Question

An inclined plane, fixed to the inside of an elevator, makes a 40 ∘ angle with the floor. A mass m slides on the plane without friction. What is its acceleration relative to the plane if the elevator accelerates downward at 0.40 g ?

Answer 1

To find the acceleration of the mass relative to the plane in an inclined elevator, we need to break the acceleration into components parallel and perpendicular to the plane and then calculate the total acceleration.

Step-by-step explanation:

To find the acceleration of the mass relative to the plane, we need to break the acceleration into components parallel and perpendicular to the plane. The parallel component of acceleration is caused by the weight of the mass and the component of the elevator's acceleration parallel to the plane. The perpendicular component of acceleration is caused by the component of the elevator's acceleration perpendicular to the plane.

The parallel component of acceleration = g * sin(40°) + 0.40 * g * cos(40°)

The perpendicular component of acceleration = 0.40 * g * sin(40°)

Therefore, the acceleration relative to the plane = sqrt((parallel component)^2 + (perpendicular component)^2)