Why does a child in a wagon seem t7jt+4p hdf/ jqo fall backward when you give the wagon a sharp pull f7pt+h/jf 4 jqdorward?

A box rests on the (frictionless) bed of a truck. The truck drivec39 a4mv4 pf35nb(iczcct av0 r starts the truck andmn9tv(3p ccaa 04vb 4ic53f cz accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no for0612ybanau1r czh 6vr ces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? C0wgkh 2)8qkm(y mme gi/* yl0wan it have y m*/gwe0gmw (k20mhq8k)ly i zero velocity? Explain.

When a golf ball is dropped to the pavementwsgxfo 1usq982psp ,8 p+n7bp , it bounces back up. (a) Is a force nee+9 x,onppfps 7g2pb8s u8q1 swded to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the ov:n4j0z9uikg pposite directiug0: nikzj9v4 on?

Why might your foot hurt if you kick a hcm5vktled2 .wv5ux u5ytn ni6(4h6z:eavy desk or a wall?

  When you are running and want to stop quickly, you must deceum8j zb* v 19i3wua2celerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed1j93w82evc*m uu aibz to come to rest.    m/s$^2$

A stone hangs by a fine thread ffw,xw 6rtw4+vrom 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 dangling thread, where is the thread likely to break: below the stone or abovvww4 xf ,+wrt6e it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-k4w;px*2 :/zhwqnmrt bg rock. Why then doesn’t the heavier ron/ :r ;wwxqpt*h b2mz4ck fall faster?

Would a spring scale carried to the Moon e;dn fli9.vnj)ga 4g:*2au wk give accurate results if the scale had been calibrated (a) in pounds, g 2je*niln4 g)fd:.;akuav9wor (b) in kilograms?

You pull a box with a constant force ajg 3tjgyyijicb. )h xp 549 b2ec2u0/tcross 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 cj / yc9tpeb53j2.giytigbj2u x)40h on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls f7g m2p u2-yhk8 oqdo) t2bsyxfpc26y *reely under the influence of gravity there is a net force mg exerted fyg x72y)2 k8 cohduots*- 6pm b2qyp2on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (o-ps9a 0h* gund ck:j5wr force) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compnk:wdu - gsph9 5*cj0aare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pul6fhok-yi et 89ls with equal force on the other team. What, then, determines which te9o 6fkh8-tiey am will win?

A person exerts an upward force of/2 9ziq2ez hnm 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) by wha izemqn22 h9/zt object it is exerted.

When you stand still on the ground, how large a force does the ground xdw1m(p3- cga exert on you? Why doesn’t this force make x gaw-3c(mp1d you rise up into the air?

Whiplash sometimes results from an automobile accident when the vyl k v67+yeg3tt6ek m7ictim’s car is struck violently from the rear. Explm+kvt6 k6 e yelg73t7yain 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 accelerak0 j fd9hj3*rvtes, the crate remai0dkj v*r9j3hfns where 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 slides up a ramp. After the block reaj n,2 ob9 :qp04cfhau9brt -hy:nn0xu ches its highest point, it slides back down but the magnitude of its acceleration is less ocnjxftr090uuhya 9 npob- 4h ,:b2:nq n the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inu8yjhq m ,o zcmg;8ou1jyclp2 r(j0 7-clined plane? Assume the mechanism functionsy8ou ;7ccq ,y( gjum2hjrjom8 lz-1p0 properly, even at an angle.

  What force is needed to accelerate a ch .udtblac) k.3ild on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 2a rg8ze 4di*z h ++qzbziw/k3).30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope w xyh5lh8 2b+isithstand 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 x5k m+hy9hcu ) $76-\mathrm{kg}$ 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 tf sg )m)5e :3ionqiv)8ccij7craveling o nc73s j:5vmgci)cfeiq8))iat 95km/h? -  

  What average force is needed to accelerate a gv oej5qjo :ntee133 o0kw*(dt85aby 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a y ot:1o0 3 5ej3vtbo*ge awk qed58nj(rifle?   

A fisherman yanks a fish verticallhkznf.;+/eov 1c ( x;hpt0bbly out of the water with an acceleration of 2.5bxfkbth le ;; vzn(+/o01hcp. $\mathrm{~m} / \mathrm{s}^{2}$ 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-m sif (nukpulgq29 :7p+ile 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 4850if6 ksb 6wc)anlqo:8 , kg ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and mink6cinb:8)oqf w,sla6imum 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 mo7ov4t5ax7aho5fbrg . 9npkp 0 f)thj1tionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, a15a7 xp h )tnboh4g.ro5 avftf kp0j79nd find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevato w2wm1n:gazt7a q n-e7r has a maximum strength of 21,750 N. What maximum upward acceleration can it give the eleva -ntwq gzaamwn7:e7 21tor without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 khqy/ dxjq1jyib3cw i43r*4u*oe4 r;hg including parachute) when the upward force of air resistance is equal to one-fourth of theiq4rb*i4wyjd i3 yq1; hhro3 uc*x/4jer 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 hjj4oeqefx , 5*v29r t(( vyfqhe strikes the ground below, he bends his knees so that his torso decelerates over an apth* v(e9f 2xq45j(,jevoqf yrproximate 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 bo zw+ve3xu e2d*x runs vertically upward over a pulley and 3we 2xdvz+ eu*a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball playwwcd )-6yw8ke er
(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 baseball (a) atqm s3kxc1a4 z r/tj3t (5u4ubm the moment it is hit by the bat, and3 /(4kust5mct j4bqrx 3a1zu m again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in ioa/lxs ,::b th:iwz. a northwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points/i bsx.a::w,:ht il zo westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wiz aancfog d;n0fjq1i4 58f -7zre" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpq7nj 5faf 4 ozf8d;a1-0zgicnoint 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 cord from another 3.5 vuvbxl49- yz2$-\mathrm{kg}$ 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.iwrpx-uxy*. mk *fk9b5n2 v a40$-\mathrm{kg}$ 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, Antarcpf w21gs8 c3xvtica, as shown in Fig. 4-46. The sum of the forces 3vpfw1g 8cs2x$\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 behinic2 odij8w p77d it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first car 2p7c 8jd7wioi $\left(F_{\mathrm{T} 1}\right)$ , 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 showlf 7( ghedd-h)n in Fig. 4-48. (a) How hard must she pull downward to raise herself s(7ldehh f -)gdlowly 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,k w50z0 c9 bdn qv*-uq,qkcv8l 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 l;vht3aos32;j3)hd0l5 i 3 ensvtifxass $ 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 jusv gq 0*,7w+md;qo x6 s+luhsurface are in contact with each other, as sh s,v j*mdoug++s xu qh;wl067qown 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. 4-52jfn,d8q5p . fbko*r52xl-chq are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [H*5.qd-xk8n offhcjrpqb5, l2 int: 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 hee :nhfo1yn6smj3 ox1;avy cord of mass 1.0 kg . Calculate the acceleration of each box and th1 e6 :n3o hjyx;1fsmnoe 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 2i7ji:j ca g+rril ,r0,g:ijfcbfz9*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 star:;b,th,s sw gne,cce)t 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 shpl960 zg)m,uq 3h as6wic.gn tanding on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between ywhsg0 , ul ac)zp3i.mq6g 69nhour feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can4u 3sr00 eaf5hbpl (xd undergo if the coefficient of static friction between the tires and the ground ishp30r d(sue lbf xa504 0.80?   

  The coefficient of static friction between hard rubber and normal - ,8k0r6zwdyg3jou /uo a3tnn street pavement is about 0.8. On hod8t0nu3 oj/ wy-z,6rouang 3kw 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 :(si xp gzox ;0o7+pusat -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 a rough 3zf;pur vy/t+trh42 wg wqz bi(*.0*ec0$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very hi5 pi:slnd2x+k 8 ekr6ygh coefficient of static fricti ke+s6dkxlni:py 258r on.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetic friction for3wg,t 8: /xq)t kqyyed 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 Figr5x *zxsi48r /zbsg*w2i:q e p. 4-32 (Example 4-20) how large a mass would box A have to have to prevent any motion fro4*z*xibz qir2/ g5:sxrs8 p ewm occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How nkr9:o7l6z i1fds(g a* k,/kn3piq pkfar will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an iniqokn,* 3 azsn6/k fr7li pi:dgk1kp (9tial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are s6se:4 yzppp32fht *tin contact and at rest on a horizontal surface (Fig. 4-5462tsp yfhpsz4e p:3*t ). 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.mn hr4np(-i8h sdzhzo21 ve) 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 andoh(n nd1szvpe m- h42.hr 8zi) still avoid having the crate slide against the cab of the truck?   

On an icy day, you we-l +gohh huar-.x rl0w4 pq*+orry about parking your car in your driveway, which has an incline ofoh alu wx.rhq+-r e-p*hlg04+ 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 ap wtz3o0)cc;f:ty -ig slide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted)79ou ue*rrfs 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 3.0 9ehmydv9 yi al q6g/stv/y+,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 sjoqmo *hz, n80rip b;/eo,.gthe 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 be0ayez/ q;mjc5s v/l+ y someone pushing on it with a force directed upward at 28/lqeeysj z;5/+c 0mv a$^{\circ}$ 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:mi(;au divn/k yc0h/ can become dangerous projectiles as they melt. Consider a chunk of snow at the ri vki0nu /:y;mhdai /c(dge 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 an automobile;wsuzs7zcdk,)b zzd m 3w.1m5 traveling at speed v is equal t kz z uddcwm,s3;71bwmz .s)z5o $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 calu+;ug l * yfltrm+i(-r slides forward on the dash when the driver decel llfr(t+*yim+-;luu gerates 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 isn1gypp(c 6f2est;ey-4h 6 gnd given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they are filled to the packing hbh04v7x69 bmiz4 viz:zv:rmstation 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 minimum transit time for evv47z i4:hhm6bvr: 9bxziz 0m ach 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 b6z.ljbvk+7sh t9e, ufriction 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 iv .rg72-o(vb-nqegv, r5ffc 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 mammaa55er w +yfatvg:x*+mlian heart, at each pulse approximately 20 g of blood is accelerated from yf 5+*g aa:m ev+txr5w 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 auto+ ujhb bhev-:3mobile crash if the deceleration is no more than 30 " g 's." Calculate the force he3b vu+jb:-h 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 accelera8jkkup+; mh hjsw1ggfc(t57)tion produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static fr hgm8+js1w);(jhu5c7fktk pgiction 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 tl) 2rr yb.6kdqhe scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate yl )kr6br dq.2the 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 4 m trave 0j otr.6yh*ylled along the road, the elevation change is 1 m). How fast is it goi*.oh ylt0 r6yjng 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 yj+5f4hg+u( quezlt5xri 68 fthe top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average foy(zrjil+55x+4tq ge u ff6u8 hrce of air resistance?   

  A cyclist is coasting at a steady speed of 12m/e(u db0; hikvfzz/*k(s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without vfz;kz( /kb0i*( h duehaving 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 redesign of a hi( z*ks0f tpl0plly 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 accele(zk0sp*l 0ptfrate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles hekopge4q77phi39ek bj jj+ 4 7hr 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 strinpgke b4ejo9hqj7+hki77 j3p 4g 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 95yfaosju lf7c 1(8at, there are to be several ramps connecting different parts of the stor aao l98ff(u7y51ctsj e.
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 7r + )c*b8adxvt lua6v*eh .ddF is needed to lift the piano (mass M ) using the pulley apparatus shx6.t ce*dda7) *+v vhlubdra8own 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 3.5,aqr10 sti q+qcai 17f $\mathrm{~m} / \mathrm{s}^{2}$ 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 fntqco/8n+ua s.7 e/s-restraint chair, an engineer considers the following seesc 7so/uaqn 8+tf/.nt 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 I ,s8fru m+wfyf*mm+x3talian train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of sd, .(2yw z2j 3lhc7jr p)zdfbczt6di1 imilar 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 th)h,t cj z62yf3zlpb w7(zd.2c 1drjiden the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is u oe5 acsz9 mut-e,gq1z7*3o thsing 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 allowewbf z 1xep1u+3d 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 climbers who are roped together 7sb.h 6v423cxrth v0 tudg6 gsare ascending an ice field inclined at364tss2ur0tvbv7ch d x.6g hg 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.