Question

. a marble rolls down an incline at 30°30° from rest. (a) what is its acceleration? (b) how far does it go in 3.0 s?

Answer 1

The acceleration of the marble rolling down a 30° incline is 4.905 m/s², and over 3.0 seconds, it travels approximately 22.1 meters.

Step-by-step explanation:

Marble Rolling Down an Incline

Let's consider the marble rolling down a 30° incline. To find its acceleration, we need to use the component of Earth's gravitational acceleration, g, which is 9.81 m/s², along the incline. Since the incline is at 30°, this component is g⋅sin(θ), which simplifies to 0.5g because sin(30°) = 0.5.

(a) Acceleration of the marble: Calculating this, we get:
acceleration = 0.5 × 9.81 m/s² = 4.905 m/s².

To determine how far the marble goes in 3.0 seconds, we use the kinematic equation for distance covered from rest under constant acceleration, which is s = 0.5 × acceleration × time².
(b) Distance travelled by the marble: Substituting the values, we get:
distance = 0.5 × 4.905 m/s² × (3.0 s)² = 0.5 × 4.905 × 9 = 22.0725 m.

The marble would have travelled approximately 22.1 meters down the incline in 3.0 seconds.

Answer 2

The acceleration of the marble rolling down the incline is 4.9 m/s^2. The marble will go a distance of 22.05 m in 3.0 seconds.

Step-by-step explanation:

To find the acceleration of the marble rolling down the incline, we can use the equation:

acceleration = g * sin(theta)

where g is the acceleration due to gravity (9.8 m/s^2) and theta is the angle of the incline (30°). Plugging in the values, we get:

acceleration = 9.8 m/s^2 * sin(30°) = 4.9 m/s^2

To calculate how far the marble goes in 3.0 seconds, we can use the equation:

distance = (1/2) * acceleration * time^2

Plugging in the values, we get:

distance = (1/2) * 4.9 m/s^2 * (3.0 s)^2 = 22.05 m