Final answer:
The acceleration of a 2.96 kg block sliding down a frictionless 32-degree incline is approximately 5.19 m/s², determined by the component of gravity acting along the plane.
Step-by-step explanation:
The student's question regarding a 2.96 kg block sliding down a smooth frictionless plane with an inclination of 32 degrees involves finding the acceleration of the block. Since the plane is frictionless, the only force causing acceleration is the component of gravity acting along the incline. We can calculate this by using the formula a = g × sin(θ), where a is the acceleration, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of inclination.
The acceleration a of the block can be found by taking the sine of 32 degrees and multiplying by 9.8 m/s². This gives us:
a = 9.8 m/s² × sin(32°)
Using a calculator, we find that sin(32°) ≈ 0.53, therefore:
a ≈ 9.8 m/s² × 0.53 ≈ 5.19 m/s²
So, the acceleration of the block down the incline is approximately 5.19 m/s².