Why does a child in a wagon seem to fall backward when you give the wagonpr/,zo vog*0vfi 3m z) a sharp 3zpo ) riv vfo0gm/,z*pull forward?

A box rests on the (frictionless) bed omq6 1 awa)l bzc8;ckq:f 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, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is am 6 a) wc1qkcqzb:8;lriding on the truck

If the acceleration of an object is zero, are no forces acting on it? Explainq vn5b/bxd*rpk ffjq 7v1z(*,.

Only one force acts on an object. Can the object have upf ) lb4*), vb9d3 *lcj pscwial39sgzero acceleration? Can it had s b,swp9*ljbl3)3vg )4 ap*9lciuc fve zero velocity? Explain.

When a golf ball is dryd2: ucdnr )b+opped to the pavement, it bounces back up. (a) Is a force needruc by:2d +nd)ed to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, wh7f+oz 8te;k2pu.db lny does the log move in the opposite direct f2.8duo7;+kzble tnpion?

Why might your foot hurt if you kick a heavy desk or wgi(qjgv+) (go 9bne 5a wall?

  When you are running and want to stop quiqq4-ma)kli 935 uitl ackly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience)l-qq i3tualm a4 5k)i9 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 section of the same threadwv z dq4i-41,nd8cdfd 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? Expla8qndi4d1cv d4w ,fzd- in your answers.

The force of gravity on a 2-kg rock is twice as great as:)d dahc7i7hzf:b y b4 that on a 1-kg rock. Why then doesn’t the heavier rock fab)7 had:f7hc4 bdz:iyll faster?

Would a spring scale carried to the Moon gi* ugmm dqom+)j 4t5gs5ve accurate results if the scale had been calibratedd*g m 5qtgj5ou)s mm4+ (a) in pounds, or (b) in kilograms?

You pull a box with a c7p5 vyos(p ahc buyzn.)c 8x0q*:g( tsmu ;6mqonstant 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 the acceleration of the box (a) remain the0bsxmca;p6hu)svp87 5o cmqz:(ynq *y(. utg same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is ee ag( ;eh2s,3kuv 3qra net force mg exerted on i3 , (h3ges uq2evr;keat 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 (or force) needed to lift a 10-kg object l6lba+hc4z; ywhen you are on the Moon with the force needed to lift it on Earth. Compare the force needed to thrl4+l hb ;cyz6aow 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. 4–3p ;ktzwc, m 6uz9 +m*r:owm:cz7) pulls withr tzw9k6cz cuw*mmo:,pz;: m+ equal force on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Desc)jn * nbmcnq frp.p906br2q k3ribe the “reaction” force (Newton’s third law) by stating (a)9nnnp0jr .qb 2q)3p* c6kbrmf its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the grgfb0l0t l u 54i*qx/rlound, how large a force does the ground exert on you? W 4 fr0l0*lui/lb gq5xthy doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victimvq+nai5 ol5 6n’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is itil6+anq5 5 ovn really?

A heavy crate rests on the bpcbakbvo-q: ea s(,**ed of a flatbed truck. When the truck accelerates, the crate remakb* ba-o aqcv*(sp:e,ins 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 slides8/-5dr lemtff up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascen e tf5/-lm8rdft. Why?

What would your bathroom scale read if you we e61 : cjj-o9 x9no/l-g22nyilnixjycighed yourself on an inclined plane? Assuj22c6 o9nn jexlyn1-/ c: yiil9- gxojme the mechanism functions properly, even at an angle.

  What force is needed to accel:gx .a nu2xwy,ngaib)7/ 0zq herate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N acce)n+s7,m saoxo)n0jwllerates 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 withstand if it isg/( .0kn 9bcd:r0 fhb ,tivhto 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 6v78crxpp0wla, u xh0 $76-\mathrm{kg}$ 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 hp 6yni77:fwnboqa 1zu/l o79 traveling at 95km/h? -ha77f6i lun9 y 7wq: bpzo1n/o  

  What average force is needed to accelerate a 7.00-gs*b 67 jfszwx(r3a3e sram pellet from rest to 125m/s over a distance of 0.8006bs e *3sfx(7sarjw z3 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the w ,9gebu 8d7opwjiy9rnyg 72r4ater with an acceleration of 2.5 en ro8yrubj,y7d9p24i 9g gw7$\mathrm{~m} / \mathrm{s}^{2}$ 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 canrpci6jcqh dg.y- p-; 1lfq1s5kx p)i5 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(sh/ n u61ktea57cse 4thw wwl r11hs/ be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting c 1e 4w(t5t7/hhas r1 n w1slsh6wkuec/able? 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. ts;mdq/lj 65 urnzyo; k,m.,ak 8f fg*When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculakm/,;om6fakud y 8jf; z,snrl.t*5qg te the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. Wha;pe(e 4q yy:wwt maximum upward acceler ee4w(:;yyp qwation can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (m2skpir9( . hkyass 132 kg including parachute) when the upward force of air resistance is equalish.9(k2 pryk to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high.:jnf 3zvi(3cas4 7xlk When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If thevf:k7n43 i lc(3zas jx 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 ,na*d:kxwq :w8d4zu a. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on tqdw kxw :n:u4*za d,8ahe 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 diagr ;dvgt 1.juk1sj o1devo b,l+dxw68) yam for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment it is hit by the iv).n uci.j*p bat, and again (b) after c)i*j.n puiv. it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. *jbfvjh- oe74A second 650-N force must be exerted in what direction so that the bj* 4hv-7fejo resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung hoebspduy/* 7)8f d-pbvrizontally between two buildings 10.0 m apart. The s -8y s7pubfpb*ddv) e/ag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless coop(.vtb;;k xw rd 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 1y -xo5 ukn;;;xfro* sfk9vvp74.0$-\mathrm{kg}$ 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 locatioi1 ))nvls)92u0r5e5fq rkq ek;oryy h/-xx ybn at McMurdo Base, Antarctica, as shown in Fig. 4-46. The irhxrk)-0ubqk; 9y x5/sy)y )2l 5q 1roenvfesum 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 behine r1l+8)au- 3ocb al9ydwnhll9ix 7 st8r.;xvd it, Fig. 4-47 . Determine the rated y9)u 8 rc+7vl.ls1 il3bxrl -98hno;taxawio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bh5 tivhp2 u9/cucket-pulley apparatus shown in Fig. 4-48. (a) How ha/t 52h9vpi uchrd must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a 6x1ent w .sx6(teri+;n5$-\mathrm{kg}$ 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 (fs wwi3:wmb :2wn.:*;c nu px:7mvadpmass $ 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 surfac;xbrtorpqq;ie)5e2zy :)z7 q e are in contact with each other, as showzeb5x:)pr2;ei7o)zqr; q qtyn 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 1.80 m au*vk*ay-lon4zg ,qn k/h9gn8bove the ground, and the massless frictionlesznoh vyq-uk9g *48kn*l a/g,n s pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a hp0 3jt9a7 n;xv+jzher eavy cord of mass 1.0 kg . Calculate the acceleration h90jv rxe;at +n 7pz3jof each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between a2,y3l qv xffdr mb2/z- 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 * kef--38ikjh+rpzuq 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. What mi :) -b6blw ll1usr+vufnimum coefficient of static friction must exist between your feet and the floor if you are not to s lw-f)sl6 u:b +brl1vulide?   

  What is the maximum acceleration a car can undergo if t*y6ao e fyim7:)amwewuku d2 9(ez(y;/j0 pfuhe coefficient of static friction between the tires and the ground is uwfp0*kej/e;)u ai9u ( em:(yfy w6oydz2am70.80?   

  The coefficient of static friction between hard rubber anoathke- :x )c.d normal street pavement is about 0.8. On how saet c-k)ho:. xteep 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 atr7-79mb/.ytorn zc.lavyq n ; -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 roupimmjob4ro/ sc7 86f/ 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 asphalt surface have a ve4+l0haweg k u-ry high coefficient of static friction. eg -+wu0ak4lh

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 fn 9 8luc l26r,qus0lqmriction 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 kjz5xem h*/1gbox A have to have to prevent any motion from occurre 5xm /1*khjzging? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides a* b9+ye x 7mdx0ma7:lt blpzw)cross the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the pu+l 0)x*7emz7t9 bp:dymbalx wsh imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , arenaz(txb+ux jr+/(x44q- zdk e in contact and at rest on a horizontal surface (Fig. 4-54). A rd zbe/ xu4x (ax+j+tnz 4q(-k620$-\mathrm{N}$ 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 coefficienpz-w e+uuhee w1j2uwtn4 ,x0ln uauh1u,f88/t 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 the crate slide against the cab of the uz 18huux+eju/utwu1a-2lfepn4 0w,e 8,n w htruck?   

On an icy day, you worr,n(jffb((texv 6d r*gy about parking your car in your driveway, which has an incline of 12e*fbnv jg(dftx6 (r,($^{\circ}$ . 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 sdca p+kwl zg+f**p)5-.ywv f llide 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. 4-5hp0hmlbi)y/n3r0ig j 6 y 2j+p .y-tvo5 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3;r 9h 0jfz.eoz.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the st, qamk2et1-2*rd;fggr,ke l - fxn4n.wp n*qieepest 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 s2yebo ff8c3 md l/ v5+(jh4edpomeone pushing on it with a force directed upward a 58 oeyd+pm4l(2jvfe h /bcf3dt 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 a s8vljl:b , viym82ph(7sch5l b1w*mk s they melt. Consider a chunk of snow at the ridge of a roof with a pithpb28k,si8l hw:clb7svm lm*vj ( 1y5ch 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 traveling at sp4. roy3k 4lytf1rycp2eed v is equal to fy21c.3 rytpkor 4l4y$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 +bj r5j9fd k* pc:bwb7dash when the driver deceleratesf *:jrjb5 kpbdb+w97 c from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initial speehhgq8e+ye c *(d $ 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 th1yo3tnz,r2tm n ll:.h ey 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 minim l2:zn.r3y, tlhont 1mum 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 ki1hp1hw*b 2e finetic 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) z- (e.zvck;w2wf5,ghqqm00ay ct;et can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse apprg*ge;s x92u ww zj-ci/9ewa:coximately 20 g of blood is accg es* wejw;/a9 2c9x-:gzwuicelerated 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 surviving6rawolh*( rj) fu-ff5 an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force onfo *f a6lw)u(j5f rrh- a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , and 9) m n+fpwx7:9cuznog4c.qs bif an object is going to "hold its place" on the ground, n c .)w:cgonx49bfq9szup +7mshow that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining lsk f 5o-w06b5lcml)mthe 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. flkmomlw5lc b6)50-s The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for oca o kh8 u3u31ad(omya4m,/teach 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reache4khmma/a31(oy3,c8a t ud o uos 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 droppe,i hg -hqarc)eixahg;s02s2 8 d from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average fs r;hig2 gh hq2a)0aci, x-s8eorce of air resistance?   

  A cyclist is coasting at a steady 3ocr;v p0 .wnvspeed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from thrvw pco;. v3n0e muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the+pk;bbh kpa.+ redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular smallb pbk;+ah. k+p 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 experiments, dangles her;pl;,h+o p2bk -pcfc vuz/x 1ub)wk ;f watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angl,cbpu/wo bx +uz;f1f;ppk2lkc ;v-) he 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 superm 2m t (qs,k9t6ozrxj5rarket, there are to be several ramps connecting different parts of the storerxr( q9z omt6s ,52jkt.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) kdd-j1a,(eb (t zsau:mo/)0r; jzxjousing the pulley apparatus s;sojmj j0z:1zx) /k-or b(aa,ted d(uhown 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 acciift9* ts 4im cy:zk:2elerating 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 cha bv+j11 -daioeir, an engineer considers the following set of condive ao -1d+1bijtions:
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 660xz,-dja:;nxt cf e(v: 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 rj-t kql f6qi74opes of similar length. Karen's rope is f7 qqtj64-kilmore 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 climber is more likely to be hurt?

A fisherman in a boat is using a " 10-1: s3v3ji.22q v vda(shs)rmrgv3 ul (w $\mathrm{~b}$ 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 maximum soi,olry4o:2m peed 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 are ascending an ice field inc bsywm5ap4( :ulined at 21.0p5uymbw s4 (a:$^{\circ}$ 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.