Final answer:
The force parallel to the incline is 24.5 N, the acceleration of the mass is 4.9 m/s², and the velocity when it reaches the bottom is approximately 3.93 m/s.
Step-by-step explanation:
The student has asked about a 5-kg mass sliding down a frictionless inclined plane, how to calculate the force parallel to the incline, the acceleration, and the final velocity when it reaches the bottom. We can address this using Newton's second law of motion and the kinematic equations.
Calculating Force and Acceleration
The force parallel to the incline is given by F = m × g × sin(θ), where m is the mass, g is gravitational acceleration (9.8 m/s²), and θ is the angle of incline. Substituting the values, we get F = 5 kg × 9.8 m/s² × sin(30°) = 24.5 N. The acceleration a is F/m, so a = 24.5 N / 5 kg = 4.9 m/s².
Calculating Final Velocity
To find the velocity when the mass reaches the bottom, use the kinematic equation v = √(2 × a × d), where v is final velocity, a is acceleration, and d is the distance along the incline. The velocity at the bottom is v = √(2 × 4.9 m/s² × 0.8 m) ≈ 3.93 m/s.