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**Unformatted text preview: **1 Chapter 7: Chapter 7: Energy of a System Introduction to Energy • The concept of energy is one of the most important topics in science and engineering • Every physical process that occurs in the Universe involves energy and energy transfers or transformations • The energy approach to describing motion is particularly useful when Newton’s Laws are difficult or impossible to use • An approach will involve changing from a particle model to a system model – This can be extended to biological organisms, technological systems and engineering situations 2 Systems • A system is a small portion of the Universe – We will ignore the details of the rest of the Universe • A critical skill is to identify the system • A valid system may – be a single object or particle – be a collection of objects or particles – be a region of space – vary in size and shape • A force applied to an object in empty space – System is the object – Its surface is the system boundary – The force is an influence on the system that acts across the system boundary – A force does no work on the object if the force does not move through a displacement – The work done by a force on a moving object is zero when the force applied is perpendicular to the displacement of its point of application • W = F Δ r cos θ Work done by a constant force , 90 , = = Δ = = W r F W θ θ r F W a a Δ = . • Work is a scalar quantity • The unit of work is a joule (J) – 1 joule = 1 Newton X 1 meter J = N ¡ m The work, W , done on a system by an agent exerting a constant force on the system = Force in the direction of the displacement X displacement 3 Work Is An Energy Transfer • This is important for a system approach to solving a problem • If the work is done on a system and it is positive, energy is transferred to the system • If the work done on the system is negative, energy is transferred from the system • If a system interacts with its environment, this interaction can be described as a transfer of energy across the system boundary – This will result in a change in the amount of energy stored in the system Scalar Product of Two Vectors • The scalar product of two vectors is written as A . B – It is also called the dot product • A . B = A B cos θ θ is the angle between A and B • The scalar product is commutative A . B = B . A • The scalar product obeys the distributive law of multiplication • A . (B + C) = A . B + A . C k ˆ j ˆ k ˆ i ˆ j ˆ i ˆ 1 k ˆ k ˆ j ˆ j ˆ i ˆ i ˆ = ⋅ = ⋅ = ⋅ = ⋅ = ⋅ = ⋅ z z y y x x z y x z y x B A B A B A B A k ˆ B j ˆ B i ˆ B B k ˆ A j ˆ A i ˆ A A + + = ⋅ + + = + + = 2 2 2 2 . A A A A A A z y x = + + = a a 4 Work Done by a Varying Force • Assume that during a very small displacement, Δ x , F is constant • For that displacement, W ~ F Δ x • For all of the intervals, f i x x x W F x ≈ Δ ∑ • Therefore, • The work done is equal to the area under the curve lim...

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