Final answer:
To find the distance the 0.50 kg block slides on a 30 degree incline after 4.0 J of work is done on it, use the work-energy principle and trigonometry. The closest answer to the calculated distance of 163 cm is choice (D) 160 cm.
Step-by-step explanation:
The student has performed 4.0 J of work to move a 0.50 kg block up a frictionless inclined plane that is at a 30 degree angle. To find the distance(s) the block slides before stopping, we can use the work-energy principle which states that work done on an object is equal to its change in kinetic energy (Work = ΔKE). Since the block stops, its final kinetic energy is zero, and the work done by the student is equal to the initial potential energy gained by the block (mgh, where h is the height).
The height can be calculated from the distance along the incline using trigonometry, h = s * sin(30 degrees). The work done by the student lifts the block against gravity, so 4.0 J = mgh = 0.50 kg * 9.8 m/s² * s * sin(30 degrees). Solving for s, we find s = (4.0 J) / (0.50 kg * 9.8 m/s² * 0.5) = 1.63 m or 163 cm. Answer choice closest to 163 cm is (D) 160 cm.