Why does a child in a wagon seem to fall backward when you give the wagon a sha.vjf/o( b9owei-d /nxrp pull forward? dewifvnx/b( /o. j-9o

A box rests on the (frice 2f1y( leq1cntionless) bed of a truck. The truck 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 (aqcn1y e 2f(l1e) 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, are no fo1r oo fe39i2v be/c3mkrces acting on it? Explain.

Only one force acts on an object. Can the object have z)wnpsert4 hb50p/ g9rero acceleration? Can it haveerht)b0r 4 w/9s5gppn zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a force j;avr 9os/z5kneeded to make it bounce back up? (b) If so, what exerta;vrkz9/sjo 5 s the force?

If you walk along a log floating on a lake, why kb88e(q)bu ue does the log move in the opposite du)b(e8qk eb8uirection?

Why might your foot hurt if you kicuck 1hkd: bb,p )-)-g nip.iqks0hk,vk a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quic/vcv o5md4o,oji v;n) kly. (a) What is the origin of the force that causes you to stop? (b) Estimate (usingvvi;5 ,doco 4/v)jnmo 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 ceiling, and a section of the wv4*/,ipmb .t.k le l.ufst7c j4rg g6same 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 ste.t 7 bsrgi mwct,.4gll/vu4j *.6fepk ady pull? Explain your answers.

The force of gravity on a 2-kg rock is od)- . f) emi.oi0gkmxn)dam+ twice as great as that on a 1-kg rock. Why then d)mmid.).aiog fne+d 0 m)x ok-oesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the sm jov r(1v+6ea 41ijuscale had been calibrated (a) in poundsi(u+ eo14vmjsjr6v a1 , or (b) in kilograms?

You pull a box with a co b1+g 0 jkd4*irf-haptd 0:jtinstant force across a frictionless table using an attached r:pt +gdjr ki-tidh4*ja00 1bfope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of grav+i:k mbn,vyxac9 6)wjity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law th9)ni jbxk v:y6, wma+ce object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or for2fz i3rhrw 3.jce) needed to lift 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 ob3 fwi j2hrz.r3ject horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war fgo2 ./ bu*dt0u ,dnsv viv;cy mi3,.7.lxvyu(Fig. 4–37) pulls with equal force on the othericl/y*fyuv o,.b,s2g0nvu73t; dxivvu . m.d team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag ofgvwx ok2d/ yen(m 4pu ;g,u4+g groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exer(ug;w2n+ ev4mo ugpxyg,d/k4ted, and (d) by what object it is exerted.

When you stand still id: *e s5zkh4gon the ground, how large a force does the ground exert on you? W5g dk :siz4h*ehy doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident whve c9q aa6 n,:0m 9w(mr:rmrvco /7 k3e0mwafhen the victim’s car is struck violently frqman9w famem06cv(, :m07ar3e9 :hck ovrw /rom 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 acceleratesf(2 5wy (a(suttkl )h)ia1zbc, the crate remains where it is on (za12tu5tbfskwyi c)ha l(()the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a rx04:yw,dqrdxi:p :n .b g2q efamp. After the block reaches its highest point, it slides back downrd,fp: : 4gnx.0eiy:qq dwxb2 but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself ob g+qz.t:ts cn2,h,dm scj 0x1( nggo/n an inclined plane? Assume the mechanism functions properly,c sgggdqh x:1(2,jb0st +/.cnozt n,m even at an angle.

  What force is needed,4i)m4dmiq xuj6mu b )+t-wk d to accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelera 4bt.p ik bdoa;7bhm97tes 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 usejj9 kw1mp)fo /d 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 * tjwolj)up ;ts/- ip2a $76-\mathrm{kg}$ 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 qfg3rs23 uz 2:y/ yyktc0h) gycar in 8.0 s if the car is travelinggqykfy0h)r 23c us/yygzt2:3 at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram mp(gd5z-t0:2p* umh w alobu5pellet from rest to 125m/s over a distance of 0.800 m along th5m5*op20 uzdpua gm w- bt(lh:e barrel of a rifle?   

A fisherman yanks a fish vertically out zp 0ab -: bx*tw1q8vhofms.k1 of the water with an acceleration of 2.bhmt8:fs* -okwq1.a p1 0 xzbv5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 xc ( +60ns akiz-s)mb(xm me/-ockqk4 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 the maxi.o.a( w-w0qw e es+xqimum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should ewoa-( i qq.ex+0 wwe.sxert 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 motionless elevator. Whe7doit d7.s( 6 h.f,t)zacvbk f6uhk0en the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the a 6 o htecisd 7bz0vth.fua(,f6d7k.k)cceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a5yb1ygep 9x7d maximum strength of 21,750 N. What maximum upwar 1xey5yd7gpb 9d acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky q634c zclw0 6ngj3ffq divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of 33 6qcz0nfgjqfc 46wltheir 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 grop/ f -aot9.bvound b-ofbo .9vp/at elow, 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 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 th.1eh+*i j +7a1xufome+ 0kj c; vnrin)8iosvbe box runs vertically upward over a pulley and a weight is hung e. obin18f*nih )xu ev acjm7k;s+jir+vo1+0from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for afgx6; rbj a:r 7dhq56e basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment it is hit byn ;v:dqg6v4r6t fsd9j the bat, and again (b) after it has left the bat and is flying toward the outfievngqt6fvr;dj9d :4 6sld.

A 650-N force acts in a northwesterly direction. A second u;jk(a .t2 bbh650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vbja kh;.bu2t(ector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two building9 mrqf;v cw4(ps 10.0 mqmrc( pvw9 f4; 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 hanging by a massless fsm7 gw2k 8ra8cord 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.t 823iag / af2qj*ticr0$-\mathrm{kg}$ 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, Anta,9jbac4h qje* rctica, as shown in Fig. 4-46. The s 4b9c,ejq*a hjum 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 beh(u9 6fx z dg,oahqat-4ind it, Fig. 4-47 . Determine the rah (og4-qa6,xatf9d z utio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upw rgs7sxrdh(5e1- kgncm44p ni)n0rg9 ard using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull dow sr74d0)ix4hnnn(p rgsgge c5- r k91mnward 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 rac0svstyr hr b4q 7e+r-8e began, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (mas myg n, )f*:p35tvruca3 rfny(s $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact ly .j7,qye2vcwith each other, as shoyycq7 evj,.2l wn 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 1.80 m above the +u(q1ml7w:ri v9a eu-w(ydg e 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: Fir7uqwuy e-1:lw(g md +ve 9ia(rst determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are con/6e2vn57i5n6mp k9ecx wndxsfxs(h0nected by a heavy cord of mass 1.0 kg . Calculate the ac5s dx wnxpee62m 9c0 /(6i5xnnks7hvfceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction be-jl:x a5 -m,alf s82/0pgnvoahlwsr /tween 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 2:s y6wje(lvpstart 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 on av-1 t pjv n:eghi+p7t* train accelerating at 0.20g. What minimum coefficient of static friction must existej tn*ti 1pv h:p+-gv7 between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car stv9pqs,0d ef3vm*4l0 z0 qwvcan undergo if the coefficient of static friction between the tires and tvls* 0 vd ,0fz3q4v0mwpqt9se he ground is 0.80?   

  The coefficient of static friction between hard rubbe w9.lr,uf7 p mi:;--oxojtgp kr and normal street pavement ismoo9:fiu., p xrgjptl--kw7; 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 decelerateoup)*y-*nx qmn e(; , njtishtt:bj 73 at -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 oni 6f7x*g0fo ky a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have70ojf8 7-tp6qyqoby h a very high coefficient of static friction 7qo6tfy opq- bjy0h87.

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 kit w16 -+cvs/e+ngbqsvnetic 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 large a mass would box A havetii e33cv j7w2 *mta1gw ,uqn.:7hv/ph*lhx w to have to prevent any motion from occ* w2 i.7m1i,tjwv/3hquehtac3lv p*hxnw :g 7urring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go, i(hoz r:d/drnvn3st+1 /f9s p given that the coefficient of kinn id9s/hodz1(sr rvnft/3:+p etic 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 contac3 y6 bvu7e3jb,2 llacst and at rest on a horizontal surface (Fj2e33l yab6v s b,l7cuig. 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 frictq1y7,zsx6i7v2plx2h7f u:l 2m 4 udxrq os d1dion between the crate and the bed of the truck is 0.75. m2yo xs i7zf x:q2prd 1usu27,d6q7x h1vd4llWhat 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 car inolcaczvr5 :+x y;.)qmsm c43u your driveway, which has an incline of 12:zrcm4xa y5;o lm.v)+cq cu3s$^{\circ}$ . 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 slu.hf .9jk;0x p eivpza nbs5.*ide 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 lyj5v,y ) 062p bfyuiioies 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 initialy i4 o1mmrkzxz. i.l.xrnl71 . 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 rea(yc *yna n +ef/.yix98ryt8nqches the top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by some97zyl)e0okig9i csc dxxp/rv x:/()i one pushing on it with a forcesxx70c9 i )k(l)ci g:yi9xez /vodrp/ directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can beco2pc;lwi y0nw4 me dangerous projectiles as they melt. Consider a chunk of sni2wyw ; lcn0p4ow at the 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 stopping distanc1a mdd3x:kwzfb a(-:p e for an automobile traveling at speed v dp x-mab z :(d1kf:3wa 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 slidp2jcugm2c )y.t+2f c qy*8jf. v:bhu des forward on the dash when the driver deceleratesfc+ pjdyyc8f ht.j.)ugb2* 2 : vcqum2 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 gi2mk0 lty*hxj/(wajr 8ven 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+4fi a(c);ramqt(,mj ;quatj where they are filled to the packing station 11.0 m away. The belt is initially stuc, i a ;qq)+( rfaamtm4jj(;tationary 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 fricu9dwazg ,3x(ce (jafhh m8- 6ction 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 iy+* 1 my o:yh4tl1qwmbicycle) 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 mamma*q c zr4;to0d:ujrd v8lian heart, at each pulse approximately 20 tc 4z8 rduv0q:jdo;r* g 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 survivinw8p6 /ebg 3ahgk;/u g6*of qofg an automobile crash if the deceleration is no more than 30 " g 's." Calculate the kopaq6/g*e fg/ ;68fowg3ubhforce on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , a t*y2pgvqb6 qod 6w+i3:8pkjnnd if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at l6di +28pjn6y qptvokg3:q*bw east $\mu_{\mathrm{s}}=a / g$ . (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 tmak.6b rz03 fthe scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a levelr 6a mf.03bztk road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m travel :h2xw/c0e btv 79uwvybfh(z9dpn3 7hed along the road, thfdu / (pxvw nhz23:cb7wthe vy0997 bhe 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 to;p5-fh.pm d4r kdizk,p of the Leaning Tower of Pisa and falls 55 m before rea-f;rdz4pdmkhk p5 . ,iching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a ylhx rs i7-4yqp6p mh8dvh20-sco,i(muddy stretch where the effective coefficient of friction is 2,7hp ihl-0myxp8ch 4v(osid-q6syr 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. An imp;mx kd8s3ydof; tt0p8v5d n 8iortant consideration is how steep the roads can be so that even low-powered cars can get up the hills w t5dptfi8yn8dxm os 8v3 0;;kdithout 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 from a thin pro)e 2*kcdz8zsdn 1j 1iece of string while the jetliner she is in takes off from JFK Airs nz )rco1zkd1d2e* 8jport (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 supe: ,+1g /vjrpudhdug)npa4l ;prmarket, there are to be several ramps connecting different parts of the store.gpl /p uav; dd+)n:u,jr 4p1gh
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 need 1j/i 8yj3g/ gdh2dpv ,ramtc,ed to lift the piano (mass M ) using the pulley apparatuscrapdvhg,dt//g,i y8 j m 132j 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 accelerp j 24rqke73weating at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engineer conside8p22hc8b k4ft umhal0 anc,, trs the following sel,0fc,8 4ubac2tkat pm2 hnh 8t 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 Itali;*-1 ypd ydg*y rfl n p;:7:hvu(kxd./jglflkan train 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 ropesw ap ujkzg2f//+og ,d(tj cf5, 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 didgj52 ztkp/gfa/w ucjf+o,(,stance 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 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 s4jy(y0 w, 6lg -ndyxoa " 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 aln7gv9l q*0 . tqdmrs1wlowed 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 (oy2-b 2f* ptqxth uf)are ascending an ice field inclined )-*byfotx(f p2 q2thu 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.