Question

a (0.298\text{ kg}) ball initially at rest, slides down a frictionless ramp that is inclined at (28.5^{circ}).
what is the acceleration of the ball as it slides down the ramp?

(a = ?\text{ m/s}^2)

Explanation:

⚡ Using what you learned: newton's laws of motion

Step 1: Identify forces parallel to the ramp

The only force acting along the direction of the incline is the component of gravity pulling the ball down the ramp:

$$ F_{\text{net}} = m \cdot g \cdot \sin(\theta) $$

Step 2: Calculate acceleration

Using Newton's second law \( F_{\text{net}} = m \cdot a \):

$$ a = g \cdot \sin(\theta) $$

Substitute \( g = 9.8 \text{ m/s}^2 \) and \( \theta = 28.5^\circ \):

$$ a = 9.8 \cdot \sin(28.5^\circ) $$

$$ a \approx 9.8 \cdot 0.4772 $$

$$ a \approx 4.68 \text{ m/s}^2 $$

Answer:

\( 4.68 \)