Why does a child in a wagon seem to fall backward when you give the wago 8g2hc,5,uoqpy-/l iiutrh6ho hid/ , n a sharp pl,8h 26qio do,-iuhcrg/ huth5 iyp/, ull forward?

A box rests on the (frictionless) bed of a truck. rb 0fj,rrav( 1The 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, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is ridfrj br ,v01a(ring on the truck

If the acceleration of an object is zero, are no forcespxue+w7c euihr p8+ts;l(:k4mnkt 9+ acting on it? Explain.

Only one force acts onod.akd4 -um 0v an object. Can the object have zero acceleration? Can it have zemva 4d0-kod u.ro velocity? Explain.

When a golf ball is dropped to the pa hapt31otqf-h i5n4)rvement, it bounces back up. (a) Is a force needed to make it bf no- 4hrqpt1i)3hat 5ounce back up? (b) If so, what exerts the force?

If you walk along a log floas 4*m+otdxv;qswn 7v (ting on a lake, why does the log move in the opposite direws(n tox d*msv7; vq+4ction?

Why might your foot hurt if you kick a heavy des wago/dk4np2/ k or a wall?

  When you are running and want to stop quickly, you must dh*.,;ydlftf q4;g o ucecelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using youd qhulg; o.yt,f;f4 c*r 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 secti-x.kl0 5f;;c(5rh eq s bugefpon 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? What if the person gives a slow and steady pull? Explain your answer; sb-e 5r.gkpxel ;fq(0cfh5us.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock. -figpea,0ac : Why then doesn’t the heavierfci- ,ae0 gpa: rock fall faster?

Would a spring scale carried to the Moon give accurzh..s9fjo( ni ,y j0vbate results if the scale had 9.bi(f vy.,n0ohzsj jbeen calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless tbz 5-sxjooa( e)*tle5t 0 s)leable using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with tlet55 joez-eas )0 lxsto*(b)he box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freel e;qkyf c+ 046iwdmu7gy under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t thu+kd4g7wc 06me y f;qie Earth move?

Compare the effort ( nee7 hrj00lh 8nr,b4xor force) needed to lift 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-kg object horizontally with ar7nej4 lnbx0 e,h08rh given speed on the Moon and on Earth.

According to Newton’s third law, eadkd i*0x/wea(8rq yf1ch team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, qf ik*ydr80a(/de x1 wthen, determines which team will win?

A person exerts an upward force of 40 N)qk v89+tjb sl to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) 8lb) q+s9t vjkits direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on themc.xblik. *9t ground, how large a force does the ground exert on you? Why doesn’t this force make you9xc *bklim..t rise up into the air?

Whiplash sometimes results from an automobile accident when7 xg2e;wt h5tj1:r)scbft7r n the victim’s car is str s7r: e bfcg17;5xtttwrj2h n)uck violently 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 acceleraz1 poo,y(srjrs7xcob 72 ye52tes, the crate remains where it is on the truck, so it, too, accelerates. What force causes the rys2o 2 75eoy,17 (cbxozpr jscrate to accelerate?

A block is given a pus ctb*pzr9ny6 /h so that it slides up a ramp. After the block reaches its highe6/ tnb 9*czyprst point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom s0yjjf 9wh+ (zxcale read if you weighed yourself on an inclined plane? Assume the mechyh0(fj+ 9zxwjanism functions properly, even at an angle.

  What force is needed to accelerate a child on0rivq25q /3(u4ix ks lrzlc8x a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and qbtzjo lzguaw)g8dh7hv*50)0m 2o(a 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 withstand if it ovop33pk;;j)t d4xulis 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 88sg5 p cajl. kvsf-l5a $76-\mathrm{kg}$ 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 *q-vj:o*:ojmo mn uv7if the car is traveli :j:-om*v oo7jnumv*qng at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet f. i*1vqvqx n 25bjh.aprom rest to 125m/s. 2jqap1 5bhvqn*.i xv over a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration o07h324yt5vw6x 89hub9x x tifxpe4 :nl vozlmf 2.5 xnp0e ivhy 3lh:fxw5v976 8 z2xmu4t9btol x4 $\mathrm{~m} / \mathrm{s}^{2}$ 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 canc.m 1jipkdg:0 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 des m9*z g2dygm 7gc.1y 7:xjsmuzigned so that the maximum acceleration is 0.0680 g . What are the maximum and minimum 9 xzym*j7c7dm 2guzmsg .1y:gforces 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 teq lt xr8 810 ,6tkdhiugs1-mscale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’sd8,r 6xe0t1kht 8u m1sqg i-lt regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator bnx )qeq2 qv5uxk p.*acx3(q(has a maximum strength of 21,750 N. What maximum upw(aqxvun(2eb5). 3 qk x*qcp xqard acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg includin u6lsnxg*7 2liig68-nr vq6mz;yi b*ug parachute) when the upwardxgi66u2g7*v*u; bn8 islz6 -qn mrlyi force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the r7u93vlaxyzo )k.dtme. c5cx)oof of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distancd.yuxk.ol7)m )a z c9tvx c5e3e 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 ro4rkzhey6g9 d+ pe tied to the box runs vertically upward over a pulley and a wk dzgrye 4h+96eight 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 bbz4mzg0 6mxz 9asketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseb24 vc4 hm:vt yzdy :/xrqr+.xsall (a) at the moment it is hit by the bat, and again (b)2d4v:+x/sz. ycrxrmhv q:y 4t 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 force must tm5ugmt+5 uujy u8 m,5be exerted in what directiomtm5+ug,8j5m y5utu un 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 horizontally between two) xol-(l iqd-vxl,h65uibur 2,rav9h buildings 10.0 m apart. The sag in the rope when she is at the midpoin29u)l6v-,b(hrvrha5olidu x i xql, -t 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 9/ ji9mwkipx6hpthrz,l+1 7k.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 14fpj.8o+gi fud6 b it.5wj06vs .0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo Base, Antar+ l2klkv vli*,ctica, as shown in Fig. 4-46. Thl+ llk2iv k*v,e sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fi8.m:t *igrwx hg ,i0zpg. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the fir .i rzh0igw:g*8pt xm,st 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 pull( hi86 qr9 puz4z hx (7t(sir;neubp :a;vsci0s herself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to rai6h : q;x a4( pcu(tv(rri9e8sb07hz sin;zpuise 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 fb 6kwhp1d6r.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 blocks/;7lp+ b5vgyxflo3yx .j 0 qx (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 arpcb/bpq3xx:0 o,gbg3 je6z85k 5ry vy e in contact with each other, as shown pgo,gby3b bv053x q 5 zxyper8:jck/6in 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 z q 7:psqphr:g4b.3dreach 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? [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. Assum:qr7 phzq.dsb r:4 3gpe it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a hearyzq4n j) az90ki,7kv 8 z5yxgvy 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 in F,0kg qzi ajnyrz4v7 x5y98zk)ig. 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 ofkn5hbem t.; nin)x9( +vzvm ;k 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 start a 5jq ,7j/u7n rpzjd( -g(i6pdum.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 standinggij 8uu8 jhvjd 5u6)pot6)p 84 ymjrj; on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slyj ompt5uj8hj dg8 j4ui)r6 8u)v6; jpide?   

  What is the maximum t u v1*6md)booacceleration a car can undergo if the coefficient of static friction between the tires and the ground i)t mo6*ouv 1dbs 0.80?   

  The coefficient of stati5 2vmvvfnqk(,c friction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum q5( n2vf mvkv,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 -47h 1rgcqp 4lkhtq0j 85.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 30v mds1,m9kop7 $^{\circ}$ 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 w 7 xnwan8twu2 oje(u+6fzml*2 ith an asphalt surface have a very high coefficient of static fric(uu+2aj6t lxeo2 m7 nz8w fn*wtion.

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 fril r;i6zi1a +5fuh ng9gction 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.c 2x hgep2q;.v 4-32 (Example 4-20) how large a mass would box A have to hpc.2;hg qxv2eave to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push np n9y4 s,(t5 /xo0itxwq *bgm d.pj1dso that it slides across the floor. How far will it go, given that the coefficie4 g/* nonw0,sdi dp5xypqt j(t9 xb1m.nt of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and + kj6 *o.maykfau 69te110 kg , are in contact and at rest on a horizontal surae66f+kau* y.km jot9 face (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 coefficient of statmf) -qhbewfa.lncl8 uai,2,9 ic 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 avoil,bhcf -awamq.e, f2)iu8n 9l d having the crate slide against the cab of the truck?   

On an icy day, you worry about pa6jpkkv s:h 4y5rking your car in your driveway, which has an incline 5 :kskv6 4hjpyof 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 witx3u 1t (n3xz:qtouewi 1qo7x 3h 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 awfz) zj(1w+; eh.9x qe ;nsmejn 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 cw9ep :co (cb6cc ,3nfn1/8 qlbbh3ba$\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the stou*hw(w 8ef1deepest 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 wallt,dnaq,v :af7 i+n jg* by someone pushing on it with a force directed upqdf7,nai:+ntgv j* , award 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 dangerousm 7u(;l(fxyjt2k1 (tnof ydn 5 projectiles as they melt. Consider a chunk of snow at the ridge of a roof with5mx((y2tyjk( ;t o7 nl fdu1nf 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 aukd)2jnmlxz* 7,-k ,gjcc vd3 fcf t9zpgei 001tomobile traveling at speed v is equlpkj nz9,zdf2)i 3dcf, xgmcj*c k 1g0t0-e7 val 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 when the driv8qpoe-./qm d zer deczd.m/q8oqp - eelerates 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 mass77: nl.k nxkpc:)thl w m is 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 j67,4 w,otetj;phhjd rd4e e7filled 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 minimum transit time for each boh,je j6e;,drd t 74 j4thwe7pox?   

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 frap paa50 czm+yb ) 3q1r3vw(j-1 ssmdriction 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 coaka arj 2p;xy2eainbz5-xpc;*av)q 4 2st 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 o pah 450r+)ag re up4;gg*qgstf a mammalian heart, at each pulse approximately 20 g of blood is accelers)g0he ag ua rp ;g544*tgr+qpated 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 surty7tl: d1qco)p ws m;6viving an automobile crash if the decelercpwot6 myql ;:ds)7t1ation is no more than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced , 8vktfo2sd3t/r5 bux by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficiedbr 35,v/utt2foxks 8nt of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident involving two cars vlz;q sttz9473sswl np74/ hl, measure 72-m-longn3 phst s9;7qlt7wlzz4v/4sl 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 m6dk*ev, m6n87do ami qeans that for each 4 m traveled along the road, the elevation change is 1 m). How fast6m ,i kvodnm*6aq 7ed8 is it going 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 t2f2t;6eedoa2g 8wq ngz 7zue5 he top of the Leaning Tower of Pisa and falls 55 m b t85gg; 2 ezne 2z7w6u2qdaofeefore reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stres 4k f+cy(x6sjtch 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 wcks+f x(4 j6syill be the speed upon emerging?   

  A city planner is working on the redesign of a 5t e.ac(vf- lnhilly 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 , cf ( navtc5.el-an accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a th*dw/zf , /+;0zclkphhnhl sg3in piece of string while the jetli,;3ph/ dkh +*n/lh cszfwg0lzner she is in takes 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 bsc88kdz,cpn8;hj .y9nqh)f be several ramps connecting different parts of the storyfzn9kpj, h;bq)hcs8 n 8.8cd 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 F is needed to lift the pianq-q0 s pzq )fb8j;,uzmo (mass M ) using the pulley appa-)q, zp08mz bqjufq s;ratus shown in

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

  A jet aircraft is accelera .62ni85r.yax;r q3hdwfc t le l2wqm9ting 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 chairpinf65j yz 348hwxwa2dd6dy h9)cl0 z, an engineer considers the following set of na yd6hiw4fzd9wxc )h0j3y 285zl6d p conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 660 metric t4+mkisd5ac 7c.7wb juons (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 similar length. Ka wozdonm*t: v x2*dt)1ren'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 rope pull on him? Which cl 2d*dxt* zmowt1n:ov) imber is more likely to be hurt?

A fisherman in a boat is using a " 9ce fsx1 sn)+h 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maxim 8mxosztrbcj 8 s63f++um 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 rjq/z4 p enkt)m b52:qsoped together are ascending an ice field inclined at 21.0 m 2jzeb)5stqnpkq4 :/$^{\circ}$ 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.