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of the peaks will be broken off, also requiring a force to maintain motion. much of the friction is actually due to attractive forces between molecules making up the two objects, so that even perfectly smooth surfaces are not friction - free. such adhesive forces also depend on the substances the surfaces are made of, ... | openstax_college_physics_2e-web_7zesafu | [
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wet concrete 0. 7 0. 5 wood on wood 0. 5 0. 3 waxed wood on wet snow 0. 14 0. 1 metal on wood 0. 5 0. 3 steel on steel ( dry ) 0. 6 0. 3 steel on steel ( oiled ) 0. 05 0. 03 teflon on steel 0. 04 0. 04 bone lubricated by synovial fluid 0. 016 0. 015 shoes on wood 0. 9 0. 7 shoes on ice 0. 1 0. 05 ice on ice 0. 1 0. 03 ... | openstax_college_physics_2e-web_7zesafu | [
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0. 02 table 5. 1 coefficients of static and kinetic friction the equations given earlier include the dependence of friction on materials and the normal force. the direction of friction is always opposite that of motion, parallel to the surface between objects, and perpendicular to the normal force. for example, if the ... | openstax_college_physics_2e-web_7zesafu | [
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drivers to note, especially after a light rain shower. why? 200 5 • further applications of newton's laws : friction, drag, and elasticity access for free at openstax. org and the thighbone ( the femur ). the hip is a ball ( at the end of the femur ) and socket ( part of the pelvis ) joint. the ends of the bones in the... | openstax_college_physics_2e-web_7zesafu | [
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strategy the magnitude of kinetic friction was given in to be 45. 0 n. kinetic friction is related to the normal force as ; thus, the coefficient of kinetic friction can be found if we can find the normal force of the skier on a slope. the normal force is always perpendicular to the surface, and since there is no motio... | openstax_college_physics_2e-web_7zesafu | [
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5. 1 • friction 201 figure 5. 4 the motion of the skier and friction are parallel to the slope and so it is most convenient to project all forces onto a coordinate system where one axis is parallel to the slope and the other is perpendicular ( axes shown to left of skier ). ( the normal force ) is perpendicular to the ... | openstax_college_physics_2e-web_7zesafu | [
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out : solving for, we find that 5. 10 | openstax_college_physics_2e-web_7zesafu | [
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5. 11 202 5 • further applications of newton's laws : friction, drag, and elasticity access for free at openstax. org we have discussed that when an object rests on a horizontal surface, there is a normal force supporting it equal in magnitude to its weight. furthermore, simple friction is always proportional to the no... | openstax_college_physics_2e-web_7zesafu | [
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this chapter. the variation in shear stress is remarkable ( more than a factor of ) and difficult to predict theoretically, but shear stress is yielding a fundamental understanding of a large - scale phenomenon known since ancient times — friction. put a coin on a book and tilt it until the coin slides at a constant ve... | openstax_college_physics_2e-web_7zesafu | [
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5. 1 • friction 203 figure 5. 6 the tip of a probe is deformed sideways by frictional force as the probe is dragged across a surface. measurements of how the force varies for different materials are yielding fundamental insights into the atomic nature of friction. phet explorations forces and motion explore the forces ... | openstax_college_physics_2e-web_7zesafu | [
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5. 2 drag forces learning objectives by the end of this section, you will be able to : • express mathematically the drag force. • discuss the applications of drag force. • define terminal velocity. • determine the terminal velocity given mass. another interesting force in everyday life is the force of drag on an object... | openstax_college_physics_2e-web_7zesafu | [
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5. 13 204 5 • further applications of newton's laws : friction, drag, and elasticity access for free at openstax. org speed. as we shall see in a few pages on fluid dynamics, for small particles moving at low speeds in a fluid, the exponent is equal to 1. athletes as well as car designers seek to reduce the drag force ... | openstax_college_physics_2e-web_7zesafu | [
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. 14 5. 15 5. 2 • drag forces 205 object c airfoil 0. 05 toyota camry 0. 28 ford focus 0. 32 honda civic 0. 36 ferrari testarossa 0. 37 dodge ram pickup 0. 43 sphere 0. 45 hummer h2 suv 0. 64 skydiver ( feet first ) 0. 70 bicycle 0. 90 skydiver ( horizontal ) 1. 0 circular flat plate | openstax_college_physics_2e-web_7zesafu | [
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1. 12 table 5. 2 drag coefficient values typical values of drag coefficient. substantial research is under way in the sporting world to minimize drag. the dimples on golf balls are being redesigned as are the clothes that athletes wear. bicycle racers and some swimmers and runners wear full bodysuits. australian cathy ... | openstax_college_physics_2e-web_7zesafu | [
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zero net force means that there is no acceleration, as given by newton ’ s second law. at this point, the person ’ s velocity remains constant and we say that the person has reached his terminal velocity ( ). since is proportional to the speed, a heavier skydiver must go faster for to equal his weight. let ’ s see how ... | openstax_college_physics_2e-web_7zesafu | [
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versus mass. which of these relationships is more linear? what can you conclude from these graphs? | openstax_college_physics_2e-web_7zesafu | [
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5. 2 • drag forces 207 weight ). using the equation of drag force, we find. thus the terminal velocity can be written as solution all quantities are known except the person ’ s projected area. this is an adult ( 85 kg ) falling spread eagle. we can estimate the frontal area as using our equation for, we find that discu... | openstax_college_physics_2e-web_7zesafu | [
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very small, is going very slow, or is in a denser medium than air. then we find that the drag force is proportional just to the velocity. this relationship is given by stokes ’ law, which states that where is the radius of the object, is the viscosity of the fluid, and is the object ’ s velocity. good examples of this ... | openstax_college_physics_2e-web_7zesafu | [
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5. 25 208 5 • further applications of newton's laws : friction, drag, and elasticity access for free at openstax. org if we compare animals living on land with those in water, you can see how drag has influenced evolution. fishes, dolphins, and even massive whales are streamlined in shape to reduce drag forces. birds a... | openstax_college_physics_2e-web_7zesafu | [
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5. 3 elasticity : stress and strain learning objectives by the end of this section, you will be able to : • state hooke ’ s law. • explain hooke ’ s law using graphical representation between deformation and applied force. • discuss the three types of deformations such as changes in length, sideways shear and changes i... | openstax_college_physics_2e-web_7zesafu | [
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size, but with different masses, what do you think he should have observed? would this result be different if done on the moon? 5. 26 5. 27 | openstax_college_physics_2e-web_7zesafu | [
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5. 3 • elasticity : stress and strain 209 makes it clear that the deformation is proportional to the applied force. figure 5. 11 shows the hooke ’ s law relationship between the extension of a spring or of a human bone. for metals or springs, the straight line region in which hooke ’ s law pertains is much larger. bone... | openstax_college_physics_2e-web_7zesafu | [
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produces the three different deformations shown as shaded segments. the string on the left is thin nylon, the one in the middle is thicker nylon, and the one on hooke ’ s law where is the amount of deformation ( the change in length, for example ) produced by the force, and is a proportionality constant that depends on... | openstax_college_physics_2e-web_7zesafu | [
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5. 29 210 5 • further applications of newton's laws : friction, drag, and elasticity access for free at openstax. org the right is steel. we now consider three specific types of deformations : changes in length ( tension and compression ), sideways shear ( stress ), and changes in volume. all deformations are assumed t... | openstax_college_physics_2e-web_7zesafu | [
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##ness because they deform less for a given tension or compression. stretch yourself a little how would you go about measuring the proportionality constant of a rubber band? if a rubber band stretched 3 cm when a 100 - g mass was attached to it, then how much would it stretch if two similar rubber bands were attached t... | openstax_college_physics_2e-web_7zesafu | [
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2. 2 table 5. 3 elastic moduli1 young ’ s moduli are not listed for liquids and gases in table 5. 3 because they cannot be stretched or compressed in only one direction. note that there is an assumption that the object does not accelerate, so that there are actually two applied forces of magnitude acting in opposite di... | openstax_college_physics_2e-web_7zesafu | [
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body serve different structural functions and are prone to different stresses. thus the bone in the top of the femur is 5. 31 | openstax_college_physics_2e-web_7zesafu | [
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5. 3 • elasticity : stress and strain 213 arranged in thin sheets separated by marrow while in other places the bones can be cylindrical and filled with marrow or just solid. overweight people have a tendency toward bone damage due to sustained compressions in bone joints and tendons. another biological example of hook... | openstax_college_physics_2e-web_7zesafu | [
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of the heart. when the aortic valve shuts, the pressure in the arteries drops and the arterial walls relax to maintain the blood flow. when you feel your pulse, you are feeling exactly this — the elastic behavior of the arteries as the blood gushes through with each pump of the heart. if the arteries were rigid, you wo... | openstax_college_physics_2e-web_7zesafu | [
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5. 32 214 5 • further applications of newton's laws : friction, drag, and elasticity access for free at openstax. org solution all quantities except are known. note that the compression value for young ’ s modulus for bone must be used here. thus, discussion this small change in length seems reasonable, consistent with... | openstax_college_physics_2e-web_7zesafu | [
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strain the ratio of the change in length to length,, is defined as strain ( a unitless quantity ). in other words, 5. 38 5. 39 | openstax_college_physics_2e-web_7zesafu | [
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5. 3 • elasticity : stress and strain 215 where is the shear modulus ( see table 5. 3 ) and is the force applied perpendicular to and parallel to the cross - sectional area. again, to keep the object from accelerating, there are actually two equal and opposite forces applied across opposite faces, as illustrated in fig... | openstax_college_physics_2e-web_7zesafu | [
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need to move their shoulders back to maintain balance, thereby increasing the curvature in their spine and so increasing the shear component of the stress. an increased angle due to more curvature increases the shear forces along the plane. these higher shear forces increase the risk of back injury through ruptured dis... | openstax_college_physics_2e-web_7zesafu | [
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5. 40 216 5 • further applications of newton's laws : friction, drag, and elasticity access for free at openstax. org figure 5. 17 side view of a nail with a picture hung from it. the nail flexes very slightly ( shown much larger than actual ) because of the shearing effect of the supported weight. also shown is the up... | openstax_college_physics_2e-web_7zesafu | [
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packed close together in liquids and solids. to compress a gas, you must force its atoms and molecules closer together. to compress liquids and solids, you must actually compress their atoms and molecules, and very strong electromagnetic forces in them oppose this compression. 5. 41 5. 42 5. 43 5. 44 | openstax_college_physics_2e-web_7zesafu | [
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5. 3 • elasticity : stress and strain 217 figure 5. 18 an inward force on all surfaces compresses this cube. its change in volume is proportional to the force per unit area and its original volume, and is related to the compressibility of the substance. we can describe the compression or volume deformation of an object... | openstax_college_physics_2e-web_7zesafu | [
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km depth, where the force per unit area is. strategy equation is the correct physical relationship. all quantities in the equation except are known. solution solving for the unknown gives substituting known values with the value for the bulk modulus from table 5. 3, 5. 45 | openstax_college_physics_2e-web_7zesafu | [
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5. 46 218 5 • further applications of newton's laws : friction, drag, and elasticity access for free at openstax. org discussion although measurable, this is not a significant decrease in volume considering that the force per unit area is about 500 atmospheres ( 1 million pounds per square foot ). liquids and solids ar... | openstax_college_physics_2e-web_7zesafu | [
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5. 3 • elasticity : stress and strain 219 glossary deformation change in shape due to the application of force drag force, found to be proportional to the square of the speed of the object ; mathematically where is the drag coefficient, is the area of the object facing the fluid, and is the density of the fluid frictio... | openstax_college_physics_2e-web_7zesafu | [
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( such as a baseball ) moving at a velocity in air, the drag force is given by where is the drag coefficient ( typical values are given in table 5. 2 ), is the area of the object facing the fluid, and is the fluid density. • for small objects ( such as a bacterium ) moving in a denser medium ( such as water ), the drag... | openstax_college_physics_2e-web_7zesafu | [
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5. 3 elasticity : stress and strain • hooke ’ s law is given by where is the amount of deformation ( the change in length ), is the applied force, and is a proportionality constant that depends on the shape and composition of the object and the direction of the force. the relationship between the deformation and the ap... | openstax_college_physics_2e-web_7zesafu | [
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5. 1 friction 1. define normal force. what is its relationship to friction when friction behaves simply? 2. the glue on a piece of tape can exert forces. can these forces be a type of simple friction? explain, considering especially that tape can stick to vertical walls and even to ceilings. 3. when you learn to drive,... | openstax_college_physics_2e-web_7zesafu | [
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5. 2 drag forces 5. athletes such as swimmers and bicyclists wear body suits in competition. formulate a list of pros and cons of such suits. 6. two expressions were used for the drag force experienced by a moving object in a liquid. one depended upon the speed, while the other was proportional to the square of the spe... | openstax_college_physics_2e-web_7zesafu | [
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5. 3 elasticity : stress and strain 9. the elastic properties of the arteries are essential for blood flow. explain the importance of this in terms of the characteristics of the flow of blood ( pulsating or continuous ). 10. what are you feeling when you feel your pulse? measure your pulse rate for 10 s and for 1 min. ... | openstax_college_physics_2e-web_7zesafu | [
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5. 1 friction 1. a physics major is cooking breakfast when he notices that the frictional force between his steel spatula and his teflon frying pan is only 0. 200 n. knowing the coefficient of kinetic friction between the two materials, he quickly calculates the normal force. what is it? 2. ( a ) when rebuilding her ca... | openstax_college_physics_2e-web_7zesafu | [
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. 6. a team of eight dogs pulls a sled with waxed wood runners on wet snow ( mush! ). the dogs have average masses of 19. 0 kg, and the loaded sled with its rider has a mass of 210 kg. ( a ) calculate the magnitude of the acceleration starting from rest if each dog exerts an average force of 185 n backward on the snow.... | openstax_college_physics_2e-web_7zesafu | [
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snow boarder is going uphill. explicitly show how you follow the steps in problem - solving strategies. 11. ( a ) calculate the acceleration of a skier heading down a slope, assuming the coefficient of friction for waxed wood on wet snow. ( b ) find the angle of the slope down which this skier could coast at a constant... | openstax_college_physics_2e-web_7zesafu | [
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allowed to slip during the acceleration. ( ignore rolling. ) ( a ) on dry concrete. ( b ) on wet concrete. ( c ) on ice, assuming that, the same as for shoes on ice. 15. repeat exercise 5. 14 for a car with four - wheel drive. 16. a freight train consists of two engines and 45 cars with average masses of. ( a ) what fo... | openstax_college_physics_2e-web_7zesafu | [
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is maintained? 5 • problems & exercises 223 19. repeat exercise 5. 18 with the contestant pulling the block of ice with a rope over his shoulder at the same angle above the horizontal as shown in figure 5. 21 ( b ). figure 5. 21 which method of sliding a block of ice requires less force — ( a ) pushing or ( b ) pulling... | openstax_college_physics_2e-web_7zesafu | [
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5. 2 drag forces 20. the terminal velocity of a person falling in air depends upon the weight and the area of the person facing the fluid. find the terminal velocity ( in meters per second and kilometers per hour ) of an 80. 0 - kg skydiver falling in a headfirst position with a cross - section area facing the fluid of... | openstax_college_physics_2e-web_7zesafu | [
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drag ( b ) with air drag. take the size across of the drop to be 4 mm, the density to be, and the cross - section area facing the fluid to be. 26. using stokes ’ law, verify that the units for viscosity are kilograms per meter per second. 27. find the terminal velocity of a spherical bacterium ( diameter ) falling in w... | openstax_college_physics_2e-web_7zesafu | [
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5. 3 elasticity : stress and strain 29. during a circus act, one performer swings upside down hanging from a trapeze holding another, also upside - down, performer by the legs. if the upward force on the lower performer is three times her weight, how much do the bones ( the femurs ) in her upper legs stretch? you may a... | openstax_college_physics_2e-web_7zesafu | [
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( b ) does the answer seem to be consistent with what you have observed for nylon ropes? would it make sense if the rope were actually a bungee cord? 34. a 20. 0 - m tall hollow aluminum flagpole is equivalent in stiffness to a solid cylinder 4. 00 cm in diameter. a strong wind bends the pole much as a horizontal force... | openstax_college_physics_2e-web_7zesafu | [
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0. 850 mm in diameter and 1. 35 m long. 37. a vertebra is subjected to a shearing force of 500 n. find the shear deformation, taking the vertebra to be a cylinder 3. 00 cm high and 4. 00 cm in diameter. 38. a disk between vertebrae in the spine is subjected to a shearing force of 600 n. find its shear deformation, taki... | openstax_college_physics_2e-web_7zesafu | [
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do you think the bottle will survive? 42. ( a ) when water freezes, its volume increases by 9. 05 % ( that is, ). what force per unit area is water capable of exerting on a container when it freezes? ( it is acceptable to use the bulk modulus of water in this problem. ) ( b ) is it surprising that such forces can fract... | openstax_college_physics_2e-web_7zesafu | [
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radius? ( b ) based on experimental data, an equation that fits the data is suggested for radius of a bead, r, which may not be correct :, where k is a constant with appropriate units and t is the time it takes for a bead to reach a determined distance. is this equation consistent with your answer from part a? explain ... | openstax_college_physics_2e-web_7zesafu | [
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6. 6 satellites and kepler ’ s laws : an argument for simplicity many motions, such as the arc of a bird ’ s flight or earth ’ s path around the sun, are curved. recall that newton ’ s first law tells us that motion is along a straight line at constant speed unless there is a net external force. we will therefore study... | openstax_college_physics_2e-web_7zesafu | [
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6. 1 rotation angle and angular velocity learning objectives by the end of this section, you will be able to : • define arc length, rotation angle, radius of curvature and angular velocity. • calculate the angular velocity of a car wheel spin. in kinematics, we studied motion along a straight line and introduced such c... | openstax_college_physics_2e-web_7zesafu | [
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6. 1 228 6 • uniform circular motion and gravitation access for free at openstax. org the arc length is the distance traveled along a circular path as shown in figure 6. 3 note that is the radius of curvature of the circular path. we know that for one complete revolution, the arc length is the circumference of a circle... | openstax_college_physics_2e-web_7zesafu | [
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6. 1 • rotation angle and angular velocity 229 angular velocity how fast is an object rotating? we define angular velocity as the rate of change of an angle. in symbols, this is where an angular rotation takes place in a time. the greater the rotation angle in a given amount of time, the greater the angular velocity. t... | openstax_college_physics_2e-web_7zesafu | [
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a car tire spin? calculate the angular velocity of a 0. 300 m radius car tire when the car travels at ( about ). see 6. 6 6. 7 6. 8 | openstax_college_physics_2e-web_7zesafu | [
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6. 9 230 6 • uniform circular motion and gravitation access for free at openstax. org figure 6. 5. strategy because the linear speed of the tire rim is the same as the speed of the car, we have the radius of the tire is given to be knowing and, we can use the second relationship in to calculate the angular velocity. so... | openstax_college_physics_2e-web_7zesafu | [
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to calculate the linear speed at this point. identify other circular motions and measure their angular velocities. 6. 1 • rotation angle and angular velocity 231 | openstax_college_physics_2e-web_7zesafu | [
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6. 2 centripetal acceleration learning objectives by the end of this section, you will be able to : • establish the expression for centripetal acceleration. • explain the centrifuge. we know from kinematics that acceleration is a change in velocity, either in its magnitude or in its direction, or both. in uniform circu... | openstax_college_physics_2e-web_7zesafu | [
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##l acceleration is toward the center of curvature, but what is its magnitude? note that the triangle formed by the velocity vectors and the one formed by the radii and are similar. both the triangles abc and pqr are isosceles triangles ( two equal sides ). the two equal sides of the velocity vector triangle are the sp... | openstax_college_physics_2e-web_7zesafu | [
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6. 13 232 6 • uniform circular motion and gravitation access for free at openstax. org then we divide this by, yielding finally, noting that and that, the linear or tangential speed, we see that the magnitude of the centripetal acceleration is which is the acceleration of an object in a circle of radius at a speed. so,... | openstax_college_physics_2e-web_7zesafu | [
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been used to test the tolerance of astronauts to the effects of accelerations larger than that of earth ’ s gravity. example 6. 2 how does the centripetal acceleration of a car around a curve compare with that due to gravity? what is the magnitude of the centripetal acceleration of a car following a curve of radius 500... | openstax_college_physics_2e-web_7zesafu | [
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6. 2 • centripetal acceleration 233. thus, and is noticeable especially if you were not wearing a seat belt. figure 6. 8 ( a ) the car following a circular path at constant speed is accelerated perpendicular to its velocity, as shown. the magnitude of this centripetal acceleration is found in example 6. 2. ( b ) a part... | openstax_college_physics_2e-web_7zesafu | [
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involved greatly decrease the time needed to cause the sedimentation of blood cells or other materials. of course, a net external force is needed to cause any acceleration, just as newton proposed in his second law of motion. so a net external force is needed to cause a centripetal acceleration. in centripetal force, w... | openstax_college_physics_2e-web_7zesafu | [
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6. 3 centripetal force learning objectives by the end of this section, you will be able to : • calculate coefficient of friction on a car tire. • calculate ideal speed and angle of a car on a turn. any force or combination of forces can cause a centripetal or radial acceleration. just a few examples are the tension in ... | openstax_college_physics_2e-web_7zesafu | [
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6. 3 • centripetal force 235 you may use whichever expression for centripetal force is more convenient. centripetal force is always perpendicular to the path and pointing to the center of curvature, because is perpendicular to the velocity and pointing to the center of curvature. note that if you solve the first expres... | openstax_college_physics_2e-web_7zesafu | [
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6. 26 236 6 • uniform circular motion and gravitation access for free at openstax. org the car from slipping, and because it is the only horizontal force acting on the car, the friction is the centripetal force in this case. we know that the maximum static friction ( at which the tires roll but do not slip ) is, where ... | openstax_college_physics_2e-web_7zesafu | [
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6. 3 • centripetal force 237 figure 6. 10 this car on level ground is moving away and turning to the left. the centripetal force causing the car to turn in a circular path is due to friction between the tires and the road. a minimum coefficient of friction is needed, or the car will move in a larger - radius curve and ... | openstax_college_physics_2e-web_7zesafu | [
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the crucial force and it is horizontal, we use a coordinate system with vertical and horizontal axes. only the normal force has a horizontal component, and so this must equal the centripetal force — that is, because the car does not leave the surface of the road, the net vertical force must be zero, meaning that the ve... | openstax_college_physics_2e-web_7zesafu | [
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6. 34 238 6 • uniform circular motion and gravitation access for free at openstax. org taking the inverse tangent gives this expression can be understood by considering how depends on and. a large will be obtained for a large and a small. that is, roads must be steeply banked for high speeds and sharp curves. friction ... | openstax_college_physics_2e-web_7zesafu | [
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6. 3 • centripetal force 239 discussion this is just about 165 km / h, consistent with a very steeply banked and rather sharp curve. tire friction enables a vehicle to take the curve at significantly higher speeds. calculations similar to those in the preceding examples can be performed for a host of interesting situat... | openstax_college_physics_2e-web_7zesafu | [
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6. 4 fictitious forces and non - inertial frames : the coriolis force learning objectives by the end of this section, you will be able to : • discuss the inertial frame of reference. • discuss the non - inertial frame of reference. • describe the effects of the coriolis force. what do taking off in a jet airplane, turn... | openstax_college_physics_2e-web_7zesafu | [
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frame of reference. ( b ) in the earth ’ s frame of reference, the driver moves in a straight line, obeying newton ’ s first law, and the car moves to the right. there is no real force to the left on the driver relative to earth. there is a real force to the right on the car to make it turn. we can reconcile these poin... | openstax_college_physics_2e-web_7zesafu | [
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6. 13 ( a ) a rider on a merry - go - round feels as if he is being thrown off. this fictitious force is called the centrifugal force — it explains the rider ’ s motion in the rotating frame of reference. ( b ) in an inertial frame of reference and according to newton ’ s laws, it is his inertia that carries him off an... | openstax_college_physics_2e-web_7zesafu | [
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6. 4 • fictitious forces and non - inertial frames : the coriolis force 241 earlier in this chapter. viewed from the rotating frame of reference, the fictitious centrifugal force throws particles outward, hastening their sedimentation. the greater the angular velocity, the greater the centrifugal force. but what really... | openstax_college_physics_2e-web_7zesafu | [
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242 6 • uniform circular motion and gravitation access for free at openstax. org figure 6. 15 looking down on the counterclockwise rotation of a merry - go - round, we see that a ball slid straight toward the edge follows a path curved to the right. the person slides the ball toward point b, starting at point a. both p... | openstax_college_physics_2e-web_7zesafu | [
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, and tropical cyclones contain particularly low pressures. thus winds flow toward the center of a tropical cyclone or a low - pressure weather system at the surface. in the northern hemisphere, these inward winds are deflected to the right, as shown in the figure, producing a counterclockwise circulation at the surfac... | openstax_college_physics_2e-web_7zesafu | [
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6. 4 • fictitious forces and non - inertial frames : the coriolis force 243 figure 6. 16 ( a ) the counterclockwise rotation of this northern hemisphere hurricane is a major consequence of the coriolis force. ( credit : nasa ) ( b ) without the coriolis force, air would flow straight into a low - pressure zone, such as... | openstax_college_physics_2e-web_7zesafu | [
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6. 5 newton ’ s universal law of gravitation learning objectives by the end of this section, you will be able to : • explain earth ’ s gravitational force. • describe the gravitational effect of the moon on earth. • discuss weightlessness in space. • examine the cavendish experiment what do aching feet, a falling apple... | openstax_college_physics_2e-web_7zesafu | [
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sections — circles, ellipses, parabolas, and hyperbolas. this theoretical prediction was a major triumph — it had been known for some time that moons, planets, and comets follow such paths, but no one had been able to propose a mechanism that caused them to follow these paths and not others. other prominent scientists ... | openstax_college_physics_2e-web_7zesafu | [
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every other particle with a force along a line joining them. the force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. figure 6. 18 gravitational attraction is along a line joining the centers of mass of these two bodies. the magnitude of th... | openstax_college_physics_2e-web_7zesafu | [
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6. 5 • newton ’ s universal law of gravitation 245 in si units. note that the units of are such that a force in newtons is obtained from, when considering masses in kilograms and distance in meters. for example, two 1. 000 kg masses separated by 1. 000 m will experience a gravitational attraction of. this is an extraor... | openstax_college_physics_2e-web_7zesafu | [
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6. 45 take - home experiment take a marble, a ball, and a spoon and drop them from the same height. do they hit the floor at the same time? if you drop a piece of paper as well, does it behave like the other objects? explain your observations. 246 6 • uniform circular motion and gravitation access for free at openstax.... | openstax_college_physics_2e-web_7zesafu | [
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see that making connections attempts are still being made to understand the gravitational force. as we shall see in particle physics, modern physics is exploring the connections of gravity to other forces, space, and time. general relativity alters our view of gravitation, leading us to think of gravitation as bending ... | openstax_college_physics_2e-web_7zesafu | [
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6. 5 • newton ’ s universal law of gravitation 247 the centripetal acceleration is the direction of the acceleration is toward the center of the earth. discussion the centripetal acceleration of the moon found in ( b ) differs by less than 1 % from the acceleration due to earth ’ s gravity found in ( a ). this agreemen... | openstax_college_physics_2e-web_7zesafu | [
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earth ’ s surface, a high tide is created on the side of earth nearest to the moon, where the moon ’ s gravitational pull is strongest. why is there also a high tide on the opposite side of earth? the answer is that earth is pulled toward the moon more than the water on the far side, because earth is closer to the moon... | openstax_college_physics_2e-web_7zesafu | [
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6. 51 248 6 • uniform circular motion and gravitation access for free at openstax. org water on the far side. the distances and sizes are not to scale. for this simplified representation of the earth - moon system, there are two high and two low tides per day at any location, because earth rotates under the tidal bulge... | openstax_college_physics_2e-web_7zesafu | [
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gravitational force near black holes is the apparent gravitational field experienced by | openstax_college_physics_2e-web_7zesafu | [
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6. 5 • newton ’ s universal law of gravitation 249 astronauts orbiting earth. what is the effect of “ weightlessness ” upon an astronaut who is in orbit for months? or what about the effect of weightlessness upon plant growth? weightlessness doesn ’ t mean that an astronaut is not being acted upon by the gravitational ... | openstax_college_physics_2e-web_7zesafu | [
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diseases. experiments flown in space also have shown that some bacteria grow faster in microgravity than they do on earth. however, on a positive note, studies indicate that microbial antibiotic production can increase by a factor of two in space - grown cultures. one hopes to be able to understand these mechanisms so ... | openstax_college_physics_2e-web_7zesafu | [
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calculating the mass of earth from the relationship newton ’ s universal law of gravitation gives where is the mass of the object, is the mass of earth, and is the distance to the center of earth ( the distance between the centers of mass of the object and earth ). see figure 6. 18. the mass of the object cancels, leav... | openstax_college_physics_2e-web_7zesafu | [
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attraction between the two suspended spheres ( ) and the two on the stand ( ) by observing the amount of torsion ( twisting ) created in the fiber. distance between the masses can be varied to check the dependence of the force on distance. modern experiments of this type continue to explore gravity. 6. 52 6. 53 6. 54 6... | openstax_college_physics_2e-web_7zesafu | [
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6. 6 satellites and kepler ’ s laws : an argument for simplicity learning objectives by the end of this section, you will be able to : • state kepler ’ s laws of planetary motion. • derive the third kepler ’ s law for circular orbits. • discuss the ptolemaic model of the universe. examples of gravitational orbits aboun... | openstax_college_physics_2e-web_7zesafu | [
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astronomer johannes kepler ( 1571 – 1630 ), who devised them after careful study ( over some 20 years ) of a large amount of meticulously recorded observations of planetary motion done by tycho brahe ( 1546 – 1601 ). such careful collection and detailed recording of methods and data are hallmarks of good science. data ... | openstax_college_physics_2e-web_7zesafu | [
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descriptive equation only, giving no information as to the cause of the equality. 6. 55 | openstax_college_physics_2e-web_7zesafu | [
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