Why does a child in a uqb gj85a*2) pt8fh icwagon seem to fall backward when you give the wagon a sharp pull for 5quac8g*thp) bfj82i ward?

A box rests on the (frictionless) bed of a truck. Th- 8ty3;qik kq ra4ung(ko bo0pno*2o:e truck driver starts the truck and accelerate ao :gkk8 n(3nyqb;r0 o2k4qoo*pt u-is 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 riding on the truck

If the acceleration of an object is zec, p2o,mla* zjro, are no forces acting on it? Explain.

Only one force acts on al5 qtt4fjt9)ro;l //zsu/ aqtn object. Can the object have zero acceleration? Can it have zero velocity? Explaiottl qfq/;ts4jla)z 9r /5t u/n.

When a golf ball is dr.1 d75-d lrp ibye(bxiopped to the pavement, it bounces back up. (a) Is a force needed to make it bounci -5xr(pebdi17 .y dlbe back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move 37y+hyur-j*+fdla b fin the opposite directi + y-rfbuady3l7fj*+hon?

Why might your foot hurt ief e9al3irz1+f you kick a heavy desk or a wall?

  When you are running and want to stopki jpcx;*o ;+p quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop?+kxj;c;popi* (b) 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 from the c0 urcado . .ieo(xb6c2eiling, 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 steady pull? Ex02uxcoa cd6e.orib (.plain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-k ug10+l5y*7 jjt oyeiz;fa2epg rock. Why then doesn’t the heavier rock fall fasli*ep07 j2g zte1 ; +5auyyfojter?

Would a spring scale carried to the Moon give accurate results iff 6u.l+ fcy vv3;kj)0kvz77h xb/vn pf the scale had been calibrated (a) in pounds, or (b) in kilogr) zpvfx7n0l f;k6 .37vkybhufc+/ jvvams?

You pull a box with a 8qk*;stg pf19n3ohcm constant force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an a1po g9;8mh*fsc qtkn3ngle 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)ric(l **dqir influence of gravity there is a net force mg exerted on it by the Earth. Ye)iqc* drr( *ilt by Newton’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 lift a 10-kg object when you are:ps;xp3e -1gdln2 a ds on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg objecls 1- pdp x32g;:aendst horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulll ldl.1luar 76ho, wo(s with equal 16,l7 or.aol(lw lh udforce on the other team. What, then, determines which team will win?

A person exerts an upward forxepu8rv4 z1zx .m6g:a pl5g; wce of 40 N to hold a bag of groceries. Describe the “rea4px wu 5gr:.lzm 6p18;e axvzgction” 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 ; l0ry)2w4 x4( ivnthzzlx l7qlarge a force does the ground exert on you? Why doesn’t this force 4v 0l; zxziw24nr7h (lqy )tlxmake you rise up into the air?

Whiplash sometimes resultucvfm2 siwt,;0 : za+ns from an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it reallytif0+msu2,za n :w ;cv?

A heavy crate rests on the bed of a flatbed truck. ho oi+c+n11 ce 0kkfv/When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to accek+1cic k 0eohf vo1+/nlerate?

A block is given a push so that ixzo9li 9i e x +i6kqs36u-a6rht slides up a ramp. After the block reaches its highest point, it slides back down but the r6hsk66 iuzx+3ii9-9qoeal xmagnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weazf3 6eciz2z40 u sdy;wdd f3ux9 u*;fighed yourself on an inclined plane? Assume the mechanism functions properly, 3eui;*f as320yfdxw4ud6cfz z 9zd ;ueven at an angle.

  What force is needed to acwsh0 68ay2ywoaxq* 5fvm33s mcelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N acceleraf0o(hbxv1 3 veeg pw 6++4tgkztes 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 used to aokf9q)r( 4cw cccelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight o,)itgi1xo,u 5x 4ti gi/jt.rxf 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 iswqhoos6)kj2,bv+a . p required to stop an 1100-kg car in 8.0 s if the car is traveling at 95km6 jb,+h2o)avsq. w pok/h? -  

  What average force is needed to accelerate a 7.00-gram pelled / n.le,ridn+t from rest to 125m/s over a distance of 0.800 m along the barrr /nl.e id,n+del of a rifle?   

A fisherman yanks a fish vertically out of the w9td tb29h q3hjater with an acceleration of 2.5 tq93hb 92jthd$\mathrm{~m} / \mathrm{s}^{2}$ 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 cover a quarter-mile track (40 is p6 as.:f9xyf7w8.a9 vyrsf4/ukq5mc* olt2 $\mathrm{~m}$) 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 the maximum acceler1 ij* q+ 6l9mqux;lwplation is +xqlm6*jlw9 qpliu;10.0680 g . What are the maximum and minimum 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 mot z0ci3a +.jds *d4naqc*f ,cmmionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find cn4 m s *a0jc+ifzqmdd.ac* ,3the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 2sf,hybgc2;i5 zz+k ;k0hgqi 2 1,750 N. What maximum upwardkg zbhs;5h f 2i2ky0+, gqiz;c acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky diversp*ed4i pjrg24 (mass 132 kg including parachute) when the upward force of air resistang4r pd*e jip42ce 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 rooe a ,kf4k(8er8:gc+h kv -gehgf of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass ofgvc :ek (hagh84ge8r e+k- ,kf 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 runs verti;a dlki97tsi6q6un mk+1b vh2t,sv7 bcally 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 thevbk19,t as b6; lvhunk7sm7i2iqt6d+ 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 playerrqtkz ,o4 0hl9 8c*iyd
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment it xakl m+/o)7h ibbnac005m0dy is hit by the bat, and again (b) aft)d0h /bb +0cklax75y0 moamin er it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly dig t*6p3 tr6socrection. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? cg*t6opt6sr 3 Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung ho 1swj: kxkq(b+rizontally between two buildings 10.0 m apart. The sag in the rope when she is at the mik w:+x (bkq1sjdpoint 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 buc2xq oq bdubgz9:k+mf62x 4o /; mt ki0yc2)sjmket is hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.2hu;sqnj m+ 6n0$-\mathrm{kg}$ 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 McMurdo Base, Antarctica, awz )n 3yqi00wls shown in 03y izn0) wqwlFig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig.ygtm/u 3w/; cthpgy. 7 4-47 . Determine the ratio of the tension in the tgygyt p.;/m 3uw/hc7 coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward us3je 1nc*yyhsiqs2j37ing the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downwacj7e2shysn 3 i31j* qyrd 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, jf53np rlm2z3a 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 bxf eyp;tsww b.z,mx t(m )*j)b87mu*nlock (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 1 oo2i xdl:nlp5itw-- contact with each other, as shown in Fig. 4-51. A fow1n2-: 5l litodo-ip xrce $\overrightarrow{\mathbf{F}}$ 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 in9 -tpqr* z7d iesu*l2xitially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the groundsr-eduq*7tlz x92 ip* . 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. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless tabl5mla : ef(oia6e are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body ali a :6me(5ofdiagrams 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 35zjj+dh*7g q( m8fdf7x$-\mathrm{kg}$ 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 r0kribq7q)i/4dg5jl iequired to 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 standing ona gmpk*j *1y(egioz(0 a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slideoap*0j(1 ge(kg y*imz?   

  What is the maximum acceleration a car9mts5f . bq+wle0iozh0p,x3y can undergo if the coefficient of static friction between the tt.szw io l95pq mxbe+30f,hy0ires and the ground is 0.80?   

  The coefficient of static friction between hard r58ncay - z6fj e3p,ickubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a cya56i 8 -, jnpkezfc3car 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 g.3; *r5pgbbgjm f wd4at -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 re8s)v(l 0tvf0a2gpbjzbi8 4f ist on a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contactxw,6 3pn psb,h with an asphalt surface have a very high coefficient of hw,,s3bpx 6 npstatic friction.

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

  The coefficient of kich r;ww6( /ukcnetic 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-n-l ugy.hsn 6;32 (Example 4-20) how large a mass would box A have to have to prevent any ;6sn -nyugh. lmotion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the flo++ 35kwtj-hznil td o8or. How far will it go, given that the coefficient of kinetic5 +kiz+on83-wjhd t lt 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 and at rest on a horizontadm0g2nt s,ru0x3+ f zal surface (Finrm0a+f ,2xtgs 0uzd 3g. 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 carryxw+c 3c*rowz; ll27vz ing a heavy crate. The coefficient 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 avoid having th3 7 w+*occ2lz rzx;vwle crate slide against the cab of the truck?   

On an icy day, you worry abo+)j*ru;pcwm r ut parking your car in your driveway, which has an inc;j pruc*r m+)wline 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 with a ie2f0* ksblf.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 plane4jr zd8yo5 *vkkn+wz5 r4)e 3ri rtwd; 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 initialymsd z:lhnd+x k cq4)qus .3-- 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 steepew;g/g8s 2yngnst 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 l3n v p3sa2rl9on it with a force dirn9ls 2prlv3 a3ected 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 co593*bnq3 w wn9xu jrby 8pl1kan become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitch 39qpbnl98 o bw15j* u3nxkrwyof $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile travelingut8(w9k5 7s7q;n w.axd zckm+ra omv- at speed v is equal z;5w(nt c7o8-rmkq a v.+sk97uxdwmato $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 ;9 et*pixiu g1+t4iyd2n(jisf* a8v ldashboard of a car slides forward on the dash when the driver dp*f d8i*l9(vnsgj2ti1yi;t u+xe i4aecelerates 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 inivww :; xql0 yxm8a-9qqtial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from where they are* j( 7a/dre5:fzruhan filled to the packing station 11.0 m away. Th5uzad/rr :(j a nhef*7e 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 coefficient of kinetic l -xde,w/ qnrrgr42h +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) o ;adcyrc4 z 8n8kzn3avlj-6 (including the 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 pu +c 5yxl-;yu phpt+od8lse approximately 20 g of blood is accelerated from+5pdo; hct u yp8-ly+x 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 crsym;;68wosv : bglhlb- l19xlash if the deceleration is no more than 30 vlllb96 18 s;:o wylhsxb;g m-" 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 produceoda/bitfbr-8 k, u+6o mi:b4ed 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 grou8it fr/ ba,6kibodbe:m-+4u ond 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 ans tzzt06-o(td3 z 5oif accident involving two cars, measure 72-m-long skidtzz 6 izof3-d5ot( s0t marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hilllb1 ah7(k wbso4e.:z k (1-in-4 means that for each 4 m traveled be wo.k4szk:7 b1hl(aalong the road, the elevation 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 L lf(ob.7x avgt0/ikhzq bjh n 1*w9);deaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of airqo0)k bw 79izbv1ga;(hf *tdxl/j n.h resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy st5 kzdjp) .dng7retch where the effective coef) jd7.nz 5gkdpficient 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 emerging?   

  A city planner is working on the redesign of a hilly portion of a city.b0;d6(s )c qve;5zsbs.muya a;o;obo An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular smam;)ay(zo vs ac.;0 b5d;sbeu 6soqb;oll 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 experim:do9-2rc vpg pents, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). S2r:op9d v-cgp he 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 bvw/ nz g6rh6-k. uh/aze several ramps connecting different parts of z hgu/nah/w.z -vr6k6the store.
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 piaskgw(i( oiij2*9pz:3o pvlne 71 x2bfno (mass M ) using the pulley appara1ipi(g9j(f27vwbl z3kx*p2s i eon:o tus 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 acc.5tl/ 9rkjgc( m:ntf)et 7aqeelerating 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 s9 gpzs:.suz6gvr6478 ekctk gw g08ba child-restraint chair, an engineer considers the following set of con87g t. w zzs8gb6ver k06sucp:ks4gg9ditions:
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 o*f fw)1-v, h)lrz es.sohvq7mass 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 similar length. Kare /f(m4cd:a hol++ar awn'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.m+dola+ (f4racw :ha/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 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 m(k0wy+3 ox ohkvd/ir slo 60;a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to i)gu: z w.b6bjreach 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 ascending a kek7/m:vyuw 1n ice field inclin1ve:wk u/7kymed at 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.