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Giancoli, Chapter 5: Using Newton's Laws: Friction, Circular Motion, Drag Forces

by: Lucille Olivia

Giancoli, Chapter 5: Using Newton's Laws: Friction, Circular Motion, Drag Forces PHYSICS 7A

Marketplace > University of California Berkeley > Physics 2 > PHYSICS 7A > Giancoli Chapter 5 Using Newton s Laws Friction Circular Motion Drag Forces
Lucille Olivia

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About this Document

These notes cover both kinetic and static friction forces, as well as the two components of acceleration (both tangential and radial) involved in uniform circular motion. Also included are examples...
Physics for Scientists and Engineers
Michael Deweese
Class Notes
Physics, Berkeley, drag forces, Friction, kinetic friction, static friction, Circular motion, uniform circular motion
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This 2 page Class Notes was uploaded by Lucille Olivia on Thursday February 18, 2016. The Class Notes belongs to PHYSICS 7A at University of California Berkeley taught by Michael Deweese in Spring 2016. Since its upload, it has received 26 views. For similar materials see Physics for Scientists and Engineers in Physics 2 at University of California Berkeley.


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Date Created: 02/18/16
Last Updated on 22nd February 2016 Giancoli: Chapter 5 chapter 5 5.1 Applications of Newton's Laws Involving Friction Using Newton’s Laws: Kinetic friction acts opposite to the direction of velocity, and is approximately proportional to the Friction, Circular normal force between the two surfaces according a constant???????? as shown in the following formula: Motion, Drag Forces ???????????? = ???????????? ???? class Static friction acts in a direction parallel to the two surfaces that are touching, even when they are Physics 7A not moving past one another. Once the maximum force of static friction is exceeded, kinetic friction Spring 2016 takes over and the objects begin moving. UC Berkeley Prof. M. Deweese ???????????? = ???????????? ???? Remember: In problems with a slope/inclined plane, the normal force is always perpendicular to the contents 5.1 Applications of slope/plane. Gravity is always vertically downward toward the center of the earth. Newton’s Laws Involving Friction 5.2 Uniform Circular Motion - Kinematics ￿ Moving in a circle at a constant speed ???? entails uniform circular motion for an object. In this type of 5.2 Uniform Circular Motion–Kinematics movement, velocity’s magnitude remains constant, but its direction changes every instant. This constantly changing direction of velocity equates to a constantly changing acceleration, which is ￿ defined as follows: 5.3 Dynamics of ????????⃗ Uniform Circular ????⃗ = ???????? Motion ￿ The object will also have a centripetal or radial acceleration directed towards the center of the circle and quantified as: 5.4 Highway Curves: ????2 Banked and Unbanked ???????? = ￿ ???? Another way of describing circular motion involves the number of revolutions per second, or fre- 5.5 Nonuniform Circular Motion quency ????, and the time required for one revolution, or period ????. ￿ 1 1 5.6 Velocity-Dependent ???????????????????????? = ???????????????????????????????????? = ???? = ???? Forces: Drag and This translates to Terminal Velocity 2???????? ???? = ???? formulas because in one revolution, the object will have traveled one circumference. ???? ????????= ???? ???? ???? ￿ 5.3 Dynamics of Uniform Circular Motion ????????????= ???? ???? ???? ￿ ????????⃗ Circular motion with a constant velocity has centripetal accelera????iand has a net force ????⃗= ????????♥ ￿ ????2 ????2 ∑???? ???? = ???????? ???? = ???? ????????= ???? ♥ ???? ￿ ???? = ♥1 This force is always directed toward the center of the circle. centrifugal force, or force heading away ???? from the center of the circle, does not exist in uniform circular motion. ￿ ???? = 2????????♥ ???? 5.4 Highway Curves: Banked and Unbanked 2 ￿ ∑???? =???????????? = ???????? ???? ♥ ￿ When an object (such as a car) travels a circular path along some surface (such as a highway ????2 curve), the force of friction acts toward the center of the circle. ????????????????????(????) = ???? ???? ♥ ￿ For this reason, banking a curve reduces the chance of skidding by allowing the normal force to act 2 2 perpendicular to the road, with a component toward the center of the circle. Because the car (or ???? = √ ????????????????+ ???????? ♥ ￿ other object) is not wholly reliant on friction, this is safer. ???? ???? = −????????♥ In fact, there is a certain speed at which the car does not rely on friction at all. This is when the ￿ horizontal component of the normal force (parallel to flat ground) is just equal to the force required ???? = ???????? ♥ ???? ???? to give a vehicle its centripetal acceleration, or when: ￿ 2 ???? ????????????(????) = ???? ???? ???? ???? The banking angle of a road, ????, is chosen so that this condition holds for a particular speed, called the ”design speed.” 5.5 Nonuniform Circular Motion ???? and ???? are always perpendicular to each other. Thus, the magnitude of ????⃗ at any given moment ???????????? ???? is ???? = √ ????2 + ????2 ???????????? ???? The velocity at any point is always tangent to the path. The acceleration can be written as a vec- tor sum of two components: the tangential component ????????????= ????????/????????, and the radial (centripetal) 2 component ???? ???? = ???? /????. 5.6 Velocity Dependent Forces: Drag and Terminal Velocity Whilefrictionactsindependentofanobject’sspeed, otherresistiveforcesdodependontheobject’s velocity. One such example is drag force, or the resistance of a liquid or gas to an object moving through that fluid. Drag force is directly proportional to the magnitude of the velocity, and contains a negative sign since it opposes the motion. ???? ???? = −???????? Within a problem, once velocity has increased to the point that the magnitude of the resistance force equals that of the gravitational force, the object has reached terminal velocity and will continue to fall at this constant velocity until it hits the ground. The terminal velocity can be calculated as ???????? ????????= ????


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