Question

A block is placed on a smooth, friction-free ramp and released from rest. The ramp is inclined at an angle of 64o above the horizontal. What is the acceleration of the block in m/s2 using down the ramp as positive?

Answer 1

The acceleration of a block down a friction-free ramp inclined at an angle of 64º above the horizontal is calculated using the formula a = g × sin(θ). For this angle, the acceleration is roughly 8.81 m/s².

Step-by-step explanation:

To determine the acceleration of a block down a friction-free ramp inclined at an angle of 64º above the horizontal, we can use the component of the gravitational force parallel to the ramp. In this case, acceleration (a) can be found using the equation a = g × sin(θ), where g is the acceleration due to gravity (9.8 m/s²) and θ is the angle of incline. For an angle of 64º, the acceleration is a = 9.8 m/s² × sin(64º).

Calculating this, we get:

a = 9.8 m/s² × 0.8988 (sin(64º) approximately)

a ≈ 8.81 m/s²

Therefore, the acceleration of the block down the ramp is roughly 8.81 m/s², with down the ramp taken as positive.