Why does a child in a wagon seem to fr(uy tkscb(v80in)d.n a.+ p xall backward when you give the wagon a sharp p((x.0 ntki nrs.d8ucp+yb a)vull forward?

A box rests on the (frictionless) bed of a truck. The ts 88k.u udbac3p7plj) ruck driver starts the truck a ldu)sbj a8c.kp8u7p3nd 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 .dyirwu *.1 gkof an object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acc 5l 3 g3vd/rp6uq-su01 b/jkv 1htbpvueleration? Can it have zero ve /j63qku30ph5pl1v1 -btd/usvub r vglocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. mfia2;i-tf (p (a) Is a force needed to make it bounce back up? (b) If so,ai(pift-m;f 2 what exerts the force?

If you walk along a log floating on1 oe stmf--p6e a lake, why does the log move in the opposite diree-e- mfp1t6so ction?

Why might your foot hurt if you kick a hedrspog7 pb6dglcp4346+m ;vg avy desk or a wall?

  When you are running and want to stop quickly, you a5kyewao/a8k55mq6b xb6+w v must decelerate quickly. (a) What 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 runno yq65vbwkem bk6aaa/ +xw855 ing 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 same thd ai 1 xt2rce-3b:gvg+read dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling gd:1 at2b3 v+i xrecg-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*b)1 n fjddjxex9 h+h)-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier ro jh+x))db9n1d *ex fjhck fall faster?

Would a spring scale carried to the Moon give ac, - 60vovjtmgvcurate results if the scale had been calibrated (a) in pounds, or (b) in kil6-mtovvj0, g vograms?

You pull a box with a constant force across a fi.nna r2x1e l u3rv8x0z)cea 6rictionless table using an attached rope held horizont6)ui.lzn r 18xexcae a2v3rn0ally. 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 freel3hi9 ep qfxvxop 3:;u,y under the influence of gravity 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. W p ,9xpf3hi:3x o;evuqhy doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you are on tw*rszrz2pnl)e6 x(3 o yw(py(he Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg objectp y*6pwl r2z)(zo( ( reynsw3x horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37t;8btdnhi ok8)rs 74s w/op; b) pulls with equal force os4o tih/8r;7 8 b wnks;o)tbdpn the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries.j 3pdx5ewl5 j- Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by wha- d35jw ljep5xt object it is exerted.

When you stand still on the ground, how large a force does the ground exeri+pp 4iw1z2 jx: nuua8t on you? Why doesn’t this force make you 4x1jwi2u +z:p8 pan iurise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s car s1 f2gwkn yq)vei2l :;mi0v ,ois struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is itv;1: w22no fk 0sgyi)v,limqe really?

A heavy crate rests on the be,ccgvp 0/2u 0dt7wa5o*tj- ywmx a)vg d 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 crate tov ,0u0 /jctwam g2)xa w*tg-vo7 pc5dy accelerate?

A block is given a push so that it slides up a ramp. After the block a c2ris6d89dvreaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than ovc2adds 8i 69rn the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined pla) 9a*wj+5yeee,n b:rxdfwh,gneeyw,de,5j+*n xhw)ar f eb:9g? Assume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at a-7lew, jhv,hz.-qe e 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ri. f6au lggti f1-o-m.wder 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 accelerate a 991zd o59czoau60$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight ofd dq/.v+c28wbj k0xsxw,rln9 a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car-zh -f1fzuu u+ in 8.0 s if the car is traveling afz-hu-uuz+ f 1t 95km/h? -  

  What average force is needed to ac- v/azu e68wcio- om0ecelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 mm 8cv 0o-zwaeou/e6 -i along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accelxvj; n 8d:,n.47svbq nkpgm;weration of 2.5ng ;.qnv s ,p xvwm:7k4d8jn;b $\mathrm{~m} / \mathrm{s}^{2}$ 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-mik:kc f1 m+p,nd1bih8zw s9, xile 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 .tlr 9l/s.wuathat the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the sularw tl. u/9s.pporting 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 t1ko9pt;ecy m x lfaol,*xc n.z/):3bscale in a motionless elevator. When the elevator begins to move, the scal:)/bp t*lkcc zo t lfyn.axmxe39o1;,e briefly reads 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 hasmg*u)y rhz ;8nxqn i+4ws1j)v a maximum strength of 21,750 N. What maximum upwas4)nm vxi)r ywjzu8+ 1*gq;hn rd acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky .sp8l/uzhx *ddivers (mass 132 kg including parachute) when the upward*/.d8 puzxhs l force of air 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 of a house 3.9-m high. When he strikes the g-. sa ;piq0iwzmzl:c/round below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excludl mwcia0zzq -;:i/.ps ing 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 t i-ceo) 4h0x:uxvfb+bkt 0rhs.g7 x d9qrd 1f;able. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the ot .gxbi1)b 7:;f4dt+drfc0xhx 9oeqh sr0v- ukher side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball player ls5(nx zx2)9v .,vjy4 uerp pl
(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 basebalmgz 53uk7ftc0 0nh9t tl :i2bel (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward the outfl7tzek 3hm:05t b0ui2 c9gtnf ield.

A 650-N force acts in a northwesterly direction. A second 650-N force must vxi k1 jv5 ihb)5ibso 5bbn3*1be exerted in what direction so that the resultant of the ) 5b5inij 1*b5bxo1vshkb3 i vtwo forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between tx (ls9sm:v: a2y8mo32 qjwogdwo buildings 10.0 m apart. The sag in the rope when shslm3m9yw v :o:as(g2j82qxdo e 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 cvuk jjk2suy40d67h34oojc 0 zord 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 14n ,f.r 8/fdjdlt) . d*yvnurz0.0$-\mathrm{kg}$ 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 Base, Antarf/ rwg60 umkv1ctica, as shown in Fig. 4-46. The v krf/6mwu1g0 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 tb3v +b:r wzz4+pvpn w7he same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling betweenbwz++3p b7n rz pwvv4: 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 herselp3z. e9ptml+u f upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull do+p tm.elu3p 9zwnward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, awic6jdzmdv-8 ef t, vfzm*o3e9,3 yg5 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 (masg5gx+20eyuz rzg g6o8s $ 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 with eso( , j r+8;omxf:xhoi;5vvtd ach other, as shown ,8oi ;oxf +;v:(hjr v5mox sdtin 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 abo)zzdcfhg 6oq.j0aa h0 k+t m43ve 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? [.zaaf ht 6qk4cozg0j h0d3 )m+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 heavy cord of mass o:e( asf)vs6wa-nbz6 1.0abnf6evz:s ) ow a-s(6 kg . Calculate the acceleration 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 between as2 ty g1 z,rtg1xgauye3v( 5w4 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 hj0/d v rzp.laqzz-+) 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 train accelerating at m5ha on wfwa6ih mixty8 ypf+75; i+,v f.2e9e0.20g. What minimum coefficient of static friction must eiefo+fx7ehvmai5f 6y,wy2n i5; w p.am+th89 xist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergohxpz q / /x ;b*y;xs-69tmspyh if the coefficient of static fric;/9 hyhpxx6;bpy-tszs mq* / xtion between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal streeq ;31.egvjk yry9r4pet pavement is about 0.8. On how steep a hi.r4peye1r;vk gjy3q 9ll (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 at -4.80 rojzx -tpyif9,pw18n2gkyk l i* j190$\mathrm{~m} / \mathrm{s}^{2}$ 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 onikfy4e) mdcv4ip4 6b* 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 jj :7lub d1z xgbk44)kvery high coefficient of stati) jkgjd:l1u7k4 xz b4bc 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 fric-x3hfgg ix6n9tion 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 have t/7aw, ;dcq jsoo have to prevent any motios7dcaq/o, ; wjn from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slidzo5em v u--4iues across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and iuu5-vz4o-m ethe push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kewn+3 gr gmxo1u(j o//12 gwxpg , are in contact and at rest on a horizontal surface3on m1w+ug rgp/ /o jxgw1(2xe (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 cr 8yuslca 1ta87ate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decs8c7u ta8y1a lelerate 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 drivewag 0c(/nnx)nht oy:k-m y, which has an incline ofc )kox0m/gn- nhnt y:( 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 ner 7hg6/1fqo thop):js 2s+g slide 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 lies on a plane 8amtn9wgfe 1/tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial spe68 kw0 lktun,jed 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 hill with a speed of 3ali9w(+1zzr w abi(8ji;wmw 1irrg66.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone pushing on it wi-fi 9jv37ye .uw qv40x5gtwt kth a force dxytvew ig.j7 t0v39fq5 -kuw4irected 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 become dangerous projewthc s 2+2, hvp tk61g8hclu2kctiles as they melt. Consider a chunk of snow at the ridge of a roof with a pigt8 hs2p+6ht,ch2wu 2vckk l 1tch 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 travel+* m -kca4darp8ordjd r.g8c2 ing at speed v i+d pk2-cor8.d* j4r8 adgmarcs equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash whenukbz*( 4cwscwr*j : )y the driver deczsu*cykj cw)(b wr:4 *elerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an +;egd 9 oqnzfs-kp f05initial 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 fi2if 5 zw72q2+s ejecqm x/jav+lled 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 decelerates for the final half of thej2f +m7z s2a2i+e/ wvqjcxq5 e 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 friction betf4vryose5 xm*(ymh. 6 ween $m_{1}$ 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 + swtasyt2*wo09 rx;f65 kg (including the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each 0hp(6 xfz*5hq lfn a 8jjydi35pulse approximately 20 g of blood is accelerated fr5iazfh5pj8(f3 *ylqxj0ndh6om 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 oc5s*)vu 6pkmd 7a1ea bf surviving an automobile crash if the deceleration is nou67m v 5a*1)pcs abked more than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is xyn1g4.bpon3) 3ew-kbdu;yp a , and 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 -3)bpwy4en doy3 ;bxkup.n 1gleast $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scene of an accident involving two cars,nj8 2z0 xmupa, 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 asu2 man zj08p,xsuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means vg: l5hi6ui*z7t (pbc +6chk(ll)q 9wl6bbuw that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? ((66i *)c tbul56(whgipblluqh7c vwl9k:z b+a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped f fzn260k5z u4c*xilu5mg: epbrom the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air reszug6*lmief uz:x20 bn 5k 5cp4istance?   

  A cyclist is coasting at a stea3au x.hk j,w/, u*ypibdy speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be theax.,i /, pk 3uhy*bjuw speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city. :00 j+vx/sun 1e mohrfAn important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of /umxn j00vr:e+ f1 hos1100 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, dang9he5oql9qgsf mk/3 kex75 t 7bles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string xl5qq/7f o k93k tmb79 shee5gmakes 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 sevezuw 0aptr:p)fpm06n(c mt7/;r ei: ih ral ramps connecting different parts of ;0p 6ht(cr:mwmtfipiau)e pr7z :0/n the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (ma;ceshptzylaho5 6zv cr-((:4 ,0tbry ss M ) using the pulley apparatus sytr , 5o6 c4thybs(zac0:vhel z ;rp-(hown 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 acco..n6zy *+spfsyyt4nelerating 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 proces1as3*v: ewmpxs for a child-restraint chair, an engineer considers the followingwv* mx1p3a:es 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 Italian train has a ma1cw6 ant1euhv;l gt08 ss 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, us*davs y iu*f9f:ku0yg)j.i x) e 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 c*ui f*y) :ui)gydfx9s .a0kvj limbing. 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 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 i adn 79fzv :*/llm8rkusing a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum speed of 3.5 (a nd8r.slal/$\mathrm{~m} / \mathrm{s}$ 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 ice field o5v sb*w-.r shinclined as 5s-bw*vo .hrt 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.