Question

A 3.39 kg block slides down a smooth frictionless incline. What is the acceleration of the block?

a) 9.8 m/s²
b) 3.39 m/s²
c) 6.17 m/s²
d) 0 m/s²

Answer 1

The acceleration of a block on a smooth frictionless incline is determined by the gravitational acceleration component parallel to the incline, but the exact value can't be calculated without the angle of the incline.

Step-by-step explanation:

The acceleration of a block sliding down a smooth frictionless incline is determined by the force of gravity along the incline. Since there is no friction, and other resistances like air drag are considered negligible, the only force acting on the block in the direction of the incline is the component of gravity parallel to the incline.

The formula to find this component is a = g × sin(θ), where g is the gravitational acceleration (9.8 m/s²) and θ is the angle of the incline. However, without the angle of the incline provided in this particular problem, we cannot calculate the exact acceleration; it will always be less than 9.8 m/s² as long as the incline angle is less than 90°.

Therefore, the precise value of acceleration cannot be determined from the information given and none of the given options a) 9.8 m/s², b) 3.39 m/s², c) 6.17 m/s², d) 0 m/s² matches the correct approach to solving this problem.

Answer 2

None of the options provided (a) 9.8 m/s², (b) 3.39 m/s², (c) 6.17 m/s², (d) 0 m/s² correspond to the calculated acceleration of the block sliding down the incline under the given circumstances.

Step-by-step explanation:

The acceleration of a block sliding down a smooth, frictionless incline can be calculated using Newton's second law of motion (F = ma) and considering the forces acting upon it. The force causing the acceleration of the block down the incline is due to gravity (weight of the block).

The force of gravity on the block (F = mg) is directed down the incline. The acceleration, assuming no friction and a standard incline, can be derived as the component of gravity parallel to the incline (mg 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 incline.

However, without the specific angle of the incline provided in the question, it's not possible to calculate the exact acceleration. Therefore, none of the given options accurately represents the acceleration of the block. The correct calculation requires the angle of the incline to determine the component of gravity parallel to it. As such, the correct answer falls outside the provided choices.\

Full Question:

A 3.39 kg block slides down a smooth, frictionless incline. What is the acceleration of the block?

a) 9.8 m/s²

b) 3.39 m/s²

c) 6.17 m/s²

d) 0 m/s²