A block on a frictionless incline of 60° has acceleration along the incline. Which is the approximate value of a = g sin θ?

A block on a frictionless incline of 60° has acceleration along the incline. Which is the approximate value of a = g sin θ?

• A. Approximately 4.9 m/s^2
• B. Approximately 8.49 m/s^2
• C. Approximately 9.8 m/s^2
• D. Zero

Answer: (B)

Gravity pulls straight down, but on a frictionless incline only the component of gravity along the slope drives the motion. That along-slope force is mg sinθ, and with no friction the acceleration along the incline is a = F/m = g sinθ. For a 60° incline, sin 60° is about 0.866, so a ≈ 9.8 × 0.866 ≈ 8.49 m/s^2. That matches the option around 8.49 m/s^2. The other values would correspond to different angles or conditions (for example, 4.9 m/s^2 would come from a 30° angle, 9.8 m/s^2 would be full gravity if there were no incline, and zero would imply no net along-slope force).

Gravity pulls straight down, but on a frictionless incline only the component of gravity along the slope drives the motion. That along-slope force is mg sinθ, and with no friction the acceleration along the incline is a = F/m = g sinθ. For a 60° incline, sin 60° is about 0.866, so a ≈ 9.8 × 0.866 ≈ 8.49 m/s^2. That matches the option around 8.49 m/s^2. The other values would correspond to different angles or conditions (for example, 4.9 m/s^2 would come from a 30° angle, 9.8 m/s^2 would be full gravity if there were no incline, and zero would imply no net along-slope force).