Question

A block slides down a frictionless plane that makes an angle of 30° with the horizontal. The acceleration of the block is:

Group of answer choices
a.9.80 m/s2
b.8.49 m/s2
c.0 m/s2
d.5.66 m/s2
e.4.90 m/s2​

Answer 1

The acceleration of a block sliding down a 30° frictionless incline is calculated using g sin(θ), yielding an acceleration of 4.90 m/s².

Step-by-step explanation:

The question pertains to a block sliding down a frictionless plane at an angle of 30° to the horizontal. Using Newton's second law of motion and the components of gravitational force, we can determine the block's acceleration. Since there is no friction and the only force acting along the incline is the component of gravitational force parallel to the incline, we calculate this component as g sin(θ), where g is the acceleration due to gravity (9.8 m/s²) and θ is the angle of the incline. For a 30° incline:

Acceleration = g sin(30°) = 9.8 m/s² × sin(30°) = 9.8 m/s² × 0.5 = 4.9 m/s²

Therefore, the correct answer is e. 4.90 m/s².