Question

Give examples of :

(a) two conservative forces, and (b) as many (but at least 3) non-conservative forces as you can think of. For each example of the conservative force, give the expression for the potential energy associated with the conservative force. For each example of a non-conservative force, give a situation where non-conservative force changes the total mechanical energy of a system.

Answer 1

Example of conservative forces:

1. Gravitational forces. Gravitation force between two particles of mass m1 and m2, separated by distance r is given by:

2. Force in a linear harmonic oscillator. The force in a harmonic oscillator is given by:

where k is the spring constant and x-x0 is the displacement from the equilibrium point x0.

Examples of Non-conservative forces:

1 Friction Force, which is given by the expression: F= μN

F= force of friction

μ = coefficient of friction

N = normal force

Friction creates thermal energy that dissipates, removing energy from the system. Furthermore, even if the thermal energy is retained or captured, it cannot be fully converted back to work, so it is lost or not recoverable in that sense as well. In this way the total mechanical energy is not conserved.

2. Air resistance force

After a baseball player hits the baseball, the ball moves through the air. The ball will make the molecules in the air vibrate faster—creating heat (microscopic motion). This is the same as the mechanical equivalent of heat, which converts the motion of fluid to heat. The more air drag there is, the faster the ball will dissipate energy.

3. Normal force

When a baseball bat hits a baseball, the hit will make a sound and the ball also gets deformed by the normal force momentarily. The ball bounces off the bat and returns to its normal shape. In that process the atoms of the bat, the ball and the air will start to move, losing some of its energy.