Question

A small smooth object slides from rest down a smooth inclined plane inclined at 30degrees horizontal.What is the acceleration down the plane?

Answer 1

The acceleration of an object down a smooth inclined plane at an angle of 30° from rest is calculated using the formula a = g × sin(θ), resulting in an acceleration of 4.905 m/s².

Step-by-step explanation:

To find the acceleration of the object down the smooth inclined plane, we can use the formula a = g × sin(θ), where 'a' is the acceleration, 'g' is the acceleration due to gravity (9.81 m/s²), and 'θ' is the angle of the incline which is given as 30°. Since the plane is smooth, we can ignore friction and only consider gravity's component along the incline.

Using this formula:

a = 9.81 m/s² × sin(30°)

a = 9.81 m/s² × 0.5

a = 4.905 m/s²

Therefore, the acceleration of the object as it slides down the incline is 4.905 m/s².

Answer 2

The acceleration is given as:

a = g sin(30°) where g is the gravitational acceleration

For g = 10 m/s^2, we get

a = 10 sin(30°) = 10 * 1/2 = 5 m/s^2