -f ,-,cjgasmua.hn (qgj ng 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 1 tbjsilaa2:dzi++m; /4.0$-\mathrm{kg}$ 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 housing unit to a new location at Mcv 6 ex-vrxsz:m .nl8efaw5bw4c6.m d9Murdo Base, Antarctica, as shown in Fig. 4-46. The sum of the fel6rm- 5adxzwncsvm4ef.wv.:8x6 9 b orces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 same mass behi6wx 3lr+rc)odk5 jsn3 nd it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the firstrs3dl x 5wr3)k 6on+jc 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 e2; o; m2wjjn7 enfqw4bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at consw22;7j wqfmejen; on4 tant 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 bega93urn.ful.un )- 72nmw ordhwn, 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 blockr8 dec,8j(zv+yh. b7 dteao6f (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 hormm04 9ev5j-n 4zc wrixizontal surface are in contact with each other, me 0xwr44vm ji9-z5cnas shown 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 initially 1.80qsgm-y;q)p* m(vva8t m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter objv-m;tqa8(y vgsp* mq)ect 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 tableq2la,vk,(by)qy wcpblt pxh(//d -7n are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension )w bp(2 dhl,7ktqpvy b/xqa/,lny(-cat 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 fricn wo9mu9jm 9:fbq2bl)tion 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 totzokxl1r6,tp )nnm8zx8 7-g -rawo/ f start 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 stanh4hu6;mzue3 rd :d0s/ult+r fding on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you udr;u4 thrzsd eu f0+h3/:ml6 are not to slide?   

  What is the maximum accelerati)zu vfnh r5h09on a car can undergo if the coefficient of static friction bhrn v5h0) uf9zetween the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street payz9jq l )g;r8di*e2 xz+g/pmavement d)lemag8j zy ;qpzgr +*x9i/2 is about 0.8. On how steep a hill (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 -4gptm a il7)o/ bmd,3z4.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 a rou6gqj m l4h6nro(/svxr k6;p8fgh 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 surface have a very hi1 cgyxf8h/(yk gh coefficient of static friction.f yh(xcg/8k1y

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 kilvdpp:94pdavj a)b88g:4 g pinetic friction 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 (Example 4-20) how l 1y. kvw3eg8w md5 )-4mwtfkmcarge a mass would box A have to have to prevent any motion frfk31m 4kwgw-ye.t 8vc m)d 5mwom occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across th(zvz8 v0-jdm pw)smx-e floor. How far will it go, givenjmzdv-x (s-p80vm zw) 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 contact z 9o8upel,ox:r/(z ic te o86qand at rest on a horizontal surface 68oqcp zoo xeu(:r let z98i,/(Fig. 4-54). A 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 coefficiec u(i,v-x8a 9 o7zdsvz7kf-ro5qj65cmjx nu4nt 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 anj7orm ,9d4kc 8 i5svnc (5q- o6x7af-uxzjzvu d still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your drivha v1fz(ao 6s*eway, which has an incl(h *z vaaf1os6ine 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 slidek6k4y,i8 5qgjw9usw e 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 Fig. 4-55 lies on a plane t7l zn *nt db2q6mm)u.bilted 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 i5 tv fgk.3rf1pnitial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ 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 reaches the top of the steepest 8x:3lu afng2g;o * xsshill 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 wall by someob w0fvta6,4paxm*a +d:ld fp:oj )az2 ne pushing on it with a force directed upward at 2b6p4*tawf af,+02mdl::vd)aj zxa po8$^{\circ}$ 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 med7mb+gcw ,n j5lk:dt8lt. Consider a chunk of snow at th,g57dk8 +ldnmbcjw t:e ridge 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 stopp p,3uvoq2 ek,m+7nchl ing distance for an automobile traveling at speed v is equal mnv2he7o+u ,,l p3ckq 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 das/;jp eite)si.. c)kjz8h /a imh when the driver decelerai/;) .jhmitp /ke) s ceajz8.ites 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 mass m is given an initialzu9**zq . dk2w sobh:ai /o.bdd 3qm8l 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 6eu fh*9dahu: p:ri1ythey 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 r9h :dy 1p :a6iehuf*uthe 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 kicoho3r0 c: x 34ts6u; 2omkrhjnetic 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 4s sti.g)ihs 7the 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 pu6efi,n5kp v .jlse approximately 20 p5ek.6i,f vjng of blood is accelerated 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 aut j5f,hfho2vp1q) oh8kao vj 01omobile crash if the deceleration is no more thaqook) jvvh2h jop ha0f,f5811n 30 " g 's." Calculate 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 prosnzwepf2 4o5rgl(zwa(): i0 aokqoh0 ,ugt ;+duced 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 the ground :hlanogs f4w(raoo+q0ewp,0u5t kz2 (z)gi; 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 ac7 - hp1) z;vfoz.pihb50nryjm cident 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 ki ;yhh-ni)5 f71bpv jz m.oz0rpnetic 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 g w/lcniebfx-i430q:hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reachicl qfwexb3: -0ni/4g es 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 Towert:te +s):xp dl of Pisa and falls 55 m before reaching the ground with a speed of What was tsdxte :)t +:plhe average force of air resistance?   

  A cyclist is coasting at a stead p8/gs(39 esc(tndl6*l /7n5njejvl3 gzmphjy speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emzlj e d9*l m(5/vh(s/6gtcpl 8enpj3sng3jn 7erge 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 hillsvj6t* /oo3 otpr)hp 6y portion of a city. An important consideration is how steep the roads can be so that evehv 6ps) jo*ptt r/o6o3n 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 physics experiments, dangles her watch frf(fz s7k *eux)om a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig.(z *)7ffxesku 4-58). She notices that the string 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 several ramps connecting dixz7(.ffav*bbqva (4i nk he3;fferent parts of the store(e( a7 ;vna.z*xibfb4vkq3hf .
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 the piano (mass M ) using the pul :uwg1(vhv 5j/qgxb/cley 5/wc1juvb : x gq(/hgvapparatus 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 accelerating at 3.5z qpj2x5;2s a7( zfcrd $\mathrm{~m} / \mathrm{s}^{2}$ 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 chd 2/ k/kgy18p3xldfluair, an engineer considers the followipxygkl ud/l3/1kd f 28ng set of 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 6+zi 5d 72v+(e fytksrl60 metric tons (660,000 $\mathrm{~kg}$) . 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 rop) 8)z9ifpxlwres of 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 by 30 cm only. How mp8)w r9zl)fixany times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a "4nkhlgz1 7b5zr5 6ozs 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 sdipm;g 675hf ..27q dtsobo1nsmzi- fpeed 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 ascending an ice field u/swb fo+,/wy t0qr-5fu -re4b3l dte z8 xd-rinclined a3s0wu /yrdwl+ -5td-te8e q,/-brbufrx4zf o t 21.0$^{\circ}$ 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.