# Energy Absorbed by a Brake

The energy absorbed by a brake depends upon the type of motion of the moving body. The motion of a body may be either pure translation or pure rotation or a combination of both translation and rotation.

Energy Absorbed by a Brake

The energy absorbed by a brake depends upon the type of motion of the moving body. The motion of a body may be either pure translation or pure rotation or a combination of both translation and rotation. The energy corresponding to these motions is kinetic energy. Let us consider these motions as follows :

1.     When the motion of the body is pure translation. Consider a body of mass (m) moving with a velocity v1 m / s. Let its velocity is reduced to v2 m / s by applying the brake. Therefore, the change in kinetic energy of the translating body or kinetic energy of translation,

E1 = (1/2) m [(v1)- (v2)2]

This energy must be absorbed by the brake. If the moving body is stopped after applying the brakes, then v2 = 0, and

E1 = (1/2) m (v1)2

2. When the motion of the body is pure rotation. Consider a body of mass moment of inertia I (about a given axis) is rotating about that axis with an angular velocity ω1 rad / s. Let its angular velocity is reduced to ω2 rad / s after applying the brake. Therefore, the change in

kinetic energy of the rotating body or kinetic energy of rotation,

E2 = (1/2) I [(ω1)2 - (ω2)2]

This energy must be absorbed by the brake. If the rotating body is stopped after applying the brakes, then ω2 = 0, and

E1 = (1/2) I (ω1)2

3. When the motion of the body is a combination of translation and rotation. Consider a body having both linear and angular motions, e.g. in the locomotive driving wheels and wheels of a moving car. In such cases, the total kinetic energy of the body is equal to the sum of the kinetic energies of translation and rotation.

Total kinetic energy to be absorbed by the brake,

E = E1 + E2

Sometimes, the brake has to absorb the potential energy given up by objects being lowered by hoists, elevators etc. Consider a body of mass m is being lowered from a height h1 to h2 by applying the brake. Therefore the change in potential energy,

E3 = m.g (h1 – h2)

Tags : Mechanical - Design of Transmission Systems - Design of Cam Clutches and Brakes
Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail