Solved: An old streetcar rounds a flat corner of radius

The floor of a railroad flatcar is loaded with loose crates having a coefficient of static friction of 0.25 with the floor. If the train is initially moving at a speed of 48 kmlh, in how short a distance can the train be stopped at constant acceleration without causing the crates to slide over the floor?

In a pickup game of dorm shuffleboard, students crazed by final exams use a broom to propel a calculus book along the dorm hallway. If the 3.5 kg book is pushed from rest through a distance of 0.90 m by the horizontal 25 N force from the broom and then has a speed of 1.60 mis, what is the coefficient of kinetic friction between the book and floor?

A bedroom bureau with a mass of 45 kg, including drawers and clothing, rests on the floor. (a) If the coefficient of static friction between the bureau and the floor is 0.45, what is the magnitude of the minimum horizontal force that a person must apply to start the bureau moving? (b) If the drawers and clothing, with 17 kg mass, are removed before the bureau is pushed, what is the new minimum magnitude?

A slide-loving pig slides down a certain 35 slide in twice the time it would take to slide down a frictionless 35 slide. What is the coefficient of kinetic friction between the pig and the slide?

A 2.5 kg block is initially at rest on a horizontal surface. A horizontal force P of magnitude 6.0 N and a vertical force Pare then applied to the block (Fig. 6-17). The coefficients of friction for the block and surface are fLs = 0.40 and fLk = 0.25. Determine the magnitude of the frictional force acting on the block if the magnitude of Pis (a) 8.0 N, (b) 10 N, and (c) 12 N.

A baseball player with mass 111 = 79 kg, sliding into second base, is retarded by a frictional force of magnitude 470 N. What is the coefficient of kinetic friction J-Lk between the player and the ground?

A person pushes horizontally with a force of 220 N on a 55 kg crate to move it across a level floor. The coefficient of kinetic friction is 0.35. What is the magnitude of (a) the frictional force and (b) the crate's acceleration?

The mysterious sliding stones. Along the remote Racetrack Playa in Death Valley, California, stones sometimes gouge out prominent trails in the desert floor, as if the stones had been migrating (Fig. 6- 18). For years curiosity mounted about why the stones moved. One explanation was that strong winds during occasional rainstorms would drag the rough stones over ground softened by rain. When the desert dried out, the trails behind the stones were hard-baked in place. According to measurements, the coefficient of kinetic friction between the stones and the wet playa ground is about 0.80. What horizontal force must act on a 20 kg stone (a typical mass) to maintain the stone's motion once a gust has started it moving? (Story continues with Problem 37.)

A 3.5 kg block is pushed along a horizontal floor by a force jl of magnitude 15 N at an angle 0= 40 with the horizontal (Fig. 6-19). The coefficient of kinetic friction between the block and the floor is 0.25. Calculate the magnitudes of (a) the frictional force on the block from the floor and (b) the block's acceleration.

Figure 6-20 shows an initially stationary block of mass m on a floor. A force of magnitude 0.500mg is then applied at upward angle 0 = 20. What is the magnitude of the acceleration of the y Lx Fig. 6-19 Problems 9 and 32. Fig. 6-20 Problem 10. block across the floor if the friction coefficients are (a) J-Ls = 0.600 and J-Lk = 0.500 and (b) J-Ls = 0.400 and J-Lk = 0.300

A 68 kg crate is dragged across a floor by pulling on a rope attached to the crate and inclined 15 above the horizontal. (a) If the coefficient of static friction is 0.50, what minimum force magnitude is required from the rope to start the crate moving? (b) If J-Lk = 0.35, what is the magnitude of the initial acceleration of the crate?

In about 1915, Henry Sincosky of Philadelphia suspended himself from a rafter by gripping the rafter with the thumb of each hand on one side and the fingers on the opposite side (Fig. 6-21). Sincosky's mass was 79 kg. If the coefficient of static friction between hand and rafter was 0.70, what was the least magnitude of the normal force on the rafter from each thumb or opposite fingers? (After suspending himself, Sincosky chinned himself on the rafter and then moved hand-over-hand along the rafter. If you do not think Sincosky's grip was remarkable, try to repeat his stunt.)

A worker pushes horizontally on a 35 kg crate with a force of magnitude 110 N. The coefficient of static friction between the crate and the floor is 0.37. (a) What is the value of fs,max under the circumstances? (b) Does the crate move? (c) What is the frictional force on the crate from the floor? (d) Suppose, next, that a second worker pulls directly upward on the crate to help out. What is the least vertical pull that will allow the Fig. 6-21 first worker's 110 N push to move the crate? (e) If, Problem 12. instead, the second worker pulls horizontally to help out, what is the least pull that will get the crate moving?

Figure 6-22 shows the cross section of a road cut into the side of a mountain. The solid line AA' represents a weak bedding plane along which sliding is possible. Block B directly above the highway is separated from uphill rock by a large crack (called a joint), so that only friction between the block and the bedding plane prevents sliding. The mass of the block is 1.8 X 107 kg, the dip angle e of the bedding plane is 24, and the coefficient of static friction between block and plane is 0,63. (a) Show that the block will not slide under these circumstances. (b) Next, water seeps into the joint and expands upon freezing, exerting on the block a force jl parallel to AA'. What minimum value of force magnitude Fwill trigger a slide down the plane?

The coefficient of static friction between Teflon and scrambled eggs is about 0.04. What is the smallest angle from the horizontal that will cause the eggs to slide across the bottom of a Teflon- coated skillet?

A loaded penguin sled weighing 80 N rests on a plane inclined at angle () = 20 to the horizontal (Fig. 6-23). Between the sled and the plane, the coefficient of static friction is 0.25, and the coefficient of kinetic friction is 0.15. (a) What is the least magnitude of the force f, parallel to the plane, that will prevent the sled from slipping down the plane? (b) What is the minimum magnitude F that will start the sled moving up the plane? (c) What value of F is required to move the sled up the plane at constant velocity?

In Fig. 6-24, a force P acts on a block weighing 45 N. The block is initially at rest on a plane inclined at angle () = 15 to the horizontal. The positive direction of the x axis is up the plane. The coefficients of friction between block and plane are fLs = 0.50 and fLk = 0.34. In unit-vector notation, what is the frictional force on the block from the plane when P is (a) (-5.0 N)i, (b) (-8.0 N)i, and (c)( -15 N)i?

You testify as an expert witness in a case involving an accident in which car A slid into the rear of car B, which was stopped at a red light along a road headed down a hill (Fig. 6-25). You find that the slope of the hill is () = 12.0, that the cars were separated by distance d = 24.0 m when the driver of car A put the car into a slide (it lacked any automatic anti-brake-lock system), and that the speed of car A at the onset of braking was Vo = 18.0 mls. With what speed did car A hit car B if the coefficient of kinetic friction was (a) 0.60 (dry road surface) and (b) 0.10 (road surface covered with wet leaves)?

A 12 N horizontal force F pushes a block weighing 5.0 N against a vertical wall (Fig. 6-26). The coefficient of static friction between the wall and the block is 0.60, and the coefficient of kinetic friction is 0.40. Assume that the block is not moving initially. (a) Will the block move? (b) In unit-vector notation, what is the force on the block from the wall?

In Fig. 6-27, a box of Cheerios (mass me = 1.0 kg) and a box ofWheaties (mass mw = 3.0 kg) are accelerated across a horizontal surface by a horizontal force F applied to the Cheerios box. The magnitude of the frictional force on the Cheerios box is 2.0 N, and the magnitude of the frictional force on the Wheaties box is 4.0 N. If the magnitude of F is 12 N, what is the magnitude of the force on the Wheaties box from the Cheerios box?

An initially stationary box of sand is to be pulled across a floor by means of a cable in which the tension should not exceed 1100 N. The coefficient of static friction between the box and the floor is 0.35. (a) What should be the angle between the cable and the horizontal in order to pull the greatest possible amount of sand, and (b) what is the weight of the sand and box in that situation?

In Fig. 6-23, a sled is held on an inclined plane by a cord pulling directly up the plane. The sled is to be on the verge of moving up the plane. In Fig. 6-28, the magnitude F required of the cord's force on the sled is plotted versus a range of values for the coefficient of static friction fLs between sled and plane: Fi = 2.0 N, F2 = 5.0 N, and f.L2 = 0.50.At what angle ()is the plane inclined?

When the three blocks in Fig. 6-29 are released from rest, they accelerate with a magnitude of 0.500 mls2. Block 1 has mass M, block 2 has 2M, and block 3 has 2M. What is the coefficient of kinetic friction between block 2 and the table?

A 4.10 kg block is pushed along a floor by a constant applied force that is horizontal and has a magnitUde of 40.0 N. Figure 6-30 on "- gives the block's speed v versus S time t as the block moves along an x "- axis on the floor. The scale of the figure's vertical axis is set by Vs = 5.0 m/s. What is the coefficient of kinetic friction between the block and the floor?

Block B in Fig. 6-31 weighs 711 N. The coefficient of static friction between block and table is 0.25; angle (J is 30; assume that the cord between B and the knot is horizontal. Find the maximum weight of block A for which the system will be stationary.

Figure 6-32 shows three crates being pushed over a concrete floor by a horizontal force F of magnitude 440 N. The masses of the crates are 111) = 30.0 kg, 1112 = 10.0 kg, and 1113 = 20.0 kg. The coefficient of kinetic friction between the floor and each of the crates is 0.700. (a) Wha t is the magnitude F32 of the force on crate 3 from crate 2? (b) If the crates then slide onto a polished floor, where the coefficient of kinetic friction is less than 0.700, is magnitude F32 more than, less than, or the same as it was when the coefficient wasO.700?

Body A in Fig. 6-33 weighs 102 N, and body B weighs 32 N. The coefficients of friction between A and the incline are JLs = 0.56 and JLk = 0.25. Angle (J is 40. Let the positive direction of an x axis be up the incline. In unit-vector notation, what is the acceleration of A if A is Fig. 6-31 Problem 25. Fig. 6- 32 Problem 26. Frictionless, massless pulley Fig. 6-33 Problems 27 and 28. initially (a) at rest, (b) moving up the incline, and (c) moving down the incline

In Fig. 6-33, two blocks are connected over a pulley. The mass of block A is 10 kg, and the coefficient of kinetic friction between A and the incline is 0.20. Angle (J of the incline is 30. Block A slides down the incline at constant speed. What is the mass of blockB?

In Fig. 6-34, blocks A and B have weights of 44 Nand 22 N, respectively. (a) Determine the minimum weight of block C to keep A from sliding if JLs between A and the table is 0.20. (b) Block C suddenly is lifted off A. What is the acceleration of block A if JLk between A and the table is 0.15

A toy chest and its contents have a combined weight of 180 N. The coefficient of static friction between toy chest and floor is 0.42. The child in Fig. 6-35 attempts to move the chest across the floor by pulling on an attached rope. (a) If (Jis 42, what is the magnitude of the force F that the child must exert on the rope to put the chest on the verge of moving? (b) Write an expression for the magnitude F required to put the chest on the verge of moving as a function of the angle (J. Determine (c) the value of (J for which F is a minimum and (d) that minimummagnitude.

Tho blocks, of weights 3.6 Nand 7.2 N, are connected by a massless string and slide down a 30 inclined plane. The coefficient of kinetic friction between the lighter block and the plane is 0.10, and the coefficient between the heavier block and the plane is 0.20. Assuming that the lighter block leads, find (a) the magnitude of the acceleration of the blocks and (b) the tension in the taut string.

A block is pushed across a floor by a constant force that is applied at downward angle (J (Fig. 6-19). Figure 6-36 gives the acceleration magnitude Q versus a range of values for the coefficient of kinetic friction JLk between block and floor: Q) = 3.0 mls2, JLk2 = 0.20, and JLk3 = 0.40. What is the value of ()?

A 1000 kg boat is traveling at 90 km/h when its engine is shut off. The magnitude of the frictional force 7k between boat and water is proportional to the speed v of the boat: fk = 70v, where v is in meters per second and fk is in newtons. Find the time required for the boat to slow to 45 km/h

In Fig. 6-37, a slab of mass 111) = 40 kg rests on a frictionless floor, and a block of mass 1112 = 10 kg rests on top of the slab. Between block and slab, the coefficient of static friction is 0.60, and the coefficient of kinetic friction is 0.40. A horizontal force F of magnitude 100 N begins to pull directly on the block, as shown. In unit-vector notation, what are the reSUlting accelerations of (a) the block and (b) the slab?

The two blocks (m = 16 kg and M = 88 kg) in Fig. 6-38 are not attached to each other. The coefficient of static friction between the blocks is fLs = 0.38, but the surface beneath the larger block is frictionless. What is the minimum magnitude of the horizontal force F required to keep the smaller block from slipping down the larger block?

The terminal speed of a sky diver is 160 km/h in the spreadeagle position and 310 km/h in the nosedive position. Assuming that the diver's drag coefficient C does not change from one position to the other, find the ratio of the effective cross-sectional area A in the slower position to that in the faster position.

Continuation of Problem 8. Now assume that Eq. 6-14 gives the magnitude of the air drag force on the typical 20 kg stone, which presents to the wind a vertical cross-sectional area of 0.040 m2 and has a drag coefficient C of 0.80. Take the air density to be 1.21 kg/m3, and the coefficient of kinetic friction to be 0.80. (a) In kilometers per hour, what wind speed V along the ground is needed to maintain the stone's motion once it has started moving? Because winds along the ground are retarded by the ground, the wind speeds reported for storms are often measured at a height of 10 m. Assume wind speeds are 2.00 times those along the ground. (b) For your answer to (a), what wind speed would be reported for the storm? (c) Is that value reasonable for a high-speed wind in a storm? (Story continues with Problem 65.)

Assume Eq. 6-14 gives the drag force on a pilot plus ejection seat just after they are ejected from a plane traveling horizontally at 1300 km/h. Assume also that the mass of the seat is equal to the mass of the pilot and that the drag coefficient is that of a sky diver. Making a reasonable guess of the pilot's mass and using the appropriate VI value from Table 6-1, estimate the magnitudes of (a) the drag force on the pilot + seat and (b) their horizontal deceleration (in terms of g), both just after ejection. (The result of (a) should indicate an engineering requirement: The seat must include a protective barrier to deflect the initial wind blast away from the pilot's head.)

Calculate the ratio of the drag force on a jet flying at 1000 km/h at an altitude of 10 km to the drag force on a prop-driven transport flying at half that speed and altitude. The density of air is 0.38 kg/m3 at 10 km and 0.67 kg/m3 at 5.0 km. Assume that the airplanes have the same effective cross- sectional area and drag coefficient C.

In downhill speed skiing a skier is retarded by both the air drag force on the body and the kinetic frictional force on the skis. (a) Suppose the slope angle is () = 40.0, the snow is dry snow with a coefficient of kinetic friction fLk = 0.0400, the mass of the skier and equipment is 111 = 85.0 kg, the cross-sectional area of the (tucked) skier is A = 1.30 m2 , the drag coefficient is C = 0.150, and the air density is 1.20 kg/m3. (a) What is the terminal speed? (b) If a skier can vary C by a slight amount dC by adjusting, say, the hand positions, what is the corresponding variation in the terminal speed?

A cat dozes on a stationary merry-go-round, at a radius of 5.4 m from the center of the ride. Then the operator turns on the ride and brings it up to its proper turning rate of one complete rotation every 6.0 s. What is the least coefficient ofstatic friction between the cat and the merry-go-round that will allow the cat to stay in place, without sliding?

Suppose the coefficient of static friction between the road and the tires on a car is 0.60 and the car has no negative lift. What speed will put the car on the verge of sliding as it rounds a level curve of 30.5 m radius?

What is the smallest radius of an unbanked (flat) track around which a bicyclist can travel if her speed is 29 km/h and the fLs between tires and track is 0.32?

During an Olympic bobsled run, the Jamaican team makes a turn of radius 7.6 m at a speed of 96.6 km/h. What is their acceleration in terms of g?

A student of weight 667 N rides a steadily rotating Ferris wheel (the student sits upright). At the highest point, the magnitude of the normal force FN on the student from the seat is 556 N. (a) Does the student feel "light" or "heavy" there? (b) What is the magnitude of ~v at the lowest point? If the wheel's speed is doubled, what is the magnitude FN at the (c) highest and (d) lowest point?

A police officer in hot pursuit drives her car through a circular turn of radius 300 m with a constant speed of 80.0 km/h. Her mass is 55.0 kg. What are (a) the magnitude and (b) the angle (relative to vertical) of the net force of the officer on the car seat? (Hint: Consider both horizontal and vertical forces.)

A circular-motion addict of mass 80 kg rides a Ferris wheel around in a vertical circle of radius 10 m at a constant speed of 6.1 m/s. (a) What is the period of the motion? What is the magnitude of the normal force on the addict from the seat when both go through (b) the highest point of the circular path and ( c) the lowest point?

A roller-coaster car has a mass of 1200 kg when fully loaded with passengers. As the car passes over the top of a circular hill of radius 18 m, its speed is not changing. At the top of the hill, what are the (a) magnitude FN and (b) direction (up or down) of the normal force on the car from the track if the car's speed is V = 11 m/s? What are (c) FN and (d) the direction if v = 14 m/s?

In Fig. 6-39, a car is driven at constant speed over a circular hill and then into a circular valley with the same radius. At the top of the hill, the normal force on the driver from the car seat is O. The driver's mass is 70.0 kg. What is the magnitude of the normal force on the driver from the seat when the car passes through the bottom of the valley?

An 85.0 kg passenger is made to move along a circular path ofradius r = 3.50 m in uniform circular motion. (a) Figure 6-40a is a plot of the required magnitude F of the net centripetal force for a range of possible values of the passenger's speed v. What is the plot's slope at v = 8.30 mls? (b) Figure 6- 40b is a plot of F for a range of possible values of T, the period of the motion. What is the plot's slope at T = 2.50 s?

An airplane is flying in a horizontal circle at a speed of 480 kmlh (Fig. 6-41). If its wings are tilted at angle () = 40 to the horizontal, what is the radius of the circle in which the plane is flying? Assume that the required force is provided entirely by an "aerodynamic lift" that is perpendicular to the wing surface.

An amusement park ride consists of a car moving in a vertical circle on the end of a rigid boom of negligible mass. The combined weight of the car and riders is 5.0 kN, and the circle's radius is 10 m.At the top of the circle, what are the (a) magnitude Fa and (b) direction (up or down) of the force on the car from the boom if the car's speed is v = 5.0 mls? What are (c) Fa and (d) the direction if v = 12 m/s?

An old streetcar rounds a flat corner of radius 9.1 m, at 16 kmlh. What angle with the vertical will be made by the loosely hanging hand straps?

In designing circular rides for amusement parks, mechanical engineers must consider how small variations in certain parameters can alter the net force on a passenger. Consider a passenger of mass 111 riding around a horizontal circle of radius l' at speed v. What is the variation dFin the net force magnitude for (a) a variation dr in the radius with v held constant, (b) a variation dv in the speed with l' held constant, and (c) a variation dT in the period with l' held constant?

A bolt is threaded onto one end of a thin horizontal rod, and the rod is then rotated horizontally about its other end. An engineer monitors the motion by flashing a strobe lamp onto the rod and bolt, adjusting the strobe rate until the bolt appears to be in the same eight places during each full rotation of the rod (Fig. 6-42). The strobe rate is 2000 flashes per second; the bolt has mass 30 g and is at radius 3.5 cm. What is the magnitude of the force on the bolt from the rod?

A banked circular highway curve is designed for traffic moving at 60 kmlh. The radius of the curve is 200 m. Traffic is moving along the highway at 40 kmlh on a rainy day. What is the minimum coefficient of PROB LEMS 135 Bolt Strobed positions Fig. 6-42 Problem 55. friction between tires and road that will allow cars to take the turn without sliding off the road? (Assume the cars do not have negative lift.)

A puck of mass 111 = 1.50 kg slides in a circle of radius l' = 20.0 cm on a frictionless table while attached to a hanging cylinder of mass M = 2.50 kg by means of a cord that extends through a hole in the table (Fig. 6-43). What speed keeps the cylinder at rest

Brake or tum? Figure 6-44 depicts an overhead view of a car's path as the car travels toward a wall. Assume that the driver begins to brake the car when the distance to the wall is d = 107 m, and take the car's mass as 111 = 1400 kg, its initial speed as Vo = 35 mis, and the coefficient of static friction as ILs = 0.50. Assume that the car's weight is distributed evenly on the four wheels, even during braking. (a) What magnitude of static friction is needed (between tires and road) to stop the car just as it reaches the wall? (b) What is the maximum possible static friction is, max? (c) If the Car Fig. 6- 43 Problem 57. Fig. 6-44 Problem 58. coefficient of kinetic friction between the (sliding) tires and the road is ILk = 0.40, at what speed will the car hit the wall? To avoid the crash, a driver could elect to turn the car so that it just barely misses the wall, as shown in the figure. (d) What magnitude of frictional force would be required to keep the car in a circular path of radius d and at the given speed vo, so that the car moves in a quarter circle and then parallel to the wall? (e) Is the required force less thanfs.max so that a circular path is possible?

In Fig. 6-45, a 1.34 kg ball is connected by means of two massless strings, each of length L = 1.70 m, to a vertical, rotating rod. The strings are tied to the rod with separation d = 1.70 m and are taut. The tension in the upper string is 35 N. What are the (a) tension in the lower string, (b) magnitude of the net force Fnet on the ball, and (c) speed of the ball? (d) What is the direction of Fnet?

In Fig. 6-46, a box of ant aunts (total mass m1 = 1.65 kg) and a box of ant uncles (total mass m2 = 3.30 kg) slide down an inclined plane while attached by a massless rod parallel to the plane. The angle of incline is 8 = 30.0. The coefficient of kinetic friction between the aunt box and the incline is f.Ll = 0.226; that between the uncle box and the incline is Jk2 = 0.113. Compute (a) the tension in the rod and (b) the magnitude of the common acceleration Fig. 6-46 Problem 60. of the two boxes. (c) How would the answers to (a) and (b) change if the uncles trailed the aunts?

A block of mass m( = 4.0 kg is put on top of a block of mass mb = 5.0 kg. To cause the top block to slip on the bottom one while the bottom one is held fixed, a horizontal force of at least 12 N must be applied to the top block. The assembly of blocks is now placed on a horiFig. 6-47 Problem 61. zontal, frictionless table (Fig. 6-47). Find the magnitudes of (a) the maximum horizontal force F that can be applied to the lower block so that the blocks will move together and (b) the resulting acceleration of the blocks.

A 5.00 kg stone is rubbed across the horizontal ceiling of a cave passageway (Fig. 6-48). If the coefficient of kinetic friction is 0.65 and the force applied to the stone is angled at 8 = 70.0, what must the magnitUde of the force be for the stone to move at constant velocity?

In Fig. 6-49, a 49 kg rock climber is climbing a "chimney." The coefficient of static friction between her shoes and the rock is 1.2; between her back and the rock is 0.80. She has reducedher push against the rock until her back and her shoes are on the verge of slipping. (a) Draw a free-body diagram of her. (b) What is the magnitude of her push against the rock? (c) What fraction of her weight is supported by the frictional force on her shoes?

A high-speed railway car goes around a flat, horizontal circle of radius 470 m at a constant speed. The magnitudes of the horizontal and vertical components of the force of the car on a 51.0 kg passenger are 210 Nand 500 N,respectively. (a) What is the magnitude of the net force (of all the forces) on the passenger? (b) What is the speed of the car?

Continuation of Problems 8 and 37. Another explanation is that the stones move only when the water dumped on the playa during a storm freezes into a large, thin sheet of ice. The stones are trapped in place in the ice. Then, as air flows across the ice during a wind, the air-drag forces on the ice and stones move them both, with the stones gouging out the trails. The magnitude of the air-drag force on this horizontal "ice sail" is given by Dice = 4CicepAicev2, where Cice is the drag coefficient (2.0 X 10- 3), P is the air density (1.21 kg/m3), Aice is the horizontal area of the ice, and v is the wind speed along the ice. Assume the following: The ice sheet measures 400 m by 500 m by 4.0 mm and has a coefficient of kinetic friction of 0.10 with the ground and a density of 917 kg/m3. Also assume that 100 stones identical to the one in Problem 8 are trapped in the ice. To maintain the motion of the sheet, what are the required wind speeds (a) near the sheet and (b) at a height of 10 m? (c) Are these reasonable values for high-speed winds in a storm?

In Fig. 6-50, block 1 of mass m1 = 2.0 kg and block 2 of mass m2 = 3.0 kg are connected by a string of negligible mass and are initially held in place. Block 2 is on a frictionless surface tilted at 8 = 30. The coefficient of kinetic friction between block 1 and the horizontal surface is 0.25. The pulley has negligible mass and friction. Once they are released, the blocks move. What then is the tension in the string?

In Fig. 6-51, a crate slides down an inclined right-angled trough. The coefficient of kinetic friction between the crate and the trough is f.Lk' What is the acceleration of the crate in terms of f.Lk> 8, andg?

If a car goes through a curve too fast, the car tends to slide out of the curve. For a banked curve with friction, a frictional force acts on a fast car to oppose the tendency to slide out of the curve; the force is directed down the bank (in the direction water would drain). Consider a circular curve of radius \(R=200 \mathrm{~m}\) and bank angle \(\theta\), where the coefficient of static friction between tires and pavement is \(\mu_{s}\). A car (without negative lift) is driven around the curve as shown in Fig. 6-11. (a) Find an expression for the car speed \(v_{\max }\) that puts the car on the verge of sliding out. (b) On the same graph, plot \(v_{\max }\) versus angle \(\theta\), for the range \(0^{\circ}\) to \(50^{\circ}\), first for \(\mu_{s}=0.60\) (dry pavement) and then for \(\mu_{s}=0.050\) (wet or icy pavement). In kilometers per hour, evaluate \(v_{\max }\) for a bank angle of \(\theta=10^{\circ}\) and for (c) \(\mu_{s}=0.60\) and (d) \(\mu_{s}=0.050\). (Now you can see why accidents occur in highway curves when icy conditions are not obvious to drivers, who tend to drive at normal speeds.)

A student, crazed by final exams, uses a force P of magnitude 80 N and angle 0 = 70 to push a 5.0 kg block across the ceiling of his room (Fig. 6-52). If the coefficient of kinetic friction between the block and the ceiling is 0.40, what is the magnitude of the block's acceleration

Figure 6-53 shows a conical pendulum, in which the bob (the small object at the lower end of the cord) moves in a horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass of 0.040 kg, the string has length L = 0.90 m and negligible mass, and the bob follows a circular path of circumference 0.94 m. What are (a) the tension in the string and (b) the period of the motion?

An 8.00 kg block of steel is at rest on a horizontal table. The coefficient of static friction between the block and the table is 0.450. A force is to be applied to the block. To three significant figures, what is the magnitude of that applied force if it puts the block on the verge of sliding when the force is directed (a) horizontally, (b) upward at r Fig. 6-53 Problem 70. 60.0 from the horizontal, and (c) downward at 60.0 from the horizontal?

A box of canned goods slides down a ramp from street level into the basement of a grocery store with acceleration 0.75 mls2 directed down the ramp. The ramp makes an angle of 40 with the horizontal. What is the coefficient of kinetic friction between the box and the ramp?

In Fig. 6-54, the coefficient of kinetic friction between the block and inclined plane is 0.20, and angle Ois 60. What are the (a) magnitude a and (b) direction (up or down the plane) of the block's acceleration if the block is sliding down the plane? What are (c) a and (d) the direction if the block is sent sliding up the plane?

A 110 g hockey puck sent sliding over ice is stopped in 15 m by the frictional force on it from the ice. (a) If its initial speed is 6.0 mis, what is the magnitude of the frictional force? (b) What is the coefficient of friction between the puck and the ice?

A locomotive accelerates a 25-car train along a level track. Every car has a mass of 5.0 X 104 kg and is subject to a frictional force f = 250v, where the speed v is in meters per second and the force f is in newtons. At the instant when the speed of the train is 30 km/h, the magnitude of its acceleration is 0.20 m/s2 (a) What is the tension in the coupling between the first car and the locomotive? (b) If this tension is equal to the maximum force the locomotive can exert on the train, what is the steepest grade up which the locomotive can pull the train at 30 km/h?

A house is built on the top of a hill with a nearby slope at angle 0= 45 (Fig. 6-55). An engineering study indicates that the slope angle should be reduced because the top layers of soil along the slope might slip past the lower layers. If the coefficient of static friction between two such layers is 0.5, what is the least angle through which the present slope should be reduced to prevent slippage?

What is the terminal speed of a 6.00 kg spherical ball that has a radius of 3.00 cm and a drag coefficient of 1.60? The density of the air through which the ball falls is 1.20 kg/m3.

A student wants to determine the coefficients of static friction and kinetic friction between a box and a plank. She places the box on the plank and gradually raises one end of the plank. When the angle of inclination with the horizontal reaches 30, the box starts to slip, and it then slides 2.5 m down the plank in 4.0 s at constant acceleration. What are (a) the coefficient of static friction and (b) the coefficient of kinetic friction between the box and the plank?

Block A in Fig. 6-56 has mass m A = 4.0 kg, and block B has mass Inn = 2.0 kg. The coefficient of kinetic friction between block B and the horizontal plane is ILk = 0.50. The inclined plane is frictionless and at angle B = 30. The pulley serves only to change the direction of the cord connecting the blocks. The cord has negligible mass. Find (a) the tension in the cord and (b) the magnitude of the acceleration of the blocks

Calculate the magnitude of the drag force on a missile 53 cm in diameter cruising at 250 mls at low altitude, where the density of air is 1.2 kg/m3. Assume C = 0.75.

A bicyclist travels in a circle of radius 25.0 m at a constant speed of 9.00 mls. The bicycle-rider mass is 85.0 kg. Calculate the magnitudes of (a) the force of friction on the bicycle from the road and (b) the net force on the bicycle from the road.

In Fig. 6-57, a stuntman drives a car (without negative lift) over the top of a hill, the cross section of which can be approximated by a circle of radius R = 250 m. What is the greatest speed at which he can drive without the car leaving the road at the top of the hill?

You must push a crate across a floor to a docking bay. The crate weighs 165 N. The coefficient of static friction between crate and floor is 0.510, and the coefficient of kinetic friction is 0.32. Your force on the crate is directed horizontally. (a) What magnitude of your push puts the crate on the verge of sliding? (b) With what magnitude must you then push to keep the crate moving at a constant velocity? (c) If, instead, you then push with the same magnitude as the answer to (a), what is the magnitude of the crate's acceleration?

In Fig. 6-58, force F is applied to a crate of mass 111 on a floor where the coefficient of static friction between crate and floor is ILs' Angle B is initially 0 but is gradually increased so that the force vector rotates clockwise in the figure. During the rotation, the magnitude F of the force is continuously adjusted so that the crate is always on the verge of sliding. For ILs = 0.70, (a) plot the ratio Fll11g versus Band (b) determine the angle Binf at which the ratio approaches an infinite value. (c) Does lubricating the floor increase or decrease Binf, or is the value unchanged? (d) What is Binf for ILs = 0.60?

In the early afternoon, a car is parked on a street that runs down a steep hill, at an angle of 35.0 relative to the horizontal. Just then the coefficient of static friction between the tires and the street surface is 0.725. Later, after nightfall, a sleet storm hits the area, and the coefficient decreases due to both the ice and a chemical change in the road surface because of the temperature decrease. By what percentage must the coefficient decrease if the car is to be in danger of sliding down the street?

A sling-thrower puts a stone (0.250 kg) in the sling's pouch (0.010 kg) and then begins to make the stone and pouch move in a vertical circle of radius 0.650 m. The cord between the pouch and the person's hand has negligible mass and will break when the tension in the cord is 33.0 N or more. Suppose the slingthrower could gradually increase the speed of the stone. (a) Will the breaking occur at the lowest point of the circle or at the highest point? (b) At what speed of the stone will that breaking occur?

A car weighing 10.7 kN and traveling at 13.4 mls without negative lift attempts to round an unbanked curve with a radius of 61.0 m. (a) What magnitude of the frictional force on the tires is required to keep the car on its circular path? (b) If the coefficient of static friction between the tires and the road is 0.350, is the attempt at taking the curve successful?

In Fig. 6-59, block 1 of mass 1711 = 2.0 kg and block 2 of mass 1712 = 1.0 kg are connected by a string of negligible mass. Block 2 is pushed by force F of magnitude 20 N and angle B = 35. The coefficient of kinetic friction between each block and the horizontal surface is 0.20. What is the tension in the string

A filing cabinet weighing 556 N rests on the floor. The coefficient of static friction between it and the floor is 0.68, and the coefficient of kinetic friction is 0.56. In four different attempts to move it, it is pushed with horizontal forces of magnitudes (a) 222 N, (b) 334 N, (c) 445 N, and (d) 556 N. For each attempt, calculate the magnitude of the frictional force on it from the floor. (The cabinet is initially at rest.) (e) In which of the attempts does the cabinet move?

In Fig. 6-60, a block weighing 22 N is held at rest against a vertical wall by a horizontal force F of magnitude 60 N. The coefficient of static friction between the wall and the block is 0.55, and the coefficient of kinetic friction between them is 0.38. In six experiments, a second force P is applied to the block and directed parallel to the wall with these magnitudes and directions: (a) 34 N, up, (b) 12 N, Fig. 6-60 up, (c) 48 N, up, (d) 62 N, up, (e) 10 N, down, and (f) Problem 90. 18 N, down. In each experiment, what is the magnitude of the frictional force on the block? In which does the block move (g) up the wall and (h) down the wall? (i) In which is the frictional force directed down the wall

A block slides with constant velocity down an inclined plane that has slope angle O. The block is then projected up the same plane with an initial speed Vo. (a) How far up the plane will it move before coming to rest? (b) After the block comes to rest, will it slide down the plane again? Give an argument to back your answer

A circular curve of highway is designed for traffic moving at 60 km/h. Assume the traffic consists of cars without negative lift. (a) If the radius of the curve is 150 m, what is the correct angle of banking of the road? (b) If the curve were not banked, what would be the minimum coefficient of friction between tires and road that would keep traffic from skidding out of the turn when traveling at 60 km/h?

A 1.5 kg box is initially at rest on a horizontal surface when at t = o a horizontal force F = (1.8t)i N (with t in seconds) is applied to the box. The acceleration of the box as a function of time t is given by a = 0 for 0 :S t:S 2.8 s and a = (l.2t - 2.4)i m/s2 for t> 2.8 s. (a) What is the coefficient of static friction between the box and the surface? (b) What is the coefficient of kinetic friction between the box and the suliace?

A child weighing 140 N sits at rest at the top of a playground slide that makes an angle of 25 with the horizontal. The child keeps from sliding by holding onto the sides of the slide. After letting go of the sides, the child has a constant acceleration of 0.86 m/s2 (down the slide, of course). (a) What is the coefficient of kinetic friction between the child and the slide? (b) What maximum and minimum values for the coefficient of static friction between the child and the slide are consistent with the information given here?

In Fig. 6-61 a fastidious worker pushes directly alon] the handle of a mop with a force F. The handle is at an angle 0 with the vertical, and f.Ls and f.Lk are the coefficients of static and kinetic friction between the head of the mop and the floor. Ignore the mass of the handle and assume that all the mop's mass 111 is in its head. (a) If the mop head moves along the floor with a constant velocity, then what is F? (b) Show that if 0 is less than a certain value 00, then F (still directed along the handle) is unable to move the mop head. Find 00,

A child places a picnic basket on the outer rim of a merry-goround that has a radius of 4.6 m and revolves once every 30 s. (a) What is the speed of a point on that rim? (b) What is the lowest value of the coefficient of static friction between basket and merrygo-round that allows the basket to stay on the ride?

A warehouse worker exerts a constant horizontal force of magnitude 85 N on a 40 kg box that is initially at rest on the horizontal floor of the warehouse. When the box has moved a distance of 1.4 m, its speed is 1.0 m/s. What is the coefficient of kinetic friction between the box and the floor?

In Fig. 6-62, a 5.0 kg block is sent sliding up a plane inclined at 0= 37 while a horizontal force F of magnitude 50 N acts on it. The coefficient of kinetic friction between block and plane is 0.30. What are the (a) magnitude and (b) direction (up or down the plane) of the block's acceleration? The block's initial speed is 4.0 m/s. (c) How far up the plane does the block go? (d) When it reaches its highest point, does it remain at rest or slide back down the plane?