Mechanical Energy

Kinetic Energy, E k Kinetic energy is the energy of an object in motion. E k = ½ mv 2 Where E k is the kinetic energy measured in J m is the mass of the object measured in kg v is the velocity measured in m/s

Work-Energy Theorem When a force acts on an object, work is defined as the product of the effective force and the displacement of the object. Since work involves a transfer of energy, work is also defined as the difference in kinetic energy between two points in time. W = ∆E k = E kf - E ki

Gravitational potential energy An object also has energy due to its position above a reference point: E p = mgh Where E p is the gravitational potential energy in J m is the mass of the object in kg g is the gravitational acceleration in m/s 2 h is the height of the object in m

Conservation of Mechanical Energy Mechanical energy is the sum of both the potential and kinetic energy of an object. E m = E k + E p Regardless of its position, an object’s E m is constant, due to the law of conservation of energy.

Ch 17 Elastic Potential Energy

Hooke’s Law When a force is applied to a helical spring, the spring undergoes a deformation; it can be squeezed (compression), stretched (tension) or twisted (torsion). The deformation can result in a change in length of the spring. Hooke’s Law states that the deformation of an elastic object like a spring is proportional to the force(s) applied. F = k ∆x, where k is the spring constant in N/m

The energy stored in an elastic object can be calculated using: E pe = ½ k (∆x) 2 The work required to restore a spring to its original shape is found using: W = E pe