Why does a child in a wagon seem to fall backward when you give the( o *w*6y7qspqhl)qf n wagon a shar(qo)psy *76 ql q*whfnp pull forward?

A box rests on the (frictionless) bed of oyodre q mky823q2-4f 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 Newton’s laws d-8qek4r 2o2omq fy3y, 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 .+/wzz-n0 yrojou/ ggobject is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acc u:jy*ed 27 c-kx-oaeleleration? Can it have yo x a72 lje*k:-uced-zero velocity? Explain.

When a golf ball is dropped to6evy /k+(lvs x the pavement, it bounces back up. (a) Is a force needed to make it boun+s vk(l6/y vxece back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does : wy6cgquuf4 vje,+y,the log move in the oppositeyu6v 4ycw, f:j+uqg,e direction?

Why might your foot hurt if you kick sryjtkq(1-w+ ei4b 2w a heavy desk or a wall?

  When you are running and want to stop quickly, you must;/mvw4/nw m ds decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using you ;nmwsmd//4 vwr 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+r)dw8h2dw1s*ucqz y 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 on the da*cdry+ 8dwqu w 1h)zs2ngling 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 648g*(t zfs3z /cbku vcuxc7 8rkpc 0 4zwhyq-rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fa p8/k-bz3k7xcf qy8(gz40c*4 uhrsvc tz6 wucll faster?

Would a spring scale carried to the Moon give accurate results if the scaleik j 6,wz5ejhi8y-te2 had been calibrated (a) in pounds, or ( yzi 2k -jji85te,ew6hb) in kilograms?

You pull a box with a consta4;jp*q lmq)e4t/: kja hq b cb l*)phq5ka1xh4nt force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does thqhahqt5bb/k *ecjq;4 a4)l lhppm1kx )*:q4je acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influe. /9. 2qt s-cfevh-gaddor5 dence 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. Why doesn’t thedcvsa 2g/.o ef- 5dr.9 -qdthe Earth move?

Compare the effort (or force) needed to qya*c() i9 stilift a 10-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-k(ayti s9 )iq*cg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37)kv2u:( ; mffm6hl/gpn pulls with equal force on the other team. What, then, determines which team will wi:ml mu/gk 6vnhf 2p;f(n?

A person exerts an upward force og xbgx1t,m795 l w gr9b+nce d9ro*;wof 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) brew5 nw 9bcx,7;btg g1xl 9+m*ord 9ogy what object it is exerted.

When you stand still on the ground, how large ag nv *zzl84t5 .bs d;/av)uxlj force does the ground exert on you? Why doesn’t this force make you rise48tu5zjg;av/lbz) * dvls n.x up into the air?

Whiplash sometimes results -0 eamxe-rsh,from an automobile accident when the victim’s car is struck violentxa-,her 0s-mely from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accez9i1;vp3y5xi 3 ruav dlerates, the crate remains where it is on the truck, so 5rv3ip3; xz1iyv u9dait, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp+tdt 5ga:j(a0y trxs0. After the block reaches its highest point, it slides back down but the magnitud5t +d0g sxtray(j a0:te of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you wt nod7ys 7mwp.e3-m6 xeighed yourself on an inclined plane? Assume the mechanism functions prope my7d7os36t-enxw mp .rly, even at an angle.

  What force is needed to accelerate a child on a sleuie zhlc; f4 /nbq* phtqwi*3;o*0bv: d at 1.25m/s$^2$?   

  A net force of 265 N accelerx25pel (bw u6xbb p(25qnzv+t ates 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 wi g4 d.*2ecs2lxc*b+qqum jo*h thstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a:f4: 5cjonf+ oa6sdnsplk*bn/(.y ca $76-\mathrm{kg}$ 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 st1iz 3xd*gtn r1op an 1100-kg car in 8.0 s if the car is traveling at 95kg nd3xz* rt11im/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 125m6j8wdcre9dj )s8 dd1vy+7 wtn/s over a distance of 0.800 m along the barrel of a rdr178) dvnjdw9tyd8c jes6w +ifle?   

A fisherman yanks a fish vertically out of the water with an acceleration ofr44 ((h 3rht lmljaunj p6p:s* 2.5 r3t:jm(n4*l a4l shrju p(6ph$\mathrm{~m} / \mathrm{s}^{2}$ 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 caswacxerl. q,6+- e d/bn 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 kfre)eomz 7b3p3m5. iwx g2w49/fykmxg ) is to be designed so that the maximum acceleration is 0xef3fixoe /). zm 7p mww9gk52y3 bmr4.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in a motionless elevator. When the elz )kq9dq-ow 3jevator begins to move, the scale briefly reads only 0.75 z) 3w-qojd k9qof 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 elevexviik.rs4 he.yvs3p70o 5 ynr 55y4rdhc 4*uator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator without*x547yr e h p0skouyi5ed nv5y34h.s 4vrc.ri breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg incpn8o:fx)2k u zluding parachute) when the upward force ) xo:8pzfun 2kof 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 hgc2dxhzs:4n 2ci 4hsha6v t1; igh. When he strikes the ground below, he bends his knees so that hisvd6hshc 4gc; ti:znx4s122 ah torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs td/ wo mj5vhm:4i2bq u9jw-u4vertically upward over a pulley and h-w oj9 m5d2mtu: / ubwiv4j4qa 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 digo7o:,a8nt /a )wq-y imgmy- iagram 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 diag 95,dg)an (s9cf9-xl hcz uzjoram of a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward t9u9f ) xzjghcls59(cao-dnz ,he outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force must ud s5xqn8;8dd.coa s7be exerted in what direction so that the resultant of the two forces points westward? Illuda5oc 8;s qx7u.8sn ddstrate your answer with a vector diagram.

  Arlene is to walk across a "high wireymo,(4ah( yy-ifc ia +" strung horizontally between two buildings 10.f ch((,iya+a4ymiy-o 0 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 bucket is hanging by a massg7 uj)y)2)u/fqutorj /sc o,oless 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..m:sz xhu j9 -/lzqngt3 z35vw0$-\mathrm{kg}$ 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 ho xg/apt+ o.o4rusing unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4p.ot+r4aox g/ -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 pullinga ngr5to7vy8kmux)9 , two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first c9 o58tkg7ra)xm nvy,uar $\left(F_{\mathrm{T} 1}\right)$ , 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 w 0e,v rao80m)kbq8l,nhfjg* using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at0 j o*8ar )mfehn ,k8v0lbgwq, 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 begu 706vl,h uoe s4hde7fan, 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/m7 oevphohxu*t2/.q (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact4fy+pp el29rc4eyp v+uzm/ k,w i j4.q with each other, as ck iuf+ pv+elp qm24y4pyj9r/ z.e4w,shown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1o 4yynz4ts72kuug-c0,lp :tb .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 syyt :y-p2t0no4glbu4, k7uszcstem 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 heavy cord of ma wfrtv qmi8;iw x5u9)3x)l(rqss 1.0 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. 9w qf( i8xtl ivu3x5wrmr;)q)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 a 87ka0 hbagv sh)g /*ed 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a 5.udej lvh0qm5( oj+v43q nb5f 27pka4v0$-\mathrm{kg}$ 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 std x/d 4l9q0;vgx3 rzeganding on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are nozvq3; gxl/x0 r gd4de9t to slide?   

  What is the maximum acceleration a car can undergo if the coeff+optux+ b1lc7 icient of static friction between th1 bx+7+u octple tires and the ground is 0.80?   

  The coefficient of static friction betwetp) hx b8a16zhen hard rubber and normal street pavement is about 0.8. On how steep a hill (maxia 1z8hhptb6) xmum 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 -zm6dqqfjn* atjl): .14.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a roup olhd(,(sx+z gh 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 asp8qcct*nqd;4x :b 0cobhalt surface have a very high coefficient of static fricttnbc c4 d qbocq*08:x;ion.

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 kineticf(b5pc2,0 xngt o 1af2xl zck) friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would box A have to d n(q obit-l7opn61y /have to prevent any motion from occurring? Assumto o7y 6l-ipb(d/qnn 1e $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across thhr +srlc /6w/*r5t x7rn )vnote floor. How far will it go, given that the coefficientl6/r ) nov/ ts7h+rrw *rnc5xt of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass h0jqb wsp8+gf - uhim:lyq)w+lwtniq ,1 +0. b75 kg and 110 kg , are in contact and at rest on a horizontal surfac ywl+ wbil-hgs+q+)qtw,hnpq:f.80m 0j1i ub e (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 he8mmrtuo5kjfa744n p3 zm7k l;avy crate. 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 decelerate and still avoid having tol 84j4m3mmaz7 ;krp 7nkt 5fuhe crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, 7v+xi*pt kt 8owhich has an inclit i8x 7+to*vkpne of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide wittukmju /4i8-y h 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 tilted at a 01x-hk jzyo h;rd-4 w81ndnrmn 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 89wpk+ sxe9+ v nge cnth1y*q6of 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 topglf)xkh8 ( .dc 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 puvo ,v1e81 v:jbbp)i xgshing on it with a force directed upward at1v b1v b)ge,joip :8vx 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 they meldcs/q adz3 q 7xc2sa64t. Conside7sasxcddz4c 36aq /2qr 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 stoppinl t(g vengzpap* alh13u4va555*zv+zg distance for an automobile traveling at speed v is equav 5l(nv *lp gz4t*+e1auzh55 p agzva3l 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 whfw wqc hz19;4pen the driver decelerates from 91wwp qzc; 4hf 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 initiag vldx7k3h e)sa+ wiz+x37 +rcl 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 cond9l/ kqmd,mw on5/fn7veyor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then 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 minik ,mmo9 /n7 fwl5dqnd/mum 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 kineti3 b5pepc9;)ovp *bxitg cd3ra *xc1vgjn+z7; c friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast down ax9ti n 9 6zfsnnd2az42 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 mammav /2vv xoucm.3.+ qpfclian heart, at each pulse approximately 20 g of blood is accelerated frovmv.c3 2f x+/c ovpq.um 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash1tp y7l o-je 85jbuuh(cze6p - if the deceleration is no more than 30 " g 's." Calculate the force on a -etp6 5j e1bohpzlyuj8 7(uc- 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 pro :ce- 2 tms8nxet tj*rh,v(-lqduced by an earthquake is a , and if an object is going to "hotc(e- -vhn xs: tql 2r,8tmej*ld 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, exa1csa yl19 d1jcmining the scene of an accident involving two cars, measurec 1 19l1yjdcsa 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 assuming a level road.   

  A car starts rolling down a 1-in-4 hzvbrx-n6z/ 1 oill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going whb nzr /v-z6ox1en it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa and falls 5,bjl,yeniq7j.*tq.r 5 m before reaching the ground with a speed of What was the average force of ai.j*.b ley,,r n7 qijqtr resistance?   

  A cyclist is coasting at a steady speed ofw kbz84gnw:t / 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 11gk/n:zt w8b w4 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion o.ojbyf r y3*cb(w+ 1tjf a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills wit r* cb(t1+3.jobjyyw fhout slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experimw*:bpu qk2 zf;ents, dangles her watch from a thin piece of string while the jetliner she is in takef*2p wkz u;qb:s off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to s47/nrk+ y3af2c.jzavqck0 c 7r fvp- be several ramps connecting different parts of the storefpac7/z r k- 0vcjrf32ak.vcyn+ sq4 7.
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 vhe zkk1 a6h: q;( taefc:l- .ikf,6rs is needed to lift the piano (mass M ) using the pulley rfflziq e-k6 e,. kas:vtk:ha1 h( 6c;apparatus 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 acceleratid lo vbt )nb4 :3cy5h4n6xuuv9ng 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 consider3ho.b 2s 7/inw5k oxzhs the following set o/n5 xikbo.s 27hz3hw 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 hs7mj( v0pfgr r)tv ),sas 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 s *:ftjpq fhl90pobcj)2 c9dz0afety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result 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 rop00 99*l)pthcq2fzb c pd:ojf je pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a gd cv1ao8+7mh2odhc 1 u.0mmv" 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 ra;z-s :izk; xeeach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together ar6j clyr 5z m(5yh3sz2xe ascending an ice field inclined mhs53lrcy65 y z2xj(zat 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.