Lecture_9 - THE WORK OF A FORCE, THE PRINCIPLE OF WORK AND...

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THE WORK OF A FORCE, THE PRINCIPLE OF WORK AND ENERGY & SYSTEMS OF PARTICLES Today ` s Objectives : Students will be able to: 1. Calculate the work of a force. 2. Apply the principle of work and energy to a particle or system of particles. In-Class Activities : Reading Quiz Applications Work of A Force Principle of Work And Energy Concept Quiz Group Problem Solving Attention Quiz
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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) 2 1 s t s F ds ! " 2 1 s t s F ds ! " # 2 1 s n s F ds ! " 2 1 s n s F ds ! " #
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APPLICATIONS A roller coaster makes use of gravitational forces to assist the cars in reaching high speeds in the l valleys z 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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APPLICATIONS (continued) Crash barrels are often used along roadways for crash protection. The barrels absorb the car ` s kinetic energy by deforming. If we know the velocity of an oncoming car and the amount of energy that can be absorbed by each barrel, how can we design a crash cushion?
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WORK AND ENERGY 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 a t = v (dv/ds) into F t = ma t , 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 of a force .
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WORK OF A FORCE (Section 14.1) 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 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 F is a function of position (a common case) this becomes = s 2 s 1 F cos θ ds U 1-2 If both F and are constant (F = F c ), this equation further simplifies to U 1-2 = F c cos ( s 2 - s 1 )
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OF A WEIGHT The work done by the gravitational force acting on a particle (or weight of an object ) can be calculated by using The work of a weight is the product of the magnitude of the particle ` s weight and its vertical displacement. If
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This note was uploaded on 02/27/2012 for the course DYNAMICS 440:222 taught by Professor Pengsong during the Spring '11 term at Rutgers.

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Lecture_9 - THE WORK OF A FORCE, THE PRINCIPLE OF WORK AND...

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