Final answer:
The work done by gravity, frictional force, and normal force can be found through calculations based on mass, the angle of incline, distance, and the coefficient of kinetic friction. The total work is the sum of the work due to gravity and friction, with the normal force doing no work.
Step-by-step explanation:
Starting from rest, a 6.5 kg block slides down a rough 30° inclined plane with the coefficient of kinetic friction being 0.44. To determine the work done by various forces as it slides 3.0 m, we use the work-energy principles.
- The work done by gravity (Wgravity) is calculated using the force of gravity component along the incline and the distance moved. Wgravity = mgh sin(θ), where m is mass, g is the acceleration due to gravity (9.8 m/s²), h is vertical height, and θ is the angle of incline.
- The work done by the frictional force is negative as friction opposes motion. The work is calculated by Wfriction = -μkmg cos(θ)d, where μk is the coefficient of kinetic friction, and d is the distance along the incline.
- The work done by the normal force is 0 J because the normal force is perpendicular to the direction of motion and does no work.
- The total work done on the block is the sum of the work done by gravity and the work done by friction since the normal force does no work.
Using these formulas, you can then substitute the given values to calculate the precise work done by each force. The correct answers are a) 97.94 J, b) -21.47 J, c) 0 J, d) 76.47 J, which corresponds to option A.