Conservation Of Energy

# Conservation Of Energy - Energy Conservation Problem...

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PCS211 – Physics II: Mechanics Click to edit Master subtitle style 5/24/10 Energy Conservation: Problem Solving Lecture 24 (Chapters 13-15) Dr. Marina Milner-Bolotin [email protected] Check Blackboard for course web site!

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PCS211 – Physics II: Mechanics 5/24/10 Part I: Lecture 24 – Energy Conservation Goals: To be able to derive and apply work-energy theorem. Learn how to use energy conservation in problem solving. Being able to combine energy and momentum conservation to solve problems. 22
PCS211 – Physics II: Mechanics 5/24/10 Another equation for working kinetics problems involving particles can be derived by integrating the equation of motion ( F = m a ) with respect to displacement . This principle is useful for solving problems that involve force, velocity , and displacement . It can also be used to explore the concept of power. By substituting at = v (dv/ds) into Ft = mat , the result is integrated to yield an equation known as the principle of work and energy . To use this principle, we must first understand how to calculate the work performed by a force. Work and Energy

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PCS211 – Physics II: Mechanics 5/24/10 A force does work on a particle when the particle undergoes a displacement along the line of action of the force. Work is defined as the dot product of force and displacement. The units of work is Joule (J). So, if the angle between the force and displacement vector is θ , the increment of work dW done by the force is Work and Force ds F s d F dW ) cos( θ = = = = = 2 1 2 1 ds F W ds F s d F dW ) cos( ) cos( By using the definition of the dot product and integrating, the total work can be written as:
PCS211 – Physics II: Mechanics 5/24/10 Work and Force (Continued) = 2 1 S S 2 1 ds s F W ) cos( ) ( θ If F is a function of position (a common case) this becomes: If both F and θ are constant ( F = FC ), this equation further simplifies to: s F s s F ds s F W C 1 2 C S S 2 1 2 1 = - = = ) cos( ) )( cos( ) cos( ) ( Work is positive if the force and the movement are in the same direction . If they are opposing , then the work is negative . If the force and the displacement directions are perpendicular, the work is zero.

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PCS211 – Physics II: Mechanics 5/24/10 66 Work - Summary Positive work: force acts in the direction of motion Zero work: force acts in the direction perpendicular to motion Negative work: force acts in the opposite direction to motion Work is a scalar quantity : it can be positive, negative or zero but it cannot have direction !
PCS211 – Physics II: Mechanics 5/24/10 77 Graphical Interpretation of Work Work can be represented as the area under the Fx(x) graph. Notice, Fx is the component of the force in the direction of object’s displacement. It is true for constant as well as the variable forces. = 2 1 2 1 ds F W ) cos( θ

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PCS211 – Physics II: Mechanics 5/24/10 The work done by the gravitational force acting on a particle (or weight of an object ) can be calculated by using: The work done by the gravitational force is the product of the magnitude of the particle’s weight and its vertical displacement.
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Conservation Of Energy - Energy Conservation Problem...

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