Final answer:
Newton's second law, F = ma, is used to determine that the acceleration of a 5.00 kg block pushed up a frictionless 30° incline with a 65.0 N force is 13.0 m/s².
Step-by-step explanation:
When a force is applied to a block to move it up a frictionless incline, the force required to accelerate the block is defined by Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). Given the problem where a 65.0 N force is applied to a 5.00 kg block on a 30° incline, we need to calculate the acceleration. We know that the force component acting along the incline is F = ma, and the component of gravity acting down the incline is mgsin(θ). Since the incline is frictionless, these are the only forces to consider.
By rearranging the equation to solve for acceleration, we get a = F/m. Hence, we'll substitute the values given in the question to find the acceleration of the block. Using the force value of 65.0 N, and the mass of the block being 5.00 kg, we apply:
a = 65.0 N / 5.00 kg
a = 13.0 m/s²
Therefore, the magnitude of the acceleration of the block up the inclined plane is 13.0 m/s².