MCE222_LN_Sec_14-1 - PRINCIPLE OF WORK AND ENERGY (Sections...

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PRINCIPLE OF WORK AND ENERGY (Sections 14.1-14.3) Today’s Objectives : Students will be able to: a) Calculate the work of a force. b) Apply the principle of work and energy to a particle or system of particles.
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READING QUIZ 1. What is the work done by the force F ? A) F s B) –F s C) Zero D) None of the above. s s 1 s 2 F 2. If a particle is moved from 1 to 2, the work done on the particle by the force, F R will be A) B) C) D) ds F s s t Σ 2 1 ds F s s t Σ 2 1 ds F s s n Σ 2 1 ds F s s n Σ 2 1
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APPLICATIONS A roller coaster makes use of gravitational forces to assist the cars in reaching high speeds in the “valleys” of the track. How can we design the track (e.g., the height, h, and the radius of curvature, ρ ) to control the forces experienced by the passengers?
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WORK OF A FORCE 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 product of force and displacement components acting in the same direction . So, if the angle between the force and displacement vector is θ , the increment of work dU done by the force is dU = F ds cos θ By using the definition of the dot product and integrating, the total work can be written as r 2 r 1 U 1-2 = F • d r
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WORK OF A FORCE (continued) 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 . If
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MCE222_LN_Sec_14-1 - PRINCIPLE OF WORK AND ENERGY (Sections...

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