In the figure, horizontal force F 1 Of magnitude 10 N is applied

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1 1 A driver's Manual states that a driver traveling at 48 km/h and desiring to stop as quickly as possible travels 10 m before his foot reaches the brake. He travels an additional 21 m before coming to rest. What coefficient of friction is assumed in these calculations? In the figure, horizontal force F 1 of magnitude 10 N is applied to a box on a floor, but the box does not slide. Then, as the magnitude of vertical force F 2 is increased from zero. (a) Does the magnitude of the frictional force f s on the box increase, decrease or stay the same? (b) Does the magnitude of the normal force F N on the box from the floor increase, decrease or stay the same? (c) Does the maximum value fs,mas of the magnitude of the static frictional force on the box increase, decrease or stay the same? (d) Does the box eventually slide? 2 A 35 kg crate is at rest on the floor. A man attempts to push it across the floor by applying a 110-N force horizontally. (a) Take the coefficient of static friction between the crate and the floor to be 0.37 and show that the crate does not move. (b) What is the maximum magnitude of the static frictional force under the circumstances? (c) Does the crate move? (d) Suppose next, that a second worker pulls directly upward on the crate to help out. What is the least pull she can exert that will allow the first worker's 110 N push to move the crate? (e) If, instead, the second worker pulls horizontally to help out, what is the least pull she can exert to get the crate moving? (a) same (b) increases (c) increases (d) no 3 (a) 110 N (b) 126 N (c) no (d) 45.9 N (e) 16.9 N In the figure, horizontal force F 1 Of magnitude 10 N is applied to a box on a floor, but the box does not slide. Then, as the magnitude of vertically applied force F 2 is increased from zero but before the box begins to slide. (a). Does the magnitude of the frictional force on the box increase, decrease, or stay the same? (b) Does the magnitude of the normal force on the box from the floor increase, decrease, or stay the same? (c) Does the maximum value F s,max of the static frictional force on the box increase, decrease, or stay the same? 5 A 10-kg box rests on a horizontal floor. The coefficient of static friction is μ s = 0.40 and the coefficient of kinetic friction is μ k = Determine the force of friction, F fr, acting on the box if a horizontal external applied force F A is exerted on it of magnitude: (a) 0 (b) 10 N (c) 20 N (d) 38 N (e) 40 N. (a) reactionay force just beore block moves the friction force doesn t change (b) decreases (c) decreases 6 (a) 0 (b) 10 (c) 20 (d) 38 (e) 29.4 Can a coefficient of friction exceed 1.0? Yes

2 7 A man is pulling on his 20 kg dog with a force of 70.0 N directed at an angle of above the horizontal. (a) Draw a free body diagram of the forces on the dog. (b) Find the x component of this force. (c) Find the y component of this force. (d) Find the normal force on the dog. 11 A baseball player with mass m = 79 kg, sliding into second base, is retarded by a frictional force of magnitude 470 N. What is the coefficient of kinetic friction μ k between the player and the ground? 8 (a) Drawing (b) 60.6 N (c) 35.0 N (d) N The man pulls with a force of 25.0 N at an angle of to the horizontal. (a) Find the x component of this force. (b) Find the y component of this force 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 km/h, in how short a distance can the train be stopped at constant acceleration without causing the crates to slide over the floor? 36 m 9 (a) 23.8 N (b) 7.73 N Determine the frictional force of the air on a body of mass 0.25 kg falling freely with an acceleration of 9.2 m/s A flatbed truck is carrying a 2500-kg crate of heavy machinery. The coefficient of static friction between the crate and the bed of the truck is What is the maximum rate at which the driver can decelerate when coming to a stop and still avoid having the crate slide on the truckbed? 0.15 N 7.35 m/s 2 10 A horizontal force F of 12 N pushes a block weighing 5 N against a vertical wall (see the figure). The coefficient of static friction between the wall and the block is 0.6, and the coefficient of kinetic friction is 0.4. Assume that the block is not moving initially (a) Will the block start moving? (b) What is the force exerted on the block by the wall? 14 A coffee cup on the dashboard of a car slides forward on the dash when the driver decelerates from 40 km/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? µ =.32 (a) No (b) 12 N to the left, and 5 N up

3 15 A 49-kg rock climber is climbing a "chimney" between two rock slabs. The static coefficient of friction between her shoes and the rock is 1.2; between her back and the rock it is She has reduced her push against the rock until her back and her shoes are on the verge of slipping. (a) What is her push against the rock? (b) What fraction of her weight is supported by the frictional force on her shoes? 18 A wooden crate with a mass of 100 kg rests on a flat, wooden floor. An effort is made to start the crate sliding by pulling on a rope that makes an angle of 30 0 with the horizontal, as shown in the diagram. If the coefficient of static friction between the crate and the floor is 0.4, what is the minimum rope tension that will start a sliding motion? F T = 368 N 16 (a) N (b).599 A 50-kg box that is resting on a level floor must be moved. The coefficient of static friction between the box and the floor is 0.6. One method to move the box is to push down on the box at an angle q with the horizontal. Another method is to Pull up on the box at an angle q with the horizontal. (a) Calculate the force necessary to move the box by each method if q = 30 0 and compare these results with those for θ = 0 0. (b) Explain why one method is better than the other. 19 In the figure, the box is stationary and the angle θ between the horizontal and force F is increased somewhat. (a) Does F x increase, decrease or remain the same? (b) Does F f increase, decrease or remain the same? (c) Does F N increase, decrease or remain the same? (d) Does F f,max increase, decrease or remain the same? (e) If, instead, the box is sliding and θ is increased, does the magnitude of the frictional force on the box increase, decrease, or remain the same? (a) F = 294 at 0 0 F = 254 at 30 0 upward F = 520 at 30 0 downward (b) The better method is to pull up on the box since theta lessens the normal force and the static friction (a) decreases (b) decreases stays the same if not moving (c) increases (d) increases (e) increases 17 A 3.5 kg block is pushed along a horizontal floor by a force F = 15 N that makes an angle θ = 40 degrees with the horizontal, as shown in the figure to the left. The coefficient of kinetic friction between the block and the floor is (a) Calculate the frictional force exerted on the block (b) Calculate the acceleration of the block. (a) 11.0 N (b) 0.14 m/s 2

4 20 In the figure, 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 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, up (c) 48 N, up (d) 62 N, up, (e) 10 N, down (f ) 18 N, down In each experiment, what is the magnitude of the frictional force on the block? (g) In which does the block move up the wall? (h) In which does the block move down the wall? (i) In which is the frictional force directed down the wall? 22 A gardener pushes a 10 kg lawn mower by applying a force of 150 N along the handle. (a) Draw a free body diagram (b) Find the horizontal component of this force when the lawn mower handle makes an angle of (c) Find the horizontal component of this force when the lawn mower handle makes an angle of 45 0 (d) Find the horizontal component of this force when the lawn mower handle makes an angle of 60 o with the horizontal. (a) picture (b) 130 N (c) 106 N (d) 75.0 N 23 Joe pushes on the handle of a 10-kg lawn spreader. The handle makes a 45 0 angle with the horizontal. Joe wishes to accelerate the spreader from rest to 1.39 m/s in 1.5 s. (a) Draw a free body diagram. (b) What is the normal force on the spreader? (c) What force must Joe apply to the handle? Neglect friction. (class) 21 (a) 12 N (b) 10 N (c) 26 N (d) 23 N (e) 32 N (f) 23 N (g) d (h) f (i) a, c, d A student, crazed by final exams, uses a force P of magnitude 80 N and angle θ = 70 0 to push a 5.0 kg block across the ceiling of his room as in the figure. If the coefficient of kinetic friction between the block and the ceiling is 0.40, what is the magnitude of the block's acceleration? 24 (a) picture (b) 107.2N (c) 13 N Wendy pushes a 15 kg lawn spreader across a lawn by applying a force of 95 N along the handle that makes an angle of with the horizontal. (a) Draw a free body diagram. (b) What are the horizontal and vertical components of the force? (c) What is the normal force on the spreader? (d) The handle is lowered so it makes an angle of with the horizontal. Now what are the horizontal and vertical components of the force? (e) What is the new normal force on the spreader? 3.4 m/s 2 (a) Picture (b) horizontal = 48 N, vertical = 82 N (c) Picture (d) horizontal = 82 N, vertical = 48 N (e) Picture

5 25 A student pulls a 125 kg box across a floor by means of a rope making an angle of 60 0 with the horizontal. He applies a 60 N force on the rope (a) What is the component of the force in the horizontal direction? (b) What is the component of the force in the vertical direction? (c) What is the normal force on the box? (d) If the angle of the rope is reduced to 30 0 and the same force applied, what will now be the magnitudes of the horizontal, vertical components and the normal force on the box? 28 A 5.0 kg block on an inclined plane is acted upon by a horizontal force of 50 N shown in the figure to the left. The coefficient of friction between block and plane is (a) What is the acceleration of the block if it is moved up the plane? (b) How far up the plane will the block go if it has an initial upward speed of 4.0 m/s? (c) What happens to the block after it reaches the highest point? (a) H= 30 N (b) V= 52 N (c) N (d) H comp. 52 N V comp 30 N F normal 26 In the figure, a woman pulls a loaded sled of mass m = 75 kg along a horizontal surface at constant velocity. The coefficient of kinetic friction μ k between the runners and the snow is 0.10, and the angle θ is (a) What is the magnitude of the force on the sled from the rope? (b) If the woman increases her pull on the rope, so that T is greater than 91 N, is the magnitude μ k of the frictional force greater than, less than, or the same as in (a)? 29 (a) m/s 2 (b) 3.83 m (c) stops A 5-kg block is initially at rest on an inclined plane, as shown in the diagram. A force F = 20 N is applied to the block in a direction parallel to the plane. Determine the acceleration of the block if the coefficient of kinetic friction is q k = (a) 91 N (b) Less 27 A block is on an incline whose angle can be varied. The angle is gradually increased from 0 0. At 30 0, the block starts to slide down the incline. It slides 3 m in 2 s. Calculate the coefficients of static and kinetic friction between the block and incline m/s 2 μ s = μ k = 0.401

6 30 A block with a mass of 2 kg is pushed by a horizontal force, F = 20 N, as shown in the diagram. Assume that the coefficient of sliding friction is q k = (a) Find the acceleration of the block if q = (b) What is the acceleration if q = 70 0? 33 The figure 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 10 7 kg, the dip angle q of the bedding plane is 24 0, and the coefficient of static friction between block and plane is (a) Show that the block will not slide. (b) Water seeps into the joint and expands upon freezing, exerting on the block a force F parallel to AA'. What minimum value of force magnitude F will trigger a slide down the plane? (a) 3.59 m/s 2 upward (b).689 m/s 2 down 31 In the figure, a block of mass m is held stationary on a ramp by the frictional force on it from the ramp. A force F. directed down the ramp instead of upward as drawn, is then applied to the block and gradually increased in magnitude from zero. During the increase, what happens to the direction and magnitude of the frictional force on the block? 34 (a) (b) 3.0 x 10 7 N In the early afternoon, a car is parked on a street that runs down a steep hill, at an angle of relative to the horizontal. Just then the coefficient of static friction between the tires and the street surface is 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? At first fs is directed up the ramp and its magnitude increases from mg sin θ until it reaches fs { sub max. Thereafter the force is one of kinetic friction directed up the ramp and has magnitude fk, a constant value less than fs max. 3.4% 32 In the picture, a slide-loving pig slides down a certain 35 0 slide in twice the time it would take to slide down a frictionless 35 0 slide. What is the coefficient of kinetic friction between the pig and the slide? 0.53

7 35 Boxes are unloaded from delivery trucks at ground level and allowed to slide down a wooden ramp to a basement. A strobe photograph of a box sliding down the 2.5 m high ramp is represented in the figure. Assume that the box is released from rest at the top of the ramp at t = 0 and slides with constant acceleration. The flashes on the strobe camera record the position of the box at 0.5 s intervals. (a) What is the magnitude of the acceleration of the box? (b) If the box weighs 240 N, what is the magnitude of the force of kinetic friction on the box from the ramp? 37 A small block of mass m is given an initial speed v 0 up a ramp inclined at angle q from the horizontal. It travels a distance d up the ramp and comes to rest. (a) Determine a formula for the coefficient of kinetic friction between the block and ramp. (b) What can you say about the value of the coefficient of static friction? Book Solution 38 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. How large must the coefficient of static friction be for the basket to stay on the merry-go-round? (a) 2.2 m/s 2 (b) 53 N In the figure, a 5.0 kg block is sent sliding up a plane inclined at θ = 37 0 while a horizontal force F of magnitude 10 N acts on it. The coefficient of kinetic friction between block and plane is What is the (a) What is the magnitude of the block's acceleration? (b) What is the 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? 39 A banked circular curve of highway is designed for traffic moving at 60 km/h. The radius of the curve is 200 m. Traffic is moving along the highway at 40 km/h on a stormy day. What is the minimum coefficient of friction between tires and road that will allow cars to negotiate the turn without sliding off the road? 0.08 (a) m/s (b) down (c) 1.14 m; (d) it stays there or goes down the ramp

8 40 Even some seasoned roller-costster riders blanch at the thought of riding the Rotor, which is essentially a large, hollow cylinder that is rotated rapidly around its central axis (see the figure). Before the ride begins, a rider enters the cylinder through a door on the side and stands on a floor, up against a canvas-covered wall. The door is closed, and as the cylinder begins to turn, the rider, wall, and floor move in unison. When the rider's speed reaches some predetermined value, the floor abruptly and alarmingly falls away. The rider does not fall with it but instead is pinned to the wall while the cylinder rotates, as if an unseen (and somewhat unfriendly) agent is pressing the body to the wall. Later, the floor is eased back to the rider's feet, the cylinder slows, and the rider sinks a few centimeters to regain footing on the floor. (Some riders consider all this to be fun.) Suppose that the coefficient of static friction A, between the rider's clothing and the canvas is 0.40 and that the cylinder's radius R is 2.1 m. (a) What minimum speed v must the cylinder and rider have if the rider is not to fall when the floor drops? (b) If the rider's mass is 49 kg, what is the magnitude of the centripetal force on her? 42 Curved portions of highways are always banked (tilted) to prevent cars from sliding off tift highway. When a highway is dry, the frictional force between the tires and the road surface may be enough to prevent sliding. When the highway is wet, however, the frictional force may be negligible, and banking is then essential. The figure represents a car of mass m as it moves at a constant speed v of 20 m/s around a banked circular track of radius R = 190 m. (It is a normal car, rather than a race car, which means any vertical force from the passing air is negligible.) If the frictional force from the track is negligible, what bank angle θ prevents sliding? 12 0 (a) 7.17 m/s (b) 1200 N 43 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? 41 A Rotor initially moves at the minimum required speed for the rider not to fall. Then its speed is increased in steps. (a) Does the magnitude of f x increase, decrease, or remain the same? (b) Does the magnitude of F N increase, decrease, or remain the same? (c) Does the value of f s,max increase, decrease, or remain the same? 44 (a) 11 0 (b) 0.19 If a curve with a radius of 70 m is perfectly banked for a car traveling 60 km/h, what must be the coefficient of static friction for a car not to skid when traveling at 90 km/h?.375 (a) same (b) increases (c) increases

9 45 A car at the Indianapolis-500 accelerates uniformly from the pit area, going from rest to 320 km/h in a semicircular arc with a radius of 200 m. (a) Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant acceleration. (b) If the curve were flat, what would the coefficient of static friction have to be between the tires and the roadbed to provide this acceleration with no slipping or skidding? 49 In 1987, as a Halloween stunt, two sky divers passed a pumpkin back and forth between them while they were in free fall just west of Chicago. The stunt was great fun until the last sky diver with the pumpkin opened his parachute. The pumpkin broke free from his grip, plummeted about 0.5 km, ripped through the roof of a house, slammed into the kitchen floor, and splattered all over the newly remodeled kitchen. From the sky diver's viewpoint and from the pumpkin's viewpoint, why did the sky diver lose control of the pumpkin? 46 a t = a r = 19,76 µ = A curve of radius 60 m is banked for a design speed of 100 km/h. If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely make the curve? On opening the parachute produced a large sudden upward force on the diver due to increased air drag and the drag force slowed the diver suddenly. To keep the pumpkin in his grip he had to slow it just as much but this required more force than he could exert. From the diver s viewpoint the apparent weight of the pumpkin suddenly and surprisingly increased and the pumpkin was ripped from his hands. From the pumpkin s viewpoint the sudden upward force on the diver ripped him away from the pumpkin. 47 (a) (b) µ = tan theta (c) v min =8.57 m/s v max = 16.6 m/s A curve of radius 60 m is banked for a design speed of 100 km/h. If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely make the curve? 50 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 other side (see the figure). 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.) My solution 48 A small twig slides down the roof of a house pitched at an angle of 30 0 with respect to the horizontal. The twig starts from rest at a point 1.5 m from the edge and strikes the ground 2 m from the house, which has its roof-line 4 m above the ground. What is the coefficient of kinetic friction between the twig and the roof? (Assume zero air resistance during the fall.) 2.8 x 10 2 N

10 51 In the figure, a crate slides down an inclined right-angled trough. The coefficient of kinetic friction between the crate and the trough is q k. What is the acceleration of the crate in terms of q k, q, and g? 54 A raindrop with radius R = 1.5 mm falls from a cloud that is at height h = 1200 m above the ground. The drag coefficient C for the drop is Assume that the drop is spherical throughout its fall. The density of water q w is 1000 kg/m 3, and the density of air q a is 1.2 kg/m 3. (a) What is the terminal speed of the drop? (b) What would be the drop's speed just before impact if there were no drag force? 52 A small mass m is set on the surface of a sphere, see the figure. If the coefficient of static friction is q s = 0.60, at what angle q would the mass start sliding? 55 Near the ground, is the speed of large raindrops greater than, less than, or the same as the speed of small raindrops, assuming that all raindrops are spherical and have the same drag coefficient? greater 56 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. θ = Solution in book wrong 53 In an earthquake, the ground is found to accelerate with a maximum value of a max. (a) If an object is going to "hold its place" on the ground, show that it must have a coefficient of static friction with respect to the ground of at least q s = a max /g. (b) Numerically, the famous Loma Prieta Earthquake that stopped the 1989 World Series produced maximum ground accelerations of up to 4.0 m/s 2 in the San Francisco Bay Area. Would a chair start to slide on your linoleum floor if the coefficient of static friction were 0.25? 5.84 or.171 (a) μ s = a max /g. =.25 (b) will slide

11 57 Assume the equation 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 (assume the pilot s mass is 70 kg). (a) Making a reasonable guess of the pilot's mass and using the appropriate v t value from the table, estimate the magnitudes of the drag force on the pilot + seat. (b) Making a reasonable guess of the pilot's mass and using the appropriate v t value from the table, estimate the magnitudes of 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 magnitude of the drag force on a missile 53 cm in diameter cruising at 250 m/s at low altitude, where the density of air is 1.2 kg/m 3. Assume C = kn the following questions: (a) What is the acceleration of a falling sky-diver (mass 60.0 kg including parachute) when the upward force of air resistance is equal to one-fourth of her weight? (b) After popping open her parachute, the diver descends leisurely to the ground at constant speed. What now is the force of air resistance on her and her parachute? (a) 6,35 m/s 2 (b) 588 N (a) 2 x 10 4 N (b) 18 g 58 From the data in the table, deduce the diameter of the 16 lb shot if C = 0.49 and the air density is 1.2 kg/m m 59 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/m m/s