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Non-Uniform Circular Motion

Non-Uniform Circular Motion. Remember that if the velocity is not constant there is also a component of the acceleration parallel to the direction of the velocity. (Assuming the velocity only has a tangential component.). Tangential force – changes speed. Radial force – changes direction.

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Non-Uniform Circular Motion

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  1. Non-Uniform Circular Motion Remember that if the velocity is not constant there is also a component of the acceleration parallel to the direction of the velocity. (Assuming the velocity only has a tangential component.) Tangential force – changes speed. Radial force – changes direction. Motion in Accelerated (Non-Inertial) Reference Frames Newton’s laws are only valid for inertial reference frames! • In accelerated reference frames objects seem to accelerate in the presence of a force, where there is no force to cause this acceleration. • This force is called a fictitious force, since it does not exist. • A fictitious force has no action-reaction partner. • Example: As car goes around a curve, the passenger slides towards the door on the outside of the curve. • The person seems to be pushed towards the door due to a Centrifugal Force. • The centrifugal force is a fictitious force. • The car is accelerating, but the passenger is continuing to move in a straight line path that is tangential to the curve. • The door exerts a force on the passenger to keep them inside the car.

  2. Motion in the Presence of Resistive Forces. Resistive forces are forces that impede the motion of an object, with the most common being drag. Resistive forces usually depend on some characteristic of the motion, such as the speed of the object. One example of a resistive force is air drag, which is approximated by the expression shown below. This particular expression can only be used to approximate air drag for an object at high speeds. Notice that this resistive force depends on the square of the velocity and the cross-sectional area of the object. R – Resistive Force – Air Drag [N] D – Drag Coefficient [Dimensionless] r – Density of air [kg/m3] A – Cross-Sectional Area [m2] v – Speed of the object [m/s] Depends on the shape of the object.D  0.5 for a sphere. • Example: An object is dropped from rest at a very high altitude. • As the object falls what happens? • The speed of the object increases which increases the drag. • The resistive force will eventually reach the weight of the object, how does the motion change when this occurs? • The weight of the object will be equal to the drag. – No Acceleration. • What can you say about the motion now? • The object is now falling at a constant speed called Terminal speed. Resistive forces can never cause an object to start moving in the opposite direction.

  3. Example: A cubic box with sides 20 cm long and a mass of 20 kg is dropped from a high altitude. The density of air is 1.29 kg/m3 and the box has a drag coefficient of 0.75. (Assume gravitational acceleration is the near Earth value.) What is the acceleration of the box when the resistive force is equal to 60% of the weight of the box? What is the terminal speed of the box? What percentage of the weight would the resistive force have to be to cause an acceleration of 7.5 m/s2? R a) y 0 W b) c) The net acceleration of the box is in the negative y-direction.

  4. Mechanics Energy and Momentum

  5. CH 5: Kinetic Energy, work and Power

  6. What is energy? Energy is an abstract quantity used to describe our ability to do something. E.g.: Describes motion and changes to motion, the likelihood that chemical reactions take place, possibility of electron transitions to generate light, etc. We are more familiar with types of energy or noticing changes due to energy transfer What are some of the main classification we use for energy? What are some types of energy transfer? Flow of energy between two points • Heat • Conduction • Convection • Radiation • Mechanical energy • Electrical Energy • Internal Energy • Nuclear Energy Methods of transferring energy. We will only be discussing mechanical energy at this time. We will be using the concept of energy to develop new techniques for looking at dynamic systems and their interactions with their environment. We will begin by defining what we mean by system and environment. • System – Small part of the universe we are examining. • Single particle or object • Collection of particles or objects • Region of space Environment – Everything not in the system.

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