Final answer:
The acceleration of a 100 kg block pushed up a 30-degree frictionless ramp can be calculated using Newton's second law and is 4.9 m/s².
Step-by-step explanation:
To calculate the block's acceleration up a frictionless ramp set at 30 degrees, we use Newton's second law, F = ma, where F is the net force, m is the mass, and a is the acceleration. Since the ramp is frictionless, the only force acting along the ramp is the component of the weight of the block parallel to the surface of the incline, which can be calculated with the formula mg*sin(θ), where g is the acceleration due to gravity (9.8 m/s²) and θ is the angle of the incline.
For a 100 kg block with g = 9.8 m/s² and θ = 30 degrees, the parallel component of the weight is 100 kg * 9.8 m/s² * sin(30°) = 980 N * 0.5 = 490 N. Plugging this into Newton's second law and solving for a gives us a = F/m = 490 N / 100 kg = 4.9 m/s².