Question

Use linear approximation to estimate the block's position on a frictionless inclined plane, making an angle θ, with a mass of 1. Choose a value of a to produce a small error.

Answer 1

The linear approximation method can be used to estimate the block's position on a frictionless inclined plane by using the formula x = L * θ. By choosing a small angle of tilt, we can make a more accurate estimation.

Step-by-step explanation:

The linear approximation method can be used to estimate the block's position on a frictionless inclined plane. By choosing a small angle of tilt, we can assume that the tangent of the angle is approximately equal to the angle itself in radians.

In this case, the linear approximation formula becomes:

x = L * θ

Where x is the block's position, L is the length of the plane, and θ is the angle of tilt.

For example, if the length of the plane is 5 meters and the angle of tilt is 0.1 radians, then the estimated position of the block would be:

x ≈ 5 * 0.1 = 0.5 meters