To calculate the amount of work done by friction in a given time period, you need to know the force of friction and the displacement of the object acted upon by friction. The formula to calculate work is:
Work = Force × Displacement × cos(θ)
In the case of friction, the force of friction can be determined using the equation:
Force of friction = μ × Normal force
where μ is the coefficient of friction and the Normal force is the perpendicular force exerted by a surface to support the weight of the object.
The displacement is the distance over which the object moves due to the force of friction.
The angle θ is the angle between the force of friction and the displacement. In the case of friction, the force of friction acts in the opposite direction to the displacement. Therefore, the angle θ is 180 degrees (or π radians).
Putting it all together, the equation to calculate the work done by friction is:
Work = (μ × Normal force) × Displacement × cos(180°)
Since cos(180°) = -1, the equation simplifies to:
Work = -μ × Normal force × Displacement
It's important to note that the negative sign indicates that the work done by friction is in the opposite direction to the displacement, as friction acts to oppose the motion of the object.
To obtain the amount of work done by friction in a given time period, you would need to know the force of friction, displacement, coefficient of friction, and normal force over that time period.