if the initial velocity is .05 m/s and its final is 1.3 m/s then how much energy is lost to friction
First of all, you need the mass of the object as well as the initial and final velocities.
Second, the speed is increasing, so kinetic energy is increasing. Some force such as gravity must have been applied. I'd need to know how much potential energy was lost to determine how much energy was lost due to friction.
You have not provided all the facts necessary to answer the question.
To calculate the energy lost to friction, you need to know the type of system in which the friction is acting. If you are considering a point mass or an object sliding on a surface, you can determine the energy lost using the work-energy principle.
The work done by friction can be calculated by multiplying the force of friction by the displacement. This work represents the energy lost to friction. The equation for work is:
Work = Force × Displacement × cos(θ)
Since the force of friction and the displacement are typically in the same direction, the angle θ between them is 0 degrees, and the cosine of 0 degrees is 1. Hence, the equation simplifies to:
Work = Force × Displacement
To find the force of friction, you need to know the coefficient of friction (μ) between the surfaces in contact. The force of friction can be calculated using the equation:
Force of friction = μ × Normal force
The normal force is the perpendicular force exerted by a surface and is equal to the weight of the object if it is on a flat horizontal surface.
Once you have the force of friction, you can calculate the work done and, thus, the energy lost by multiplying it by the displacement.
Without additional information, such as the distance or time over which the velocity changes from 0.05 m/s to 1.3 m/s, it is not possible to determine the energy lost to friction.