Why does a child in a wagon seem to fall backward when you give the ww:w)k+ lg9 h -ajhskh0agon a sharp pull forwarkk9wg-+ ahjl :)hhw 0sd?

A box rests on the (frictionless) bed of a truck. The tk+au6 c4l.zamo ijiz: jsgu)1h.9x4 oruck driver starts the 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 beside the truck and (b) by Chris who is ridi )uk4l6hzo9.1xsa icuja4zjom +g :.ing on the truck

If the acceleration of an object is zero, are no forces acting on it? En tc8lb s ;0 dax*bcuxbdrwu4-*9f9b,xplain.

Only one force acts on an object. Can thb62-6*ld 4 oc jchw 8kur;juo4yxy0zh.kih :ne object have zero acceleration? Can it have zero velocity? E*6jkh8 ucnby;:6hk4. dox4c2hjuo 0rz wil y- xplain.

When a golf ball is dropped to the pa sq-vy j4ijv.1cr5* oh*e mz. /dq0tydvement, it bounces back up. (a) Is a force needed to make it bounce 0c4yyivjq/ .zvrt-m** h 5 ed.dsj1q oback up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why z:5 6bk,woj jfdoes the log move in the opposite direw5o j6b,j: kzfction?

Why might your foot hurt if yo i-j6 zy9uwwi e3sxo;ee* -q7ou kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickl;ejm/ -z0i8l g)ibgh py. (a) What is the origin of the force that causes you to stop? (gl/)i 8imz;0jp -bhgeb) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread fr,sujceo 1zz5 ; 3kd7usom the ceiling, and 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 person gives a slow and stso73z cs; 1, j5ukduezeady pull? Explain your answers.

The force of gravity on kxe9d vk9q2 i6a 2-kg rock is twice as great as that on a 1-kg rock. Why the9kk6 i9qe v2dxn doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate resulflq;la qf)5*gb(l - nxts if the scale had been calibrated (a) in pounds, or (b) in kilogr a5x qqg)f;fl *bll(n-ams?

You pull a box with a constant fozbjsd ub2ri2 zvl zc9pk x4l;,i3;.n+ rce across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal ( k2xv;.+d94r sjp bl 3;inc,l2zzuz ibwith 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 influeabqgf iaijc+3t 8-k25nce of gravity there is a net force mg exerted on it by the Earth. Yet by Newtbja g3c +a52-tf8ik qion’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to l)p1*4yqrlyopr x eozas* .(-wift a 10-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 a given speed on the Moon anr-1w4plo .rxeoyz*)*p (s a qyd on Earth.

According to Newton’s third law, each team ing5fxkl( hxp,8 x) 3 ti7m-oxro a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then,gt5hf8l)x3 ,-7mxip xo ( rxok determines which team will win?

A person exerts an upward force of 40 N to hold a bag o0iio.7ey h0ta aj54um f groceries. Describe the “reaction” force (Newton’s third law)yiaeai 5tuo07m 4j h.0 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 doynz6-/hj :gcoes the ground exert on you? Why doesn’t this force make you rise up into hyz6 -jg:cn /othe air?

Whiplash sometimes results from an automobile accident wh(aq z j9xxd0;iwrv*c:8w, louen the victim’s car is struck violently from the rear. Explain whr89j*l u d(vacxw0xw q:z,;oiy 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 accelogboc,38jvmqr3o9 kayqz)t h;m3/c7 erates, the crate remains where it is on the truck, so it, too, accelerates. What force cause3ghqjb79 /8t, 3zrmmo oq ;)ayv3ockc s the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reachewm8*mj2bbdfes(2d/ p s its highest point, it slides back down but the magnitude of its acceleration is less on the desc2dp8m b/*(efdw2mj b sent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined plane ch-ghtj+k4+ty 4seq1nh 7, el? Assutec,hyn4 1 4- +7gk tehq+ljhsme the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled atinah4b9m5 *myp ztq0+ 1.25m/s$^2$?   

  A net force of 265 N ac68m wlvu /k+9 e)x 06zwdw*ypvt ,ezgncelerates 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 withstand if it is usedxge3wotkw - b/7v75hk to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight op- d wxgl1mj /reh405ui -nej:f 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 q1,ztluyc1t l)1evv )kvp;q4 /kyr2fto stop an 1100-kg car in 8.0 s if the car is traveling at 95km/h?zyvq u 41r1lpf q/v y,2c)lk1ve )k;tt -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 125mrae((g8pt7y q/s over a distance of 0.800 m along the barrel of a eg(arp8q(y t7 rifle?   

A fisherman yanks a fisvqx:y yb6i.ik oqp30cfo5l - 7h vertically out of the water with an acceleration of 2.5 b:7pofc 0-yy.ivq5 6x3ol qki$\mathrm{~m} / \mathrm{s}^{2}$ 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 covh1,a* *bta29vvczfjx er 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 that thdf 55mt5g5o bye maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on tgtfo5m5 55bdyhe 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 eswqp g0xri2uamkypqp+u 8 k g 5;/,64a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the kgpq4p, 0u86x;ymsaru+ eg5kpw q2/ iperson’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 maxim .d0vmb/:br-e o ec2uyum strength of 21,750 N. What maximum upward acceleration can it give the elevator without breaking? e -o:uvrybdebc/.m 20    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg includingi8afs0k(h8sf d xk, x+ parachute) when the upward force of air resistance is equal to one-fourth of their weight? dfas8xf0(8 +kxk i sh,  
(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 .f p ,s.bdw-gf1dsi:vk0qk -sground below, he bends his knees so that his torso decelerates over an approximate dist,ks. v0k-diqfw df .pssg-: 1bance 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 the box wdr/yx4/ ny/oruns vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the tayw/n 4//xyrdoble 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 fo+pd(b/ aj z( )ui:zjdur 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 dinrkt tvpv1x.-m c9fs+ *so :,dagram of a baseball (a) at the moment it is hit by the bat, and agais:tm91- , sp t+.vvxornf*dkc n (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force i b,3:vmlkpb: l.sfhdm:92 igmust be exerted in what direction so that the resultant of the two forces points westwark9fi:b dl:g., l2vbm:im3ph sd? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strunhmozhgo:(zn .ey ;9g9 7zs(sng horizontally between two buildingszhnn7ozs: hz sg.oy(em ;9(g 9 10.0 m apart. The sag 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 hang05*kd ix) hp1oi m)m j-gxknt:ing 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.u d-q-s prv 5t3tq42fu0$-\mathrm{kg}$ 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 t)4d.p 9 (fn7q xxgcetlo a new location at McMurdo Base, Antarctica, as shown in F g(fcxqtn 4.lpd 7x9e)ig. 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 carpawpy;8x.:h(cl 1w+kooiu4o pr y(k )+ul 3sks of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling+cy lkw 1;l(w:ooky(u)p4+sxk . i38u rppoha 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.ft hub1bt3o8 -whnf--pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at cw1tu3-h bn.8f bt-o hfonstant 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, a b0 czbw px bd;+;+jmd265$-\mathrm{kg}$ 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 agc.wr8y t*(vblock (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 ar. 2k*ohrjz0x le in contact with each other, as shown in Fjh*o0r z. xk2lig. 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 abo3ad.w 07tnwkqmff n04ve the ground, 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 heavier one hits the ground. This is its "launch" speed. Assmdfft.wn wn03k74q 0aume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are conngv*3vg) p.1bdqj/ fb sected by a heavy cord of mass 1.0 kg . Calculate the acceleration of )1gdbf3 p*s g/jvbv q.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 kinet 7zg7l9 m:oqgtfa7,ekic friction 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 5.0 4lmdyw;k5f dd78lssbz5t -7n$-\mathrm{kg}$ 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 on a train acceleratinv5umtn 65oe 5 g+jz)lfy.gsn7g at 0.20g. What minimum coefficient of static frigo5n5sn julz.7ge v65mtf)y +ction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car s(g wthup i1 *0syo.kwtx-oyw4w5z6 (can undergo if the coefficient of static friction between the tires an(4 6-xo.su k0 gpwyz(itoyhwsw 5t w1*d the ground is 0.80?   

  The coefficient of static friction b/i-m wm ;0wgobz,df) 1nu9f zgetween hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car -mf)zfgnwm9oudz/1wg,;b 0iparked?   $^{/circ}$

  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 yadj m -l)3qxj1cye2mr0 5 j0c -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 a rough gy4uj ik(m+t w3e+dv +qjva92 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 k eldx e d.:(x,7a0nghvery high coefficient of static frictigae(:n,l7e xhdxdk0. on.

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 friction fe4 4z/lqzy:g6v5 kqmcor 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 ((-qqda) k4l kws7h pk(Example 4-20) how large a mass would box A have to have to prevent any motion from occurrqs (dphk4qk (7-a)wkling? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides acvyf8nn qsuf4ed7 z;/(9 j lt+q+tbqk)ross the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed oquz/9)dsjfqt ;b8 ( et+ly f4v qk+7nnf 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 7bz hh8 /dpc3gggg*9) o5 kg and 110 kg , are in contact and at rest on a horizontal surface (Fig.)hod g8 9/p*h3zcgbgg 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 coefficient of static fra.g20 qk 9n3pkcy b2jhiction between th n2 yaq23pkjk9cbhg. 0e 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 cab of the truck?   

On an icy day, you worry about parking your cajev.a 2we6+tl.3 tiug g6o1aar in your driveway, which has an incline ofavi1glejoat+62 3 .uwg6 et a. 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 slij84t9 dukwmz1 jtp-p1de 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 lie3w,3+oxh f k0r1r jj;fatd4mas 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 sv-ash .5 be*ffpeed 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(7cq- a-qct ox 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 wall by someone pushing on it wtml3ts t2yk7,ith a force directed upwardm, 7sl3 ttyt2k 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 projec bup:-j7dl l(utiles as they melt. Consider a chunk of snow at the ridge of a roof with a7ujlbl( :-dup 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 miqmjso)hr /02je*in,d nimum stopping distance for an automobile traveling at speed /m0 jsio h,2req*d nj) v is 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 p ea5yb(oj:e6-gnop8 the dash when the driver decele6op:yj-5eeb (ga on 8prates 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 *y1ty9 k ue vds4olw76wdzu-w :q8w 8em 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 q twpm*0z4ey-b ,be:x where they are filled to the packing station 11.0 m away emew,*zb-q40 tyxbp:. 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 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 coefficiopleq .90txv )i qr,;erlo.s:ent of kinetic 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 the bicycle) can coast6p5 gsvt( nh31ez9oa i 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 eache2+41fjdmn5t2wk mji pulse approximately 20 g of blood is accelerated from 0.25 ind1 2kej5 2j+f4mmtw $\mathrm{~m} / \mathrm{s}$ 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 reasoxh6k9dp m-bdydp8 gy2y0l-rk6dxlh0 g9;o (f nable chance of surviving an automobile crash if the deceleration is no yd9df-ydy 0 6pkbopxdr0m96l2 gg8-l;(h hxkmore than 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 produced by an earthq: 0 5rg(c7i a9ydyxuinuake is a , and if an object is going to "hold its place" on the grunrai(d x:957ycig 0yound, show that the coefficient of static 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 accident h2 b/jav0fa,c involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficib 2j ,afv/ha0cent 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-inod5 p ab(; d1lslvh49c*rq,wrq g99gu -4 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 reaches the bottom after traveling 55 m? (a) Ignor,uw l hr5qc*s 9qgbapdgv4991r;d lo(e friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from thq9i zq4oy3f(mlwv,c 5e top of the Leaning Tower of Pisa and falls 55 m before reaching the gr(,5iwycofv 9q qm l43zound with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 1 zr77jcho ga6:2m/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 forcjzr7:6 goa7 h 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hi8 )r,c ofya/ikdxq6zp j.fo)9 lly portion of a city. An important consideration is how steep the roads can be so that even low6)qk,/dfoa8.o)izp fxyj 9 rc-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 f62gduf c; +vbxj2w)cvdhxg81 rom a thin piece of string while the jwu6vf+h2cd x1 d8)j 2cggbv; xetliner she is in takes off from JFK Airport (Fig. 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 ra z 73ic)un.evb)b yk7rmps connecting different parts of the store)k ebrcv.7)i3 zunb y7.
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 ) jrcz4 ;ccuw5v+wlak-d n7p lv.;xn-piano (mass M ) using the pulley apparatusj-lr ud+.l )k74cn vvcw;p cwnx az;-5 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 a5ntdef5ga8l0jbe6 1s 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 f6c 6d3+wi ifvt 8)bvisor a child-restraint chair, an engineer considers the following set of conditionsd8 vicifi6)s3bt wv+6:
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 trai a4mb gi)gh)1on has a mass of 660 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 ropes of simij5 rp*x2m rh*v/uof s5lar 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 tr*/2* prm oj5v5fsxu hhe 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 boat is using a uk:4jq0l oby6nq 2 xm*" 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 a gb*8 q03q xejtk6wbsn vi:2.fllowed 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 b33i8o ; wdl1inukx a33eq( htpk+g(rascending an ice field inclined a 33xlkr+gnahkwi8 ;qei(1u(bd 33tpot 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.