Why does a child in a **wkonq,,ov/ taf5s p wagon seem to fall backward when you give the wagon a sharp pu va*tqfk*,n/po5 wso,ll forward?

A box rests on the (frictionless6)s+ pa o0t xarjgi;d6) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newr)+d t a6xgia;0psjo6ton’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;r k:fw3 em -st*mz(kt no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Can it vhtlk/g q:5-xhave zer -/q5lv hxg:tko velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a force mj(j4 lucgg3o9 ):jujneeded to make ituju l9gmjjc)j(o:g 43 bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the lxx1 :)0od)ymt xmdj4eog move in the opposite di xyj4dmx)met 0o :xd)1rection?

Why might your foot hurt if you kick a h( (g )uwo6a w1hp(6w3aum91gfv aro uaeavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. (a)b a iv)meo799v;t:t7zu x s4ba What is the origin of the force tt7b:tez s 4)9uia7maxvb;9vo hat causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a sectrr .0ytj -7cj /ducyyxrc-;6o ion of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? Wcdjy -r6-; xryc yot7rucj./ 0hat if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kgi6h6e+ p- ujde rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier roidh6e eju+6p- ck fall faster?

Would a spring scale carried to the Moo:6/d)x;y uyv8sk guydn give accurate results if the scale had been calibrated (a) in pounds, or (b) in kiy d;):uxv 6/g ky8uydslograms?

You pull a box with a constant force across a frictionless table using an attach9nylq7v 0(esu4(mwcr ed rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) deq0secl7u4 wv(n(9 rmy crease? Explain.

When an object falls freely under the influence of gravity there is a net force yug.3:d 17kkml pt8id mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite kl1y mdugd 7k:8 3t.piforce on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object hk)x5 le(vu b:tjn59swhen you are on the Moon with the forc:kxe (9hv5tl)n sb5u je 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 tugmi0,tn2d 5yc y 2myc1bws-vp r;rc2a- of war (Fig. 4–37) pulls with equal force on the other team. What, then,sctmv0 pb a5rwmy -rdc-in;y 222c1,y determines which team will win?

A person exerts an upward force qn jri6srj2,q 0/ :gjvof 40 N to hold a bag of groceries. Describe the v0 ij:q 2 rrsjq,/6ngj“reaction” 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 foogembdiq1 0(0rce does the ground exert on you? e i0ob0qd1gm (Why doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident ysn/bvub)jm lxf8y (re.*2(u 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 situation/l bmv xf jy*y(8srub(2. un)e. Is it really?

A heavy crate rests on 33.5daue jh.5pvgvf wmqb3; z the bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, mp3z 3 wj .evfbg5u.h 3;d5qavso it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up ak,c0bb8cfkvq t:70k vwkc3d ( ramp. After the block reaches its highest pointc70fkbd8cwk3t(qv v0kc , b:k, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourslw4nxa0q ;n n) hk;(e:bp/3chte5unu elf on an inclined plane? Assume the mechanism functionp h4; (n c/3ubhax5ueqwnln e)0kt ;:ns properly, even at an angle.

  What force is needed to accelerate a child on a sled at u 3r0f3xead) *hcysq* 1.25m/s$^2$?   

  A net force of 265 N accelerate eo5inif/t ewz9/tg5(s a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withsta lqf8te,4sq/e.z cu/-y 4pwwfnd if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of sx c(z0e-ta( ta $76-\mathrm{kg}$ 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 rll 1 b )v9fbn840jpah1. vwujdequired to stop an 1100-kg car in 8.0 s if the car is traveling )h4jnbv vf j.l01a81d9 l pubwat 95km/h? -  

  What average force is needed to accele)lb mt4mqxp2cqc g5 -+rate a 7.00-gram pellet from rest to 125m/s ovt+5 2m-)cp qlqbx 4mgcer a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleratio 04do27(cnfgexm+ ni zn of 2. 74zcix(fenm0n +odg25 $\mathrm{~m} / \mathrm{s}^{2}$ 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 q4c oi9k2p*xi9kh f 9dcan cover a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so that the maxi fbix)(yz lx.kl*9lw+mum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert ob*+lwyi(.lk) fx9xz l n 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 eleck9xx (vyjv9n* g+c6d5j:r)h1y8n b uv dlem.vator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calcul*nmh+bgyv(j j6vxd8xve9nd9 c 15c) r:k yul. ate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kycyn61;)x slg+iy.r tg elevator has a maximum strength of 21,750 N. What maximum upward acceleratiox)isyyc6.1rnt+yl; g n can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg includnvxk2)c mj( 6p epcwp3 59wz+ls-)iowing parachute) when the upward forc9jc6p sz)w5e 2pocn 3miwxk -(w)plv+e 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 th3pb(u hc pex4hu7zw+1e ground below, he bends hbwp hu71 4xzcep+ hu(3is knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied)gn1bvtv w p(/ 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 other side of the puv(bvnp tg )1/wlley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball player 4raly es2x,xxz*+u5ht(4 * xazf:i st
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagramj53xe3 qkdd bw )6ou3h of a baseball (a) at the moment it is hit by the bat, and agai3j5uw3 qbk63xdeho)dn (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force87vi4vpmmb u(k2(6 , / lher keihlcz* must be exerted in what direcevc km/(e,2b mlzvu6liip kr(hh748 *tion so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally4:/itvkkrh k4g cj3n8 between two buildings 10.0j84:4 k 3r/hnkcigt vk m apart. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint buckex4:un/d b wgs6t is hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.0k 5f.ul. (cuzhdr8r7.k9 ffvb $-\mathrm{kg}$ 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 h dw3s (r5twj7o(c fp8x,k+ xnfousing unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forcer8xknw3cs jwp +(xo,( df 75tfs $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 thc++gus3 *l peoe same mass behind it, Fig. 4-47 . Determine the ratio of th+cs*3po l+ugee tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using thepn*;ew5lpakq8nq64b 6af9 2 b.ucepb bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she p9f8e4b*;ba2aq pe.5npb lcwkpq n6 u6ull 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 began, a niu rr.z b1v9ixz70(nah6ga765$-\mathrm{kg}$ 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 bl1*z drz2lmow 3ock (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictifzfwp z8tbs-(67 . yoconless horizontal surface are in contact with each other, as shown in Fig. 4-51.osbf7( z 6cpyz8.t fw- 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 initiallyf iatv// ).ni o0k+ifo 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 lig0i/ .ikt o/+ao )fvnifhter 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 bn rb6+a :i7)wcmuv vpmy.9yb+g0w m:jy a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown brgycb.m+w7v)mw vi6 p mj0n9+ua ::yin 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 jv xibr 19 e*e3nam6fubq(7u3 kinetic friction between 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 stbmx6y0xe0, xq8w h-kj art 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 standingli.q ne*7(nf pje5 6s* xg-r+y:ta byu on a train accelerating at 0.20g. What minimum coefficient of static ff g(*pb*y6nsree a.n 5:qj+tu-7xi ylriction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of statics/ a aaldp z4fvq u:i *qz3-;5tda3;iw friction between the tires and the ground is 0wvi5;apl3q*: 3f ;d4tzdzuq i/s aaa-.80?   

  The coefficient of static friction between hard rubber and normex q:n33dst -, kp08 n/jedotdal street pavement is about 0.8. On hond t0os-eet d:8 ,qdpx3knj/3w 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 ey1:7on78yn0oia(moht97 r2ye gmby at -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on y es+qt6)-ytk vtde4w8+kh7n 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 ve2 dei9 aupon:)ry high coefficient of si9u)o:pa2 d netatic 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 frictp 1rpmb5v)zikh6 -k8cion 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 k+f )e trw-v1 kv/b8va4-20) how large a mass would box A have to have to prevent any motion from occurring? tk+vbv1ea/r ) vfwk-8Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across thhdb8wg /: q wwfnm*53i2mo:v ye floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial spemybwminw/ 2 gv5h 3qo*:wd 8f:ed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg ,3y3k urm mo,-won/;yc are in contact and at rest on a horizontal srnyumoc oy;- w33,k/m urface (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 coen1d+ ej4sr1xck4 w16)tpc 5j8er8ntz2pal ef fficient of static friction between the crate anz1 4el1stj p ecr6xe4d8kj n1antf8 )2cpwr+5d 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 cab of the truck?   

On an icy day, you worry about parking your car inq,x l i)dc50ug your driveway, which has an incline of5c) i0lqdug,x 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 ader w ev(vsi.)8wkc s9gw-0:s 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 tilted at an ez(aur 2p4 hj.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 3.0r l )sw /+el(4bcm4ghx $\mathrm{~m} / \mathrm{s}$ 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 t(9invoi1 yw m(0ro7d rhe top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone pushingc*uvyk3 u c+d) on it with a force directed upwc uy d)*kv+uc3ard 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 projectiles as t 7 7zz4lo6ibgjf :rdl.hey melt. Consider a chunk of snow at the ridge of a roof with a p:z goi7b7.fdj l46 zlritch 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 mi0a ejt7d m47r nd*gnw7q0hy*d nimum stopping distance for an automobile traveling at speed v y m7rn4nw0*q j7*7gd0ah eddt is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forwar3s /ob :gguwc/d on the dash when the driver decbw 3og u/gcs:/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 initial sr7et7j+ir7 rlpeed $ 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 convey0add c0z6i k7hor belt from where they are filled to the packing station 11.0 m away. The belt is init0kcd 6hdia7 z0ially 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 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 b fe8sla),n9rwetween $m_{1}$ 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 (inclu6kimk/ q77bsf tl.5 uu jf3-gwrin3b)ding 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 simplifieoj 31wdwn)bn.ehq nc(z 9 l uuv(q.u95d model of a mammalian heart, at each pulse approximately 20 g o )n.uwujcn(9ln( . vwdq9h5ueqb z3o1f blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surv +j x)yd:mr( b)p08.0s 9mgokz2 rkyj4 yvptztiving an automobile crash if the deceleration is no more than 30 " g 's." Cp4 mx8d+ojgt)s: )r (rt0vkkyzybpz29ym 0.j alculate 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 earthqu ,(yfvvgncf4)zw6ht4p6p* v make is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static fricn*g pw,cp z6 yf(vvv4)h t4fm6tion 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+v6fnfx9 q8l y the scene of an accident involving two cars, measure 72-68+yvqfx 9 nflm-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each fmrm a uv87pz cm-;qd+zn986b 4 m traveled along the road, the elevation change is 1 m). How fast is it gqzf dvz98ran8+7b ;m u- p6mcmoing when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tow 4vdm ivyhbr;- ;tt(+ter of Pisa and falls 55 m before reaching the ground with a b-d4(tytvr ;t vm+h;ispeed of What was the average force of air resistance?   

  A cyclist is coasting at a stead(ey 9i g2bpvwfm6bw 86y 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 the speed vi eb(w9m p6yg82f6wbupon emerging?   

  A city planner is working on the rede+9nuo .(eigplsign 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 a level road from rest to 2in.9uoe(+g pl1$ \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 ae(sxn6l4j e1 (0-xmobp yfk6d thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She n66o41dx-(eexkn(l 0b sp yjm fotices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, there are to be several ramps connecting difuuj7b* rtx 2/oferent pjub /7to r2*xuarts of 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 (f,ffnc1. qgxlk p)3hzh2m)th a*)4 rd mass M ) using the pulley apparatus sxlh.4fmtg2fnaz))f cdhq)h1 * ,3p krhown in

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

  A jet aircraft is accelerating at 7d5 9-i 9cto3x:wdowcbd q/sl 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 enginee ;jgmwg 5fgu50r considers the following set of conditm 5j u;ggfwg05ions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass uxmp kk547gl (:9zb ynof 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 f1ofe1 :j qliv 9wj9w0and Karen, 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. (Expressqi:f 1ofwvj1w99 jle0 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 isnn8lt4olj8c +;h,j9h f9 jtg l using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed t d/m rmm2wp3-c ad0c1;cx 5ytio reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers who are ropedhf n(4 solcj4 *amo4qlga: +f2 together are ascending an ice field inclined at f4 4c2lsfho4mq+ (l*oaga :nj21.0$^{\circ}$ 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.