The acceleration of a 2.0 kg block on a frictionless 30° incline is 4.9 m/s², the normal force is approximately 17 N, and to maintain a constant velocity, an upward force of 9.8 N should be applied parallel to the ramp.
To determine the acceleration of a 2.0-kg block on a frictionless ramp inclined at 30°, we need to apply Newton's second law of motion. The gravitational force causing the block to accelerate down the ramp can be calculated by breaking the force of gravity into components parallel and perpendicular to the ramp's surface. Since the ramp is frictionless, the only force causing acceleration is the component of the gravitational force along the ramp:
Fparallel = m · g · sin(θ)
Where m is the mass of the block, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of the ramp. Substituting the values in, we get Fparallel = 2.0 kg · 9.8 m/s² · sin(30°) = 9.8 N. Using Newton's second law, F = m · a, we can solve for acceleration (a) as follows:
a = Fparallel / m = 9.8 N / 2.0 kg = 4.9 m/s²
The normal force (N) exerted by the ramp on the block is equal to the perpendicular component of the gravitational force:
N = m · g · cos(θ)
So N = 2.0 kg · 9.8 m/s² · cos(30°) = 16.97 N or approximately 17 N.
To maintain a constant velocity, an external force equal in magnitude to the parallel component of gravity but in the opposite direction needs to be applied. Therefore, a force of 9.8 N would need to be applied upward along the ramp.