Why does a child in a wagon seem to fall backward when you give tvi1np6(dc/y+nkx bl0r9f: tg he wagon a sharpv+ b0f:y rclx 96/gp(kdni 1tn pull forward?

A box rests on the (frictionless) bed o 6ippvr0+tzp; f a truck. The truck driver starts the truck and accelerates forward. The box immediatel; p+ri 6pt0pzvy 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 zero, a b.- brvvw94-w5xz zexre no forces acting on it? Explain.

Only one force acts on an objecttj5qc*9y (e za. Can the object have zero acceleration? Can it have zero velocity? Explai*y(t59ec jazq n.

When a golf ball is dropped to the pavement, it bounces back up. (a) ht qskbj0 *6 p,2)gbc.nmd 7xdIs a force needed to make it bounce back up? (bbbm6jch*2).dx0 ng qps,d tk7) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move inkzdqly 408tz 3g+wlm+ the opposite direc tmqz4 80ll +dkg+z3ywtion?

Why might your foot hurt if you kick a heav79k130g tjuc -r v+zbvigr n;iy desk or a wall?

  When you are running and want to stop quickly, you must b) (fip t wnlc07zahu3fja6wo06(qg0 decelerate quickly. (a) What is the origin of the force that causes you to stop? (bi7(t u 60)h0qczw pf wla gnjf0a6o3(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 of the samegpklt nl:u(+bo4b:aqjw 5 /y8 thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on bpl5u(ko+/nt y8 :4 ljawgq:bthe dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twicegq x1d( d,qe9-dhoe/ k as great as that on a 1-kg rock. Why then doesn’t theoe,d/(egd k1x9qq- hd heavier rock fall faster?

Would a spring scale carriem;*+ z,lsf gsfd to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in*l m,ffs;+z sg kilograms?

You pull a box with a constant force aca/ p -9ma0wrl/r+jc t7k hsa)aross a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box p/ kh-0 7tr)wjaars a+ca9l/mremaining 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 gr r 9 av:kwf968w7hxdfcj58ds(icd8p a avity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why w: xrw7 avf8chsiad5 ( pdf86dk98 cj9doesn’t the Earth move?

Compare the effort (or force) needed to lift a7ij d+*r,ksntecz4 f1 10-kg object when you are on the Moon with the forcef rz4cjs1*ie, tkd7+ n 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 in a tug of war (s76i 6g za:6(fvqlsa9yc p:zpFig. 4–37) pulls with equal force on the other team. What, then, determinap76z :6zsi gs9l6:f( y capqves which team will win?

A person exerts an upward suq.lmg-g ;i3 force of 40 N to hold a bag of groceries. Describe the “reacm-. lgg; iu3sqtion” 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 large a force does the groueqz1;(i9jjprgp7cv+ 6r0xg /:clz sf/vp zk8nd exert on you? Why doesn’t this force make you risegjpppvqz ;+9(z/i 6 e/cl 8srx7rzf kvg:cj10 up into the air?

Whiplash sometimes results from an )z3* wru2hhztdhby* 3 5c 8a9eo )nzsvautomobile 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 sitz8 5zc owb9yd2ehsat*)n)h 3v3zru *huation. Is it really?

A heavy crate rests on the bed of a flatbed truck. (gf2+md s srj* hqyo3)When the truck accelerates, the crate remains where it im o3sj)dr s+h2f*g(y qs on 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 ramp. After the block reaches itsyyj9 i0d7dcx j4cfnp2 6gba 76w+)lnm highest point, it slides back down but the magnitude oyj70a+ c2)jn66f7 c idyngdpbxl9wm4 f its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read iflxiaj5;rccsf 0w+934 v(qm9 s w0asqr you weighed yourself on an inclined plane? Assume the mechanism functions pr9i4csafw r qv0(m+9sq5 w3cls aj;0 rxoperly, even at an angle.

  What force is needed to accelerate a child on a sled at 1ykht n 92j7/9 zrmxui hlt37 3j5,gkoq.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider3h+ir +xys obakq0 7*w 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 ao25p n-z rhqab 2 v-eg7d*rl,jccelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a +ejl2w;+z p.,xdkkx w$76-\mathrm{kg}$ 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 requpnv l5oi p; v ytx0.6jr8uyy,9ired to stop an 1100-kg car in 8.0 s if the car is traveling at 95km/h? -ly6t.ryjvvu,iy 89p0o ;5pn x  

  What average force is need0mu9qp d5 x x hy:w0mdtmw2-v9ed to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel owmm wdd52:0pxh- 0mv9 9yqtx uf a rifle?   

A fisherman yanks a fish vertically out of the water wivfi.uvs mw a(o 664ps-th an acceleration of 2.(vfmuw.vos i6p a4s 6-5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 (402e 6:i qyj0e;ll $\mathrm{~m}$) 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 desil k(,b; cq ,e9bb,v r +sd,zys+j6wayrgned so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should +s(je 9ldk, bz,vs wqcr6+r,;b,bayy 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 motionless elevator. When the elevator zh xjr)vq a0xm-ic(-x-)hce/begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, an zr-c j0cqh i-(h)mxa)ex-x/vd find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximu;d)p+ 92 orejbuynn(asl,w6 rm strength of 21,750 N. What + 6n;obpdr)jwn,2 9ys a( rulemaximum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (massn4ha6t8yoxg4,+r0 qrj sdn *j 132 kg including parachute) when the upward force of airjxnq j r4+t 8n06rsgoh4* d,ya resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof ml 9y0ft, 2sgyof a house 3.9-m high. When he strikes the ground below, he bends his knees so m0 , tlyfgs2y9that 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 the box runs ve9;weei x 4(w(6s7 yyk14 tqh uxkuefv9kmrj: .rtically upward over a pulh xtyyk9 6vj4k;: eem(4xui.kw q1ew sfru(97ley and a weight is hung from 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 a baskezf /kxy 7d0gzktbll8 ( 4i8tclyu5q(* tball 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 zvo or9+ s:d9rlv szs-7 rct.;baseball (a) at the moment it is hit by the bat, and again (b) after it-.r; o7tdvv:sz+c 9ozsr rl9s has left the bat and is flying toward the outfield.

A 650-N force acts in a north kpoyvu9.(s+ swesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a ve u 9k(os+psvy.ctor diagram.

  Arlene is to walk across a "hig0 stnt0(ot/g ih wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is 10.ngot0t/ t(s0i 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 cord frodj d0.1*k5svi6wxuw mm 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 1a260 99z p-f;)izy.db fdy, relsttfh lj+(jm4.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo n4ca wrs 98q8jBase, Antarctica, as showncqwaj4n8s r 89 in Fig. 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, z2ofexb6u -0 ba.hilo* m48,bulkx4aFig. 4-47 . Determine the ratio of the tension in the coupling between the locomx4i2kbb*ol -. 8ba0xou a,ez fmu4l6hotive 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 usiern ed*rub+d8 t:sjpyp6:lu/v5nr8 g(1l;dgng the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard musdl: n dy+r prv:e6rg8p1/; ds(5uub8jtgl e n*t 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 bega)oxmh 3l yu-a /n+ suy )tk3mjy,.(khqn, 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 (masljgjzd7 1o*c q.z0pc,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 surfyu7be6 l)- uenace are in contact with each other, as shown in Fig. 4-51.u7e-nu6y)e bl 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 arelbit f,2) v*vb 02 z4xddkwu1e each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mas0dl bk 2uz1 d,)b4etxf2w viv*s 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 conne,v,.d1c hgot-dhk4j)kq04 ff- j efjpcted by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at eacdfh e jg-0t ,kh4fd1,q )f-.jocpvjk4h 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 bet(w*zpcx2/ l trmgz77xween 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 isvaj q5kb3jt )xqr7ow0i32 qn : required 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 on a trait*qo n:cj, 1 hdbr;3fen accelerating at 0.20g. What minimum coefficient of stbhd3t1 en;cjo rf*:q,atic friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo ifl0+(0zk a;ea b7x gkaf the coefficient of static friction between the tires 0 z(xgak0k +bfeal 7;aand the ground is 0.80?   

  The coefficient of static friction between hard rubber andf3q4 a5cv tl ,kyw3+nd normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car p3da fnk34+lwy,ctq5varked?   $^{/circ}$

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

  A car can decelerate at -4.ok4)z+4 yc8h8q ley zwvk;tn*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 rek;u) 0hb-mnxz st 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 contact with an asphalt surface have a very high coefzg(zl im.7rnpi1d- s(ficient of stat-rm.ip( szg i 7nlzd1(ic 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 kinetic friction for a awj3: 7/mzvknqk). fd$ 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) ho+h 8z cotoi+x0uq/ 5l 1wyr1hzw large a mass would box A have to have to prevent any/hqr0owluoci1 8+ 5 zht1 +yzx motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far ,jalg z/ p4(fcwill it go, given that the coefficz4pjgl/,f (ac ient 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 h5aroj)+4ooj .q2gm vb 4wg+mkg and 110 kg , are in contact and at rest on a horizontal surface bmohv2)qjj5 o +gam4+owr 4g. (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 st nf:lvw8 c/z;u ;rk6odatic 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 the crate slide agfvcoz8 /;k; nlw6u rd:ainst the cab of the truck?   

On an icy day, you worry about parking your carllf z2wqh.j9a( s,/h w in your driveway, which has an inclfw.za lqhlj/, s9h (2wine 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 -y3w. ide3g yx: rz,wta 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 liei q2m*e8l m p2cx9f8 oaay,gz2s 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 initivaued9ot gnja4xj6, .- tj.5qal 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 steepet0 pv.ofdrq.r:*9 fgdg7sf 6fst 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 wal; zccx0**oqjscx+a, em9 pty 2l by someone pushing on it with a force directed upward ax* 90ms ;*yto+pa,q ecc2jxzct 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 prymks0 --fiq; 5k1xfx jojectiles as they melt. Consider a chunk of sfx ;ki-x-q j1km5yf0snow 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 dista.z-h ewyit*dvl8fygjx+ a + 9;nce for an automobile traveling at speed v is equal to jge.v yz9*d8w- lh+ +yafit;x $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash whet d f*y-q6np)xn the driver decelerate-dt6py)*nfx q s 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 givengoxp5)(::b ngug(qqk edwaf2. 59vb zv9by(n 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 arjo a ;y)jcw8e;e filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then dwe;o y8a;c)jj ecelerates 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 k70a3mlw;/co8nj tqie ue mdb- 0mg9k:inetic 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 kkcpzja ;+el52*fp) y :km,qsk g (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 modtvb;d7xkl17 z cj ;et(u4owgw*nk/) cel of a mammalian heart, at each pulse approximately 20 g of bloo;e(cto/k1x;7 kgw4n*bd )t7 luwzv jcd 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 ;j v0ff4 w r+5i)i7qrzz s7pshsurviving an automobile crash if the deceleration is no more than 30 " g 'sv+5i7s)jrihf 7qsfp r0z;w4 z." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an eart07nwukzl3 xg :hquake 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 mustnwgux:k 37 l0z 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 investigatorsvc(.2-ip dtrz 87joiyh5f e v.s(j0zz.hi xc6, examining the scene of an accident involving two cars, measure 72-m-l 52p7ycvh . ir(f(i tsj.- zjzevhzi8oc.x0d6ong 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 level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4uvc (yrh2a +h3-fi 6y;+clcj d m traveled along th+ ;a+ ch6f3yvu-rld2j hyci (ce 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 /d5r9u* 5axr-u8j0 4 tg cadhnt7flxx qu9e;xtop of the Leaning Tower of Pisa and falls 55 m befhtx 0ut;u7d5e9d/4 xgx8a*j-fulrxcqr9na5 ore reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coastinbakgt3i,/f 4g4d s3ahg at a steady speed of 12m/s but enters a muddy stretch where ths4a,3tikgd 4gb3a h/f e effective coefficient 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 rt9*3lxe wcw;iedesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slw9tl;i 3xew c*owing 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 */jk:f a+zkw kugfcpb.; /ks/g6b7qxog69p e piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 2ubwq / bak.s /x+ g*gke:67 k;6zfp9/kgopjfc5$^{\circ}$ 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 ram( o5gdrlq.h, hps connecting different parts of the store.hlq5go.h (d ,r
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 forcj n gtx8,h1h7se F is needed to lift the piano (mass M ) using the pulley apparatus shown in 8,j tg17shnxh

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 3.5 -(ref v*c ed hs3p78wf$\mathrm{~m} / \mathrm{s}^{2}$ 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 conside0lr0mgl 7no,. e:*ltqe9*qynd(jsuvf* p e; i rs the followinf 0*om:*0n7p .lqergyn*l9l jvst e ,quid ;e(g set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italiad- sd7c-r hxi. j9lw)cn 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 K6.n);g- jo9cg fjsjtzaxc 8*p aren, 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 distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result tancj) pz*gf 8.jgo9; 6cxj- sin multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a "x 1.nhli3*bpoqxb+3k0mq2ii 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximpv ol5a9rle 5mt1*d/.lf .eigb1 g7z sum 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 an ic2lgmpd 0eyd1 :uhxm8 6e field inclined at 2:xe1gh d62y l80 pudmm1.0$^{\circ}$ 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.