Question

When a 40 N force, parallel to the incline and directed up the incline, is applied to a crate on a frictionless incline that is 30° above the horizontal, the acceleration of the crate is 2 m/s². What is the mass of the crate?

Answer 1

To determine the mass of the crate on the frictionless incline, Newton's second law is applied, which leads to a calculation showing that the mass of the crate is 20 kg.

Step-by-step explanation:

To find the mass of the crate on a frictionless incline, we can use Newton's second law, which states that the sum of the forces equals mass times acceleration (F = ma). The force applied up the incline is 40 N and it produces an acceleration of 2 m/s². We are asked to find the mass (m) of the crate.

According to the problem:

• Applied force (Fapplied): 40 N
• Acceleration (a): 2 m/s²

Using the equation F = ma, we rearrange to solve for the mass:

m = F / a

Plugging in the known values:

m = 40 N / 2 m/s²

m = 20 kg

Therefore, the mass of the crate is 20 kilograms.