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Lecture_9

# 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 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 ! " #
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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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?
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 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
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 θ are constant (F = F c ), this equation further simplifies to U 1-2 = F c cos θ ( s 2 - s 1 )

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WORK OF A WEIGHT The work done by the gravitational force acting on a particle (or weight of an object ) can be calculated by using
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