Work done on an object as it moves from position r1 to ri is equal to the change in its kinetic energy.
A force that is perpendicular to the path of motion will not do any work.
Work of a force: As long as the particle is displaced in the same direction as the force applied to the particle. In general, U1-2 = ∫∑F ds
If a force that opposes motion (such as friction) then it does negative work. A force in the same direction as motion will do positive work.
Work of weight: U1-2 = -mg(y2 - y1) The work is independent of the path of motion. Positive when the weight moves downward.
Work of a linear spring: U1-2 = -.5 k (S2 ^2 - S1 ^2)
- U1-2 is the sum of the work done from position 1 to position 2
- m is the mass of object
- g is the gravitational acceleration (9.81 m/s^2 or 32.2 ft/s^2)
- k is the springs constant
- S is the stretched/compressed length of the spring
Principle of Work and Energy
T1 + U1-2 = T2
T1 is the initial kinetic and T2 is the final kinetic energy
T = .5 m v^2
- m is the mass
- v is the velocity
Conservative Forces
If the work of a force is independent of the path, only depending on the initial and final position then it is a conservative force. Example: weight and spring
Conservation of Energy
∑T1 + ∑V1 = ∑T2 + ∑V2
- T = .5 m v^2
- V = Vweight + Vspring
- Vweight = mgy
- Vspring = .5 k s^2
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