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# lecture+notes+9 - 14:440:222 Dynamics(Lecture Note#9...

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14:440:222 Dynamics (Lecture Note #9) Instructor: Prof. Peng Song Rutgers University Today’s Lecture • Work and energy

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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? Applications 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? Applications (cont’d)
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. Work and Energy A force does work on a particle when the particle undergoes a displacement along the line of action of the force.

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