Final answer:
The work done by the frictional force on a 2.0-kg block sliding down an incline over a distance of 2.0 m with a frictional force of 4.86 N is -9.72 J, indicating that the frictional force does negative work on the block.
Step-by-step explanation:
To calculate the work done by the friction force on a 2.0-kg block sliding down an incline, we can use the formula for work: Work = Force × Distance × cos(θ), where θ is the angle between the direction of the force and displacement. The force due to friction is the product of the coefficient of kinetic friction, the normal force, and the distance over which it acts.
With the given coefficient of kinetic friction, μ_k = 0.26, mass of the block m = 2.0 kg, and distance d = 2.0 m, the frictional force F_friction can be calculated using the equation F_friction = μ_k × m × g × cos(α), where α is the angle of the incline and g = 9.81 m/s² is the acceleration due to gravity. However, keep in mind that for a block sliding down an incline, the normal force is not just m × g, but rather m × g × cos(α).
Since the question lacks the angle of the incline but provides the frictional force directly, we'll use the given force to calculate the work done over the distance:
- Calculate the frictional force: Given F_friction = 4.86 N
- Calculate the angle θ between the direction of motion and the force of friction. Here, θ = 180° because friction always opposes motion.
- Calculate the work done by friction using the work formula with θ = 180 degrees, which gives us the cosine of θ as -1 (cos(180°) = -1).
- Work done by friction = F_friction × d × cos(180°) = 4.86 N × 2.0 m × (-1) = -9.72 J