Final answer:
The magnitude of energy lost to friction when a box is dragged across a rough surface with a given coefficient of kinetic friction and at an angle is 607.5 joules.
Step-by-step explanation:
The student has asked how to calculate the magnitude of energy lost to friction when a box of mass 1.79 kg is dragged across a rough surface with a certain coefficient of kinetic friction and a force applied at an angle. The student specified that the kinetic friction force was given as 45.0 N.
Since kinetic friction acts in the opposite direction of the box's motion and is constant, we can calculate the work done by friction, which represents the energy lost, using the formula Work = friction force × distance × cos(θ). Here, since kinetic friction and displacement are in opposite directions, θ = 180° or cos(θ) = -1.
Substituting into the equation:
Work = 45.0 N × 13.5 m × (-1) = -607.5 J
The minus sign indicates that energy is lost to friction, so the magnitude of the total energy lost is 607.5 joules.