Why does a child in a wagon seem to fall backward when you give the wagon/sb3l(+* t;:u ob g2kf9k 8hiwbm lptl a sharp pulkuw 8; h 2klmpbit g* bolt+3l9b(fs:/l forward?

A box rests on the (frictionless) bed of a truck. The truck driver starts nk 8x7 n 1dg:58euwfjlthe truck 8 x 8dlkfn51j:7 gwnueand 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 riding on the truck

If the acceleration of an objec29em cz gwu7(mt is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zerpgso w9foa3.1fzd +3fh i/mr4 gn n:2do acceleration? Can it h3hmp. gg+n/o:92fffn4 dzaw3 s odi1rave zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a forcf(oa9hl s3q0x e needed to make it bounce back up ( hoa0q9xs3lf? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log mo ) svh713ei(dny.hh dwve in the opposite directe d( hw.vs3hn7)i yd1hion?

Why might your foot hurt if you kick a heavy devo3 94ext)cd jsk or a wall?

  When you are running and want to stop quickly, you must decelerate qw pa;dm.b0gk(q u7bd ,uickly. (a) W augq. wpmd0k,db(7 ;bhat is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section oe2hm x47wr49e6thad)z i6 e wrf 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 like9rw 7ieh4x hw2m64rz6t)ade ely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg ro- 1rsn37qjv rmck. Why then doesn’t the heavier rock fall fan3rm j7qs1-vr ster?

Would a spring scales t6gt( det1.c carried to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) .(6tcsedt1gtin kilograms?

You pull a box with a constant force across nkk-/ eabe 2y1a frictionless table using an attached rope 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) ie1 ak2ebnk-y/ncrease, or (c) decrease? Explain.

When an object falls freely under the influence of graveyswpu kj3opx q6 4)yv5o )s)ijo+f39ity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and o vx p3s5y)p i6s) jjwk)e3qyu+o94foopposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you areu yij vv;69o2kv 1bvn2 on the Moon wit1o62vvbyn9v2iu j; vkh 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 and on Earth.

According to Newton’s third law, each team sy 84 *um/4ynd0gqgg qjx)2oein a tug of war (Fig. 4–37) pulls with equy8g/2o dug ymq *4xgeqn0s4)jal force on the other team. What, then, determines which team will win?

A person exerts an upwardakuj + 4imuiv x;:c,/w2le:r d force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object ilv x:,wduc;m:2e /j4+aki ur it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force dt;+4)4zorsa ot az mdfmlsbb) :65,etoes the ground exert on you? Why doesn’t this force make you rise up into t,;t+mt):a 4aoobs 4ze 5s zr btf6lm)dhe air?

Whiplash sometimes results from an automobile accident when the victim’s car is8*b -rv ujtva/ struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. *8v t-jauvb/r Is it really?

A heavy crate rests on tu) *5.wrnaefnhe bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the cua nw)f*5. enrrate to accelerate?

A block is given a push so that it slides up a ramp. After the block/z -:es0kiwb l reaches its highesti :wzs0/-be kl point, it slides back down 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 on an incl97wqcw j 1pjw7ined plane? Assume the wqcp 791 7jjwwmechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at ;6emt 1b7filz 1.25m/s$^2$?   

  A net force of 265 N accelerates a bikelaa:llw;biz*rlmb4 h 6 5;. tn and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must aq :7whql:d r.o rope withstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a jhx :-,tc6u gh $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg car id+7obtwrggx* ge- *ys .uo 5(en 8.0 s if the car is traveling at 95km/h? od* ysg bo5eeugxr*.w7- g(t+-  

  What average force is n4kuub6c0wvk./uv+ t e eeded to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a rifl40 ck.twvv bu6u/u+kee?   

A fisherman yanks a fish vertically out of the water with an acce o7k7d9dp59 mdutiph+leration of 2.5 t7d9d+d597iupkop mh $\mathrm{~m} / \mathrm{s}^{2}$ 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-miwe u nrm e6+j6 unxleym;s4;01axy-9n le 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 maximum acrmu,8s t571 ihom (*f8ai hdacceleration is 0.0680 g . What are the maximum and minimum forces the motor should ex mo ri88(fu5sd ,hchm*t7aa 1iert 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. Whenbn qidk6a .:8y the elevator begins to move, the scale briefly reads . dy68bainqk: only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strejw3,hv9o)u ybde +1e qngth of 21,750 N. What maximum upward acceleration can it give the elevator withoq,v+ud9 w3)o1 yejhb eut breaking?    ( two decimal places)

  (a) What is the acceleration of i f9u9f-2w- zkirob/i.b ai:xtwo falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of their w:-o.uwxiikf99 /fzbir ai - 2beight?   
(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. 7 ,nhbx*9zsmwk/ xo7zkf -a.d9-m high. When he strikes the ground below, he bends his knees so that his tokkfx- zb9xh7 azd/ n,somw7* .rso 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 rop 6hr4*0s:uze1xfoo wxe tied to the box runs vertically upward over a pulley and a weight is hung f0 e6hfxw zs*uo14r xo:rom 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 d1qa2vfb/+q,5htjie w3s yp e4st n 3h3iagram for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the mom*o s)fd ;ut*dow;7guqa:o +pfent it is hit by the bat, and again (b) after it has left the bat and iao w:tdf7qu ;+ ;sf*og)*pduos flying toward the outfield.

A 650-N force acts in a northwester:v ev7s -do -i, inr5ep8pmrw6ly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westwai7,p5-wpm:s i vr8-o rdn6eev rd? Illustrate your answer with a vector diagram.

  Arlene is to walk across atf*toy7ni5f (wpv9 y3 "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rop(w9t* t73ypioffv5y ne 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 byclqw ;+bnk/,fc: uk .:wziix4 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.(ct eozlp3c*m6 g+oh30$-\mathrm{kg}$ 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 M v +8lcciwz)1*r9y-g4xohird3c xk ,hcMurdo Base, Antarctica, as shown in Fig. 4-46. ly,rw*rix9k 3c-1coi )hg +c zd48 xvhThe 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 masse4m k92yy+o 4 fk:6maer4mqet behind it, Fig. 4-47 . Determ ya4tf+k qe446mm2e mkoe9r:yine the ratio 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 upward using the bucket-pulley apparatus sh88u .o 5yguk8fjybqa0mtlx,8own in Fig. 4-48. (a) How har8 jxoq mfblt8.a 088,ku gu5yyd must she pull downward 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 qonv( w2/ hfn1began, 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 blocku+3- xzn tc*tuec9c5m (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 hor3cwmp gp;s6f 2j;-c3i)aq woeizontal surface are in contact with each other,pioq m2-6 ww3s fec p);gjc3a; as shown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each ir3 +f(ruaim2c3kb, op nitially 1.80 m above the ground, and the massless frictionless pulley is,ri2a3pb 3(mf+okrc u 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. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavya+ij jhpim3,n ) z(v1g cord of mass 1.0 kg . Calculate the acceleratio nh3j iz1)i(v+,pgam jn 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 betwee8 wq;tc:)h3 e gqhgrz5n 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 5.0feaa b 8m95jt3$-\mathrm{kg}$ 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 accelerating at 0.20g. What miniu1m pv hwrp,gd:o j4q 54cy5jzyu)gz;z:k c3 7mum coefficien chgqw5 yykrz,4z pmjo5:z4) pgv7;u: dcju31t of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum accelerhl /9v/4 ahh3 petjg(lation a car can undergo if the coefficient of static friction between the tires and the g e3j4ha/hh(plvl/t 9ground is 0.80?   

  The coefficient of static 8xj7fg4hb vryoz q-0lgqu3+ju- d+ )a p23gnlfriction between hard rubber and normal street pavement is ab n x7 8bu0 +qjv 33-ghgqry4 g)p+jzullo-d2afout 0.8. On how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate ijg9/ w+0fc57yvqbnaez5l/;y9 na haat -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 g: 8 t 6talx/prvr,ta ;.pgk(5amtls4 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very h/2 p 9j0.ddqvu(kcbo xigh coefficient of /d2 kpbxqujodc.09v(static 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 kinet)wbqyb9 lbl7s::o n z/ic 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) h 49nsoeirv9w (z-eeu:ow large a mass would box A have to haveerswou:ev9 z 4ne(i- 9 to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a pushvzd.ma9kn rh( y8qs9; rn.vh5 so that it slides across the floor. How far will it go, given that the coef. m9 zn yr8sh;.k (aq9hnv5rvdficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 jaomm5.0( -vmrda1;0ifl,g nnrs+mw kg , are in contact and at rest on a horizontal gwl(orf5 mnmd.r, ma m+i1 j0snv 0;a-surface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static f vmw0 nz5ke,x7mgp,9 eriction between the crate and the bed of the truck is 0.75. What is the maximum rate at which th,g5 m e xznkmp,79vew0e 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 in your driveway, which 0hu g9(on6abghas an incline of 129gnoga0h6( b u$^{\circ}$ . 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 ql,*aco l; huhm)i8 3a28$^{\circ}$ 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. 4-5 4zfb2p pp)zy)wdck/(k cvg.25 lies 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 initi wr: vnk5c po +2wtr)g6t0p2uial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hu6h d -3b0ffdhill 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 againslsog 05v2sb)p t a rough wall by someone pushing on it with a force directed upward at 5op2 0sslg)bv 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles nr)gy/o1f 9 lqtgt86tas they melt. Consider a chunk of snow at the ridge of a roof with a gl6ytr)fn8o 9tq/1gtpitch 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 distance for an automobile traveling af32 bp k:vdt8bgs*-m kjzi) .ot speed v is equal to bim )k o*2:3pk8zdbg j-vf. ts $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 twxvi unk7y66 gwcw,l. d+b*l0he dash when the driver deceleratnv ,+*ibgw 6 yw607l wdkcu.lxes 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 gi) q)3 wx;x2 uwr(bksmq)1ff imeuhy;6ven 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 where they are filled 5:.av+lo-z3 e nzgby pto the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the di. n gvl-eyb:ap3zoz5+ stance, 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 fric f yy)u0l j 70wkz(bl3te4vu;ition 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 coast down a 6.1sl1qrp3 t*vl0$^{\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 mammalxp.0)q8esf((f s 9k:6lj2ttd xzzy dwian heart, at each pulse approximately 20 g of blood is acq8) 2l:(xzt0skpe.yf9 sd w tdzx(jf6celerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile cbjrttc6 kpx +a+nsn uq;(9+/s rash if the deceleration is no more(nusc6kpb xqttan/++ 9sj;r+ 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 accelth)d7fo-fi z* eration produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground-f)ioh f*t7z d 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 ths63 l5dfdh o.re 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 collidlf5sd 36.odrh ing. 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 hill (1-in-4 wp(me4x mv0 :wmeans that for each 4 m traveled along the road, the elevation change is 1 m) vx4pw :m(mw0e. How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of it)w jt)wz --n*eo)ol Pisa and falls 55 m before reaching the ground with-)*wi to)enlj-)zow t 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 muddy stre5i/ xu4/pni uq 5:gknetch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stx/n5 ik:e gu4in q5u/pretch 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 ci,bvw.u22c3jw +v a.5x6i qp1 nmpebfity. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowin2.v u2j3 pqixaw .mb1n,+ pibvcwf56 eg 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 thi 1gko/k8fx;c plnx4 y fc.54tmn piece of string while4/kg4 kf.cmpfntl 5 ;xy18xoc the jetliner 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 ramps ceu(fl;:a ilcr yc1; z/onnecting different parts of the store 1if rlc/yue (l:z;ca;.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) uskrz4 +td 4x a:l11rgoving the pulley apparatus ao4+zx:rrt g 4v ldk11shown in

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is accelerating at 3.xg:fy nld-yc -mo*e lw.*9v5j 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 engineerfx47eu o a86va considers the following seta eofu 487avx6 of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian train has a mass of 660h isy ia *g-cia9(id/qiq.7d2 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 Kan.;dwmwr 0js mt :t0+5w7bbk+ zze6 cbren, use safety ropes 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 di70sbw0w6jn5; cmbkt rt zed+z:.b+m wstance 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 boatlmr 0ma* o42jn is using 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 6.pu vapvx.- fr1+mysis allowed 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 tx (tj1(hbzkd g*t 1o0o8e8efmogether are ascending an ice field inclined at 21de(me8ot0 bzfjk 81o*1gx( h t.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.