Why does a child in a+k(3jnsn yxw6 wagon seem to fall backward when you give the wagon a sharp pull forwaj nyx nk3sw6(+rd?

A box rests on the (frictionless) bed of a truck. The truck xk4o10cugb 3 i8lm ;hidriver starts the truck and accelerates forward. The box immediately starts to slide t 3ihxk80bolg4c ;imu1 oward 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, are no forces acting on it?x.veuqjx 6.t l3wn 8a. Explain.

Only one force acts on an object. Can the object have zero acceleratixdcq j1 29,qv-4kdqus on? Can it have zero velocity? Exqcv9s,k u4- ddq 2q1jxplain.

When a golf ball is dropped tpy f vy304zua1wrpkf76la 4 d(o the pavement, it bounces back up. (a) Is a force needed to makeypw0347 p ykuf r6l4z1ad(fva it bounce back up? (b) If so, what exerts the force?

If you walk along a log flo)fhyh0k; 59h cax8fqlgvb 8,kating on a lake, why does the log move in the opposite directiong9vfxh)80l ba5 hfkh8q cyk ;,?

Why might your foot hurt if you kick a heavy desk or a ,(i ssep;1+ ( hmwb0 4dieybtbwall?

  When you are running and want to stop quick* ba ..ap -ktxxim(a7mly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum ra.am-x.i ak x p7(atb*mte of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fin w3z+ m7lvzi vg(b2p9fe thread from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull ong73ivw2 lv+ p9m(zzbf the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is t+ie1m amy+ 3n7*fe nnmwice as great as that on a 1-kg rock. Why then doesn’ta3 nei1mmne+7my *f+ n the heavier rock fall faster?

Would a spring scale carried to the Moon give accurpbjo d71b/d *oate results if the scale had beenb odd7p o/1j*b calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionle3ntx me 8,j7 7y(i6/yzxrrc cwss table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the 67r z x,mnirtwj/y( 78y3excc horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity3 ae:zf3yhbcc ). o8xb there is a net force mg exerted on it by the Earth. Yet by Newton’s third e bcz.3:)hxc 8oybf3alaw the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10q0yrydom6tx 3 h6 b-1n-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on E616n xborq md3 y0t-yharth.

According to Newton’s third law, em-nt0c om jy8s07a1o each team in a tug of war (Fig. 4–37) pulls with equal fc8s 0o- mtjen 07ymoa1orce on 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. Describe jics fj eet6j 8(g9g3-,8s dyc25od1mzr qf (uthe “reaction” force (Newton’c3q9 zgjs ,8tcreomfdi 6ujsgj(8 y 51e2(d-fs 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 grounby(ju(ke( )mdd exert on you? Why doesn’t this force mak((yme (dbu jk)e you rise up into the air?

Whiplash sometimes results from:jui,9at6l g-vz/khu an automobile accident when the victim’s car is struck violently from the rear. Explain why ,/-9tluizug6hv: ja kthe head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a eih *+/t 7kkdwflatbed truck. When the truck accelerates, the crate remains whet+ he dw*/kki7re it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slidp ,.* a fzp8ncqufw)4fxe6hd*es up a ramp. After the block reaches its highest point, it slides back down but the magnitude opx d u,hn)* c4.6w8 faqfzf*epf its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read ifu7gt3j w( ac545qefhtfe8t8xt)+aa j you weighed yourself on an inclined plane? Assume the mechanism functions properly, eventjwgff tacej48(3 e hut75aq+ 8)5xa t at an angle.

  What force is neededb7(demkf w9tl u2-, iex 4hvi1 to accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ri:skra *b+xfo2+ehlp2c /s)le der 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 ,eh7ux *642gmtpqy rf960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a d (f tmkldyqbno,u(0* .k8bw5 $76-\mathrm{kg}$ 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 in 8.0 s if the car is trbtcm2* strr k8+xoq4h1hv.a6 am.ac br8q2ksx 4vh t+*o16thrveling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pelle61 4 8drsay6re)f cgoot from rest to 125m/s over a distance of 0.800 m along the barrel of ar 1)eoo6d yfrca8gs46 rifle?   

A fisherman yanks a fish vertically out of the water with an)fi:gdwe) s9xk -da9v acceleration of 2.fivk 9swd-:xg eda) 9)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-)gej0bi0 ixi/4/x h ;dk8pvt nqqw,/kmile 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 des lg9uk0cv:nj) 0w(dvu igned so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? max cvnu vwgklj)(9ud: 00 =    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 ig/o 7s44i u6ho sto4q2d4 ebxfn a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s r/ 46o4q424uei sbohdgt 7xsfoegular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125- ptzaopj 672,23xv ssqkg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevatorqj2 x s6p tazs3p2o7,v without breaking?    ( two decimal places)

  (a) What is the acceleration g.y yn5ipwdx i1+coh*1 /qv5u of two falling sky divers (mass 132 kg including parachute) when the upward force of air ux+1ip*n5 /qc .v1gyoyw5idh 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 93ygb .g kd0bws(j0gb 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass003ydg9bs. ggbkb j( w 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 runbylf t5r -y *7-4zkfyps vertically upw4zyl-* y5 7-brpkytff ard 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 other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body dzzd2,5a0k9pchmb ,l/ l5xzxep1 o ug7iagram 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 basebjnwwn3n; 5n.tall (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flwn nt35w. ;jnnying toward the outfield.

A 650-N force acts in a northwesterly dirv8pi bhi u+73z1*w -ck y*twlvwj:8e bection. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer z**wk-7 e hyu+bwtb ivj8i8 v3l:cw1p with a vector diagram.

  Arlene is to walk across a "high wire fvs23mwp0 qz uwog6-1" strung horizontally between two buildings 10.0 m apart.ov0w1qsp- 6z2wf g3u m The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucket is hanging by a massless k ron4iv s o8-lj 548cg.uie*rcord 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 1dmh k-0ds* tqjvlliy9r:8 p.r74nn :g 4.0$-\mathrm{kg}$ 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, Antarctica, j 5os1ibna3 :vas shown:oja5n 3iv1 bs 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, Fig. 4-2 :o y a9rne gqye9yx3)n,fav747 . Determine the ratio of the tension in the coupling between the l9xye,:2 r)n af3 vo9nq7gyeyaocomotive 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 sho;9ojvv 7)q hqqwn in Fig. 4-48. (a) How h9o qv)j7vqh;qard 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 be5ymia/c,mmj4 )ou ws6 gan, 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 (m 0d 9vczn6 (q)xjcbwu4ass $ 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 each othe 0vn d,r5(ixsgahgu/8r, as sh80,s( v /hnggi5xu adrown 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 eachf8pe*uxpdms ldju:lv2; vd+ b;s,j6- initially 1.80 m above the ground, and theud8 +d;mvds:epl-pxs ul; *b,6f vj j2 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 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 k;t twag3ap ssb.-h- ;heavy cord of mass 1.0 kg . Calculate theaga -;k3- b. ;pwshstt 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 betweeokl.(fh)3j :xl dm4jk n 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 au5eup1r 6kg steyg r,.h d5-i1 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 0.20g. What minimum c;ho4 4ievr(9aog-sgch t b5dka9- nh 4oefficient of static friction must exist between your feet and the floor if you arsvhb -do5t;a(-i4 9erg hk a4ho9ngc4e not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of stat 9sdm zeo5c-3bic friction between the tires and the ground is 0.80? s emz -93b5cdo  

  The coefficient of static frict k :4js7djjwq)ion between hard rubber and normal street pavement is aj k4d)jw:s7 qjbout 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 at -4.brr mom7tpy:5 ,z1(m w80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 re0y6b uz8/i qyost 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 vm71fc 5rvwn-kery high coefficient of stati5r7 k1mv fwc-nc 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*s s z 7muw4kp18rx:);iumflgnt9q8ution 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 4t, xa3pnhakv*q f45 n0-20) how large a mass would box A have to have to prevent ananankth v,xf*4qp05 3y motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far wicf*ndl gi) qt:-dz1p5ll it go, given that the coefficient of kinetic friction is 0.20 and the pushd*i 1:d5nzqftglpc-) imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest8 f-6dxasj;)g(7vi ika ,ou ge on a horizontal surface (Fig. 4-54). juaie -; 7xgo,k8(vagf 6 isd)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 oeho3 y;kqg1;hqa 79e5cpp) qfaplu(9f static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cabh9pa (; qecg9 ;1khapqo 75 qyp)f3uel of the truck?   

On an icy day, you worry about parking your car in y ql(n/n;grx 8nour driveway, which has an incline of 18lr(q g nnn/x;2$^{\circ}$ . 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 9 t ni2-untt- gufg2o7 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 Fi bmb; 8.a+v:l(tpu4 .zux)wr qmiip9p g. 4-55 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 initial speed of ;mg7yo1kye plnq jl1m 6h3x ;7 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 th)ezp a6r23 c)d/8w 2knqqevvue steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by som ni43ufl/ pxy:eone pushing on it with a force directed upward at l/ uifyx3p:4n 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 dangero,gn +v ha jt.:hnx:4ow3 1syfyus projectiles as they melt. Consx gjh:vn+1t3 fwhy:yo san.,4ider a chunk of snow 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 distance for an6 euvau);s wy3 automobile traveling at speed v is equal 6w;sv3 uueya)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 fys,1us fk87 hiorward on the dash when the driver decelerasy hu7 i1,f8kstes 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 initial spxz sjvb yay:/rv uypo+2+k,+0eed $ 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 to the packingij,ng1yire)yy opz v; 2vn0 77 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 hal;yg07v 1pz 2yn, i)v7oiny jerf the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of kinetic friction between ju +8j9l ucwz7s3nsp, $m_{1}$ 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 (includ(c apobo m 2 hoyxs1a5m*g-8w,ing 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 ea9 1 2ek mefw1vcn kmvgl5jswi5u)n (q9,3voo)ch pulse approximately 20 ekfm1j 5in5v99vskm (v3 goq2),lecuow)1 wng of blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable 8;xxla2 fxit,,su /hnchance of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force on a 8ui ;ft xa2hx ,xn,l/s70$-\mathrm{kg}$ 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 acce(q5yx(ib wc+lv dbqjek ea8zcc2j; gt06 u4 45leration produced by an earthquake is a , and if an object is going to "hoic0y 4cvz(kxe;l4 cjbwe 5qqgatdu 5j(+8 b6 2ld its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of anc2a-b8sn 6-b;bzweb)q )a tb wc6l 7dy accident involving two cars, measure 72-m-long skid marks of one of the cars, which near qz 6a6cl)b-b-;yd 8n es7 wb2)bcabtwly 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 me,a y hz r6hu/.oiu(.buans 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? (a) Ignore frictio hr.u,b/u au(6hzo .iyn.   
(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 Pisk 2l 6:c 4drwwsaa-t4oa and falls 55 m before reaching the ground with a speed of What was the averaw a4- l:aot24w6ckdr sge force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a jjt :/ )zgly fg.bg;semw(-45; amhhvmuddy stretch where the effective coefficient of friction is gw-.hjeg/5b:(m;;lfyhj4 mtagsz) v 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 redesig,cty39awb 2v un 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 slowing down. A particular small car, with a mass of 1100 kg , can accelerate on b v u,a2t3yc9wa 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 exp6wpz7a7 yj+yra;* xaw/mt z3 ueriments, dangles 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 makes an angle rwxwz/+y6;ja3*za 7tyua7 pmof 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, t bs(ibw3+tn 8xhere are to be several ramps connecting different parts of thsbixb8n w+ 3t(e 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 (mua*ro+f:fcjbp( t.+va 4m7z gass M ) using the pulley ++c bgfa apot :(z4.r*7 ufmvjapparatus shown in

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

  A jet aircraft is accelera,6 -vzopilzqj8 (c r9gy+4d7(ojkkoiting at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engineer considers the f85p6vh 9vgf9qu. czl8 ;nzzrzollowing 9z h98v npqlz .gz58;uf6 czrvset 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 tyf0h s/zms nf9ud d1x6 ,iw2;5mj- egnrain has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safety ropes ofh3mpvst1 8ms) 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 consta 8ssmh3 1tmvp)nt, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a +izdpj+d, ,w u" 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 allowedrxt0 ri+52 kb6p7u vmu 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 climbe/sout)8 h9yk.anm5a 0rte wx5rs who are roped together are ascending an ice field inclineuo 50rmh x).kna 9a8wts/5eytd at 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.