Final answer:
Greater steepness of an incline results in greater acceleration for an object moving down it because the component of gravity along the plane increases. In the absence of friction, acceleration is calculated with the formula a = g sin(θ). Friction acts to reduce this acceleration when present.
Step-by-step explanation:
The question refers to the relationship between the steepness of an incline and the acceleration of an object moving down that plane. A further steepness of the incline means greater acceleration down the plane, assuming other factors like friction remain constant. This is because the component of gravitational force acting along the incline, which propels objects down the slope, increases as the angle of the incline increases. According to the general physical principle, the acceleration down a frictionless incline can be calculated with the formula a = g sin(θ), where a is the acceleration, g is the acceleration due to gravity, and θ is the angle of the incline with respect to the horizontal.
For example, with g approximated as 9.81 m/s² (the acceleration due to gravity on Earth's surface), if the incline angle increases, the sin(θ) value increases, thus increasing the acceleration of an object sliding down the plane. Friction, when present, acts to oppose the motion and decrease the acceleration. In situations where friction is not negligible, the acceleration would be less than the acceleration due to gravity alone.